1. Wavelength-selective optical devices: AWGs & MRRs

Transcription

1 1. Wavelength-selective optical devices: AWGs & MRRs Flat-top Arrayed-waveguide gratings (AWGs) [1]. Daoxin Dai, Shuzhe Liu, Sailing He, and Qincun Zhou. Optimal design of an MMI coupler for broadening the spectral response of an AWG demultiplexer. IEEE Journal of Lightwave Technology, 20(11): , Pages 1-5 [2]. Daoxin Dai, Weiquan Mei, and Sailing He. Using a tapered MMI to flatten the passband of an AWG. Optics Communications, 219(1-6): , Pages 6-12 [3]. Daoxin Dai, S. Liu and Sailing He. A flattened AWG demultiplexer with low chromatic dispersion. Fiber and Integrated optics, 22(3): , Pages [4]. Salman Naeem Khan, Daoxin Dai, Liu Liu, L. Wosinski and Sailing He. Optimal design for a flat-top AWG demultiplexer by using a fast calculation method based on a Gaussian beam approximation. Optics Communications, 262(2): , Pages Modeling and analysis of AWGs [5]. Daoxin Dai, and Sailing He. Analysis of multimode effects in the free-propagation region of a silicon-on-insulator-based arrayed-waveguide grating demultiplexer. Applied Optics, 42(24): , Pages [6]. Daoxin Dai, and Sailing He. Fast design method for a flat-top arrayed-waveguide-grating demultiplexer using the reciprocity theory. Journal of Optical Networking, 2(12): , Pages [7]. Daoxin Dai, and Sailing He. Calculation of the spectral response of an arrayed-waveguide gating demultiplexer with a wide-angle beam propagation method in a cylindrical coordinate system. Optical and Quantum Electronics, 36(11): , Pages [8]. Daoxin Dai, and Sailing He. Accurate two-dimensional model of an arrayed-waveguide grating demultiplexer and optimal design based on the reciprocity theory. Journal of the Optical Society of America A, 21(12): , Pages [9]. Daoxin Dai, and Sailing He. Reduction of multimode effects in a SOI-based etched diffraction grating demultiplexer. Optics Communications, 247(4-6): , Pages [10]. Daoxin Dai, Jianjun He, and Sailing He. Elimination of multimode effects in a silicon-on-insulator etched diffraction grating demultiplexer with bi-level taper structure. IEEE Journal of Selected Topics on Quantum Electronics, 11(2): , Pages [11]. Daoxin Dai, Liu Liu, and Sailing He. Three-dimensional hybrid method for efficient and accurate simulation of AWG demultiplexers. Optics Communications, 270(2): , Pages SOI-nanowire AWGs [12]. Daoxin Dai, L. Liu, L. Wosinski and S. He. Design and fabrication of ultra-small overlapped AWG demultiplexer based on alpha-si nanowire waveguides. Electronics Letters, 42(7): , Pages [13]. Daoxin Dai and S. He. Design of a polarization-insensitive arrayed waveguide grating demultiplexer based on silicon photonic wires. Optics Letters, 31(13): , Pages [14]. Daoxin Dai, and Sailing He. Novel ultracompact Si-nanowire-based arrayed-waveguide grating with microbends. Optics Express, 14(12): , Pages [15]. Daoxin Dai, and Sailing He. Ultra-small overlapped arrayed-waveguide grating based on Si nanowire waveguides for dense wavelength division demultiplexing. IEEE Journal of Selected Topics on Quantum

2 Electronics, 12(6): , Pages [16]. Zhen Sheng, Daoxin Dai, and Sailing He. Improve channel uniformity of an Si-nanowire AWG demultiplexer by using dual-tapered auxiliary waveguides. IEEE Journal of Lightwave Technology, 25(11): , Pages [17]. Daoxin Dai and Sailing He. Novel ultracompact AWG interleaver based on Si-nanowires with spirals. Optics Communications, 281(13): , Pages [18]. Daoxin Dai, Y. Shi, S. He. Theoretical Investigation for Reducing Polarization-sensitivity in Si-nanowire-based arrayed-waveguide grating (de)multiplexer with polarization-beam-splitters and reflectors. IEEE Journal of Quantum Electronics, 45(6): , Pages [19]. Yaocheng Shi, Xin Fu, and Daoxin Dai. Design and fabrication of a 200GHz Si-nanowire-based reflective arrayed-waveguide grating (de)multiplexer with optimized photonic crystal reflectors. Applied Optics, 49(26), , Pages [20]. Daoxin Dai, Xin Fu, Yaocheng Shi, and Sailing He. Experimental demonstration of an ultra-compact Si-nanowire-based reflective arrayed-waveguide grating (de)multiplexer with photonic crystal reflectors. Optics Letters, 35(15), , Pages [21]. X. Fu, and Daoxin Dai, Ultra-small Si-nanowire-based 400 GHz-spacing arrayed-waveguide grating router with microbends, Electron. Lett. 47(4): , Pages [22]. Sitao Chen, Xin Fu, J. Wang, Yaocheng Shi, Sailing He, and Daoxin Dai*, Compact dense wavelength division (de)multiplexer utilizing a bidirectional Arrayed-waveguide Grating integrated with a Mach-Zehnder Interferometer, IEEE Journal of Lightwave Technology, 33(11): (2015). Pages SU-8/SiN AWGs [23]. Bo Yang, Yunpeng Zhu, Yuqing Jiao, Liu Yang, Zhen Sheng, Sailing He, and Daoxin Dai, Compact arrayed waveguide grating devices based on small SU-8 strip waveguides, IEEE Journal of Lightwave Technology, 29(13): , Pages [24]. Daoxin Dai, Zhi Wang, Jared F. Bauters, M.-C. Tien, Martijn J. R. Heck, Daniel J. Blumenthal, and John E Bowers, Low-loss Si 3 N 4 arrayed-waveguide grating (de)multiplexer using nano-core optical waveguides, Optics Express, 19(15), (2011). Pages MRRs for optical sensing [25]. Daoxin Dai and Sailing He. Highly sensitive sensor with large measurement range realized with two cascaded microring resonators. Optics Communications. 279: 89-93, Pages [26]. Daoxin Dai, and Sailing He, Highly sensitive sensor based on an ultra-high-q Mach-Zehnder interferometer-coupled microring, Journal of the Optical Society of America B, 26(3): , Pages [27]. Daoxin Dai. Highly sensitive digital optical sensor based on cascaded high-q ring-resonators. Optics Express, 17(26): , Pages [28]. Jianwei Wang, and Daoxin Dai, "Highly sensitive Si nanowire-based optical sensor using a Mach-Zehnder interferometer coupled microring," Optics Letters 35(24), , Pages [29]. Jing Hu, and Daoxin Dai, Cascaded-ring optical sensor with enhanced sensitivity by using suspended Si-nanowires, IEEE Photonics Technology Letters, 23(13): , Pages [30]. X. Wang, X. Guan, Q. Huang, J. Zheng, Y. Shi, and Daoxin Dai, "Suspended Submicron-disk Resonator on Silicon for Optical Sensing," Optics Letters 38, (2013). Pages [31]. Xu Sun, Daoxin Dai, Lars Thylen and Lech Wosinski. "High-sensitivity liquid refractive-index sensor

3 based on a Mach-Zehnder interferometer with a double-slot hybrid plasmonic waveguide," Optics Express, 23, (2015). Pages [32]. Xu Sun, Daoxin Dai, Lars Thylén and Lech Wosinski, Double-Slot Hybrid Plasmonic Ring Resonator Used for Optical Sensors and Modulators, Photonics, 2(4): , Pages [33]. Mao Mao, Sitao Chen, Daoxin Dai*, Cascaded ring-resonators for multi-channel optical sensing with reduced temperature-sensitivity, IEEE Photonics Technology Letters, 28(7): , Pages MRRs for optical filtering [34]. Zhechao Wang, Daoxin Dai, and Sailing He. Polarization-Insensitive Ultrasmall Microring Resonator Design Based on Optimized Si Sandwich Nanowires. IEEE Photonics Technology Letters, 19(20): , Pages [35]. Daoxin Dai, Liu Yang, and Sailing He. Ultrasmall thermally tunable microring resonator with a submicrometer heater on Si nanowires. IEEE Journal of Lightwave Technology, 26(6): , Pages [36]. Daoxin Dai, B. Yang, L. Yang, Z. Sheng, and S. He, compact microracetrack resonator devices based on small SU-8 polymer strip waveguides. IEEE Photonics Technology Letters, 21(4): , Pages [37]. Daoxin Dai, L. Yang, Z. Sheng, B. Yang, and S. He. Compact microring resonator with 2 2 tapered multimode interference couplers. IEEE Journal of Lightwave Technology, 27(21): , Pages [38]. Di Liang, M. Fiorentino, T. Okumura, Hsu-Hao Chang, Daryl T. Spencer, Ying-Hao Kuo, Alexander W. Fang, Daoxin Dai, Raymond G. Beausoleil, and John E. Bowers, "Electrically-pumped compact hybrid silicon microring lasers for optical interconnects," Optics Express 17, , Pages [39]. Daoxin Dai and Sailing He. Proposal of a coupled-microring-based wavelength-selective 1 N power splitter. IEEE Photonics Technology Letters, 21(21): , Pages [40]. Daoxin Dai, Yaocheng Shi, Sailing He, Lech Wosinski, and Lars Thylen, Silicon hybrid plasmonic submicron-donut resonator with pure dielectric access waveguides, Optics Express 19(24), (2011). Pages [41]. Daryl Spencer, D. Dai, Y. Tang, M. Heck, and J. E. Bowers, Realization of a novel 1 N power splitter with uniformly excited ports, IEEE Photonics Technology Letters, 25(1): 36-39, Pages [42]. Li Jin, Jianwei Wang, Xin Fu, Bo Yang, Yaocheng Shi, and Daoxin Dai, High-Q microring resonators with 2 2 angled multimode interference couplers, IEEE Photonics Technology Letters, 25(6): (2013). Pages [43]. Li Jin, Xin Fu, Bo Yang, Yaocheng Shi, and Daoxin Dai, "Optical bistability in a high-q racetrack resonator based on small SU-8 ridge waveguides," Optics Letters 38, (2013) Pages [44]. Pengxin Chen, Sitao Chen, Xiaowei Guan, Yaocheng Shi, and Daoxin Dai*, "High-order microring resonators with bent couplers for a box-like filter response," Optics Letters 39, (2014) Pages [45]. Yaocheng Shi, Daoxin Dai, and Sailing He. Ultracompact triplexer based on photonic crystal waveguides, IEEE Photonics Technology Letters, 18(21): , Pages

4 JOURNAL OF LIGHTWAVE TECHNOLOGY, VOL. 20, NO. 11, NOVEMBER Optimal Design of an MMI Coupler for Broadening the Spectral Response of an AWG Demultiplexer Daoxin Dai, Shuzhe Liu, Sailing He, Senior Member, IEEE, and Qincun Zhou Abstract Optimal design of a multimode interference (MMI) coupler for broadening the spectral response of an arrayed-waveguide grating (AWG) demultiplexer is considered. By using a Gaussian beam approximation, an analytical expression for the spectral response of an AWG demultiplexer (with an MMI section) is obtained. A simple analytical formula is derived to relate the optimal MMI length to the separation between the peaks of the twofold images in the MMI region. This peak separation is related to the width of the MMI section. In the proposed design method, a required 1-dB passband width determines the peak separation, which then determines the optimal value for the length of the MMI section according to the analytical formula. The designed flat-top AWG demultiplexer is verified by the beam propagation method. Index Terms Arrayed-waveguide grating (AWG), flattened spectral response, Gaussian approximation, multimode interference, wavelength-division multiplexing (WDM). I. INTRODUCTION ARRAYED-WAVEGUIDE grating (AWG) demultiplexers [1] have been widely used as key components in wavelength-division multiplexing (WDM) systems. It is well known that an AWG demultiplexer with a flattened spectral response is desirable. The spectral response for a conventional AWG demultiplexer is of Gaussian type. For an AWG demultiplexer of Gaussian type, the ratio of the 1-dB bandwidth to the 30-dB bandwidth is small. In other words, the shape of the passband response is not square enough. This limits its application in WDM systems. A Gaussian spectral response requires a strict wavelength control in a network. A flat-top AWG demultiplexer can relax the requirements on wavelength control for lasers and filters in a WDM system. Many methods have been introduced to achieve a broadened spectral response of an AWG demultiplexer by using, e.g., multimode output waveguides [2], two cascaded grating devices [3], multiple gratings [4], multiple Roland circles [5], a multimode interference (MMI) coupler [6], or a Y-junction [7]. In this paper, we consider the method of connecting an MMI sec- Manuscript received May 16, 2002; revised August 6, This work was supported in part by the provincial government of Zhejiang Province of China under MajorRresearch Grant D. Dai, S. Liu, and Q. Zhou are with the Centre for Optical and Electromagnetic Research, State Key Laboratory of Modern Optical Instrumentation, Zhejiang University, Yu-Quan, Hangzhou, China ( dxdai@ coer.zju.edu.cn). S. He is with the Centre for Optical and Electromagnetic Research, State Key Laboratory of Modern Optical Instrumentation, Zhejiang University, Yu-Quan, Hangzhou, China, and the Division of Electromagnetic Theory, Alfven Laboratory, Royal Institute of Technology, S Stockholm, Sweden ( sailing@tet.kth.se). Digital Object Identifier /JLT Fig. 1. Configuration for an AWG demultiplexer with an MMI coupler connected to the input waveguide. tion at the end of the input waveguide since this method is simple and effective. In [6], the length of the MMI section was chosen according to the self-image principle [8] so that the twofold self-image was formed at the end of the MMI section. Such an MMI coupler is not optimal for broadening the spectral response of an AWG demultiplexer. In this paper, we consider an optimal design of an MMI coupler for broadening the spectral response of an AWG demultiplexer. A Gaussian beam approximation is used to derive an analytical expression for the spectral response of an AWG demultiplexer with an MMI coupler connected at the end of the input waveguide. We then derive a simple explicit relation between the optimal MMI length and the separation between the peaks of the twofold images in the MMI region. It is well known that flattening of a spectral response will introduce some additional insertion loss for the WDM device. Therefore, an appropriate passband width should be specified first in a design. In the present design method, a required 1-dB passband width determines the peak separation, which then determines the optimal value for the MMI length according to our simple analytical formula. II. PRINCIPLES FOR AN AWG DEMULTIPLEXER AND THE SELF-IMAGE THEORY An AWG demultiplexer consists of a waveguide array, input/output waveguides, and two free propagation regions (FPRs). To broaden the spectral response, an MMI coupler is connected at the end of the input waveguide (see Fig. 1). According to the self-image theory, a twofold image can be formed in the MMI region and the separation between the two /02$ IEEE 1

5 1958 JOURNAL OF LIGHTWAVE TECHNOLOGY, VOL. 20, NO. 11, NOVEMBER 2002 At the self-imaging position [when ], the total field is given by the following sum of two laterally displaced Gaussian distributions: where (5) Fig. 2. Geometrical configuration for the MMI section and the Gaussian beam for the twofold images at z = 0. image peaks is (see Fig. 2), where is the effective width of the MMI section given by and where is the width of the MMI section, is the wavelength in vacuum, (for the TE case) or (for the TM case), and and are the refractive indexes for the core and the cladding, respectively. The twofold image is formed at the end of the MMI section with the following length [8]: (1) and is the separation between the peaks of the twofold images in the MMI region. In this paper, we assume that the optimal MMI length is, where the offset is to be determined. We use a propagation formula [9] for a Gaussian beam in a slab waveguide region to obtain an approximate expression for the field profile near the self-imaging position. We choose a coordinate system as shown in Fig. 2. Since each Gaussian beam is focused at the self-imaging position, the waist is at. Thus, one can obtain the following field distribution near the self-imaging position: where (6) (2) where. Note that this expression for is approximate since the effective widths for the high-order modes of the MMI section are assumed to be the same as that for the fundamental mode. One can obtain a more accurate value for by using more accurate methods, such as beam propagation method (BPM). The twofold images at the end of the MMI section will have their images at the AWG focal plane, where the entrances of the output waveguides are positioned. The spectral response is then obtained by the overlap integral between the field distribution at the AWG focal plane and the fundamental mode of the output waveguide. Such an MMI section with a length is usually not optimal for broadening the spectral response of an AWG demultiplexer. In the following section, we derive some explicit formulas for obtaining the optimal length of the MMI section. III. EXPLICIT FORMULAS FOR THE OPTIMAL DESIGN The fundamental mode fields (normalized for the intensity) for the input and output waveguides (with widths and, respectively) can be approximated by the following Gaussian distributions: (3) (4) and where and is the effective refractive index in the MMI region. Note that here is the curvature radius of the phase front for the approximate Gaussian beam at in the MMI region. Equation (6) is reduced to (5) when (i.e., at the waist position of the Gaussian beam). It is well known that an AWG is a dispersive device. The focal point shifts when the frequency changes. The shift of the focal point is proportional to the frequency change, i.e.,, where is the dispersion coefficient. The dispersion coefficient is defined as, where is the spatial separation between two adjacent output waveguides and is the channel spacing. The spectral response can be obtained by the overlap between the field distribution at 2

6 DAI et al.: OPTIMAL DESIGN OF MMI COUPLER 1959 the AWG focal plane (where the entrances of the output waveguides are positioned) and the fundamental mode profile of the output waveguide. The twofold image at the end of the MMI section will have its images at the AWG focal plane. If aberrations are ignored, the AWG can be considered as a perfect 1 : 1 imaging system for the field distribution at the end of the MMI section (not the one at the self-image plane). Thus, the spectral response is given by the following overlap integral: (7) In this paper, we assume that the output waveguides have the same width as the input waveguide. Thus, one has. Substituting (4) and (6) into (7), one obtains where and Hereafter, we call and the normalized frequency shift and normalized separation, respectively. To obtain simpler expressions for the derivatives of the spectral response [given by (8)], we wish to avoid taking any derivative of the absolute value of any exponential term. Let (8) Fig. 3. The relation between the 1-dB bandwidth and the optimal normalized separation h. Thus, the point (corresponding to the central frequency) is a local maximal (or minimal) point of the spectral response. To make the spectral response flat at this central frequency, the curvature of the spectral response should be zero at the central frequency, i.e., Since Then one has one obtains the following condition for a flat spectral response at the central frequency: (10) Equation (8) can be rewritten in the following form: It follows from (9) that From the above equation, one can easily check that (9) The above equation gives a simple analytical relation between and (the normalized separation between the peaks of the twofold images in the MMI region) for an optimal flat-top AWG demultiplexer. The optimal length of the MMI should then be chosen as (11) For each value of, one can obtain a corresponding optimal value of [according to (10)], and thus consequently a corresponding flattened spectral response [according to (9)], as well as the corresponding 1-dB passband width (this one-to-one mapping is illustrated in Fig. 3). A flattened spectral response is associated with an increase in the excess loss of the AWG demultiplexer chip. Thus, in the design of a flat-top AWG demultiplexer, one usually specifies first an appropriate passband width. In the present design method, a required 1-dB passband width determines the normalized separation (from a one-to-one mapping figure), which then determines the optimal value for the MMI length according to the simple explicit relations (10) and (11). 3

7 1960 JOURNAL OF LIGHTWAVE TECHNOLOGY, VOL. 20, NO. 11, NOVEMBER 2002 TABLE I PARAMETERS FOR THE NUMERICAL EXAMPLE The dispersion characteristic the design of an AWG demultiplexer. by [12] should be considered in can be calculated where [12] is the group delay characteristic, which is given by Fig. 4. The one-to-one mapping for the normalized separation h and the end position z of the MMI section for a flat-top AWG demultiplexer. where is the central wavelength, is the velocity of the light in vacuum, and is the phase response of the AWG demultiplexer. IV. NUMERICAL RESULTS An example with the parameters listed in Table I will be used to illustrate the present design method. The separation between two adjacent output waveguides is 20 m, and the channel spacing is 100 GHz. For each value of, we obtain a corresponding optimal value of according to (10), and then consequently the corresponding flattened spectral response according to (9). The corresponding 1-dB passband width is thus obtained from this flattened spectral response. The one-to-one mapping between the 1-dB bandwidth and the normalized separation is shown by the solid line in Fig. 3. In this figure, the 1-dB bandwidth is given in percentage with respect to the channel spacing. Relation (10) between the normalized separation and is plotted in Fig. 4. As an example, we require the 1-dB bandwidth to be 50% of the channel spacing. From the solid curve in Fig. 3, one sees that the corresponding has a value of Correspondingly, one has m [from the definition for and (1)] and m. From Fig. 4, one obtains m for. Thus, the optimal length of the MMI section is m. The solid line of Fig. 5 gives the corresponding flattened spectral response calculated with (9). The dotted line of Fig. 5 indicates the Gaussian spectral response for the same AWG demultiplexer without the MMI coupler. To verify the present design, BPM [10], [11] is used to calculate the spectral response for the designed AWG demultiplexer, and the results are shown in Fig. 5 with a dashed line. From Fig. 5, one can see that the present design method is simple and reliable. Further numerical simulation has shown that the present design method is suitable for use when is in the range of 0 50 m, corresponding to a 1-dB bandwidth up to 70% of the channel spacing, which is large enough for most of the applications. Typically, one prefers a flat-top AWG demultiplexer with a 1-dB bandwidth close to 50% of the channel Fig. 5. The flattened spectral response for the designed AWG demultiplexer. spacing. In cases where a more accurate solution is required (e.g., when the required bandwidth is specified at the 0.5-dB points), the present analytical method can provide the first approximation, and some slight adjustment can be made in the neighborhood of the first approximation by using a more accurate method such as the BPM. Fig. 6 shows the dispersion characteristic calculated with BPM for the designed AWG demultiplexer. One can see that the designed AWG demultiplexer has a good dispersion characteristic. The dispersion is quite flat in the 3-dB passband, and is only about 8 ps/nm at the central wavelength. V. CONCLUSION In this paper, a Gaussian beam approximation has been used to derive an analytical expression for the spectral response of an AWG demultiplexer with an MMI section connected at the end of the input waveguide. From this analytical expression, we 4

8 DAI et al.: OPTIMAL DESIGN OF MMI COUPLER 1961 [7] C. Dragone and L. Siliver, Frequency Routing device having a wide and substantially flat passban,, U.S. Patent , May [8] L. B. Soldano and E. C. M. Pennings, Optical multi-mode interference devices based self-image: Principles and applications, J. Lightwave Technol., vol. 13, no. 4, pp , [9] P. A. Besse, M. Bachmann, H. Melchior, L. B. Soldano, and M. K. Smit, Optical bandwidth and fabrication tolerances of multimode interference couplers, J. Lightwave Tech., vol. 12, no. 6, pp , [10] R. Scarmozzino and R. M. Osgood, Comparison of finite-difference and Fourier-transform solutions of the parabolic wave equation with emphasis on integrated-optics applications, J. Opt. Soc. Amer. A., vol. 18, no. 5, pp , [11] R. Scarmozzino, A. Gopinath, R. Pregla, and S. Helfert, Numerical techniques for modeling guided-wave photonic devices, IEEE J. Select. Topics Quantum Electron. Lett., vol. 6, no. 1, pp , [12] M. C. Parker and S. D. Walker, Adaptive chromatic dispersion controller based on an electro-optically chirped arrayed-waveguide grating, in Optical Fiber Communication Conf., vol. 2, 2000, pp Fig. 6. The dispersion characteristic for the designed AWG demultiplexer. have obtained a simple explicit condition for a flat spectral response at the central frequency, which relates the optimal MMI length to the normalized separation. The normalized separation is related to the width of the MMI section. These explicit formulas can be used to make a quick design for a flat-top AWG demultiplexer with a required 1-dB bandwidth. With a conventional numerical simulation method such as BPM, one may have to make a two-dimensional search for and in order to obtain a desired flat-top AWG demultiplexer. The present design method can be conveniently used to simplify the procedure for designing flat-top AWG demultiplexers. The designed flat-top AWG demultiplexer has been verified independently with the beam propagation method. Daoxin Dai received the B.Sc. degree from the Department of Optical Engineering of Zhejiang University, China, in Currently, he is working toward the Ph.D. degree, and his research activities are in the design, simulation, and fabrication of dense wavelength-division multiplexing devices. Shuzhe Liu was born in Currently, he is an undergraduate student with the Centre for Optical and Electromagnetic Research, State Key Laboratory of Modern Optical Instrumentation, Zhejiang University, Hangzhou, China. His research activities are in the design of integrated optical waveguides. REFERENCES [1] M. K. Smit and C. V. Dam, Phasar based WDM devices: Principles, design and applications, IEEE J. Select. Topics Quantum Electron., vol. 2, no. 2, pp , [2] M. R. Amersfoort, C. R. de Boer, F. P. G. M. van Ham, M. K. Smit, P. Demeester, J. J. G. M. van der Tol, and A. Kuntze, Phased-array wavelength demultiplexer with flattened wavelength response, Electron. Lett., vol. 30, no. 4, pp , [3] Y. P. Ho, H. Li, and Y. J. Chen, Flat channel-passband-wavelength multiplexing and demultiplexing devices by multiple-rowland-circle design, IEEE Photon. Technol. Lett., vol. 9, no. 3, pp , [4] A. Rigny, A. Bruno, and H. Sik, Multigrating method for flattened spectral response wavelength multi/demultiplexer, Electron. Lett., vol. 33, no. 20, pp , [5] K. Okamoto and A. Sugita, Flat spectral response arrayed-waveguide grating multiplexer with parabolic waveguide horns, Electron. Lett., vol. 32, no. 18, pp , [6] J. B. D. Soole, M. R. Amerfoort, H. P. LeBlanc, N. C. Andreadakis, A. Rajhel, C. Caneau, R. Bhat, M. A. Koza, C. Youtsey, and I. Adesida, Use of multimode interference couplers to broaden the passband of wavelength-dispersive integrated WDM filters, IEEE Photon. Technol. Lett., vol. 8, no. 10, pp , Sailing He (M 92-SM 98) received the Licentiate of Technology and Ph.D. degrees in electromagnetic theory from the Royal Institute of Technology, Stockholm, Sweden, in 1991 and 1992, respectively. Since 1992, he has worked at the Royal Institute of Technology. He has also been with the Centre for Optical and Electromagnetic Research of Zhejiang University, China, since 1999 as a Special Professor appointed by the Ministry of Education of China. He is also the Chief Scientist for the Joint Laboratory of Optical Communications of Zhejiang University. He has authored one monograph and more than 140 papers in refereed international journals. Qincun Zhou received the B.Sc. degree from the Department of Optical Engineering at Zhejiang University, China, in Currently, he is working toward the Ph.D. degree, and his research activities are in the simulation and fabrication of wavelength-division multiplexing devices. 5

9 Optics Communications 219 (2003) Using a tapered MMI to flatten the passband of an AWG Daoxin Dai a, Weiquan Mei a, Sailing He a,b, * a Centre for Optical and Electromagnetic Research, Joint Laboratory of Optical Communications of Zhejiang University, State Key Laboratory of Modern Optical Instrumentation, Zhejiang University, Yu-Quan, Hangzhou, People s Republic of China b Division of Electromagnetic Theory, Alfven Laboratory, Royal Institute of Technology, S Stockholm, Sweden Received 21 June 2002; received in revised form 17 February 2003; accepted 17 February 2003 Abstract A tapered multimode interferometer (MMI) is used to flatten the passband of an arrayed-waveguide grating (AWG). The tapered MMI is connected at the end of the input waveguide of the AWG. The influences of the tapering angle to the performances (such as the 3 db passband width, the ripple, the crosstalk and the insertion loss) of the flat-top AWG are studied. An AWG which has simultaneously a good flat spectral response and a good dispersion characteristic is designed by choosing appropriately the tapering angle and the length of the tapered MMI. Ó 2003 Elsevier Science B.V. All rights reserved. Keywords: Taper; MMI; Flat-top; Spectral response; AWG; WDM 1. Introduction An arrayed-waveguide grating (AWG) [1] has been widely used as a key component in a wavelength division multiplexing (WDM) system. An AWG consists of a waveguide array, an input waveguide, many output waveguides and two free propagation regions (FPRs). It is well known that an AWG with a flat spectral response is desirable. The spectral response for a conventional AWG is of Gaussian type. The 3 db passband width of a Gaussian type of AWG is narrow, and this limits its application in WDM systems. A Gaussian spectral response requires a strict control over the * Corresponding author. Fax: address: sailing@tet.kth.se (S. He). laser wavelength in a network. Compared to a Gaussian type of AWG, a flat-top AWG has many advantages such as the insensitivity to the wavelength shift (caused by e.g., the laser quality, temperature change or the polarization dispersion) and the suitability for high-speed modulation. Many methods have been introduced to achieve a flattened spectral response of an AWG by using e.g., multimode output waveguides [2], two cascaded grating devices [3], multiple gratings [4], multiple Roland-circles [5], a multimode interference (MMI) coupler [6] or a Y-junction [7]. These methods have some limitations or drawbacks such as an increase in the size or the insertion loss of the device. Among these methods the method of connecting a MMI section at the end of the input waveguide of an AWG is simple and effective. The MMI section converts its input field /03/$ - see front matter Ó 2003 Elsevier Science B.V. All rights reserved. doi: /s (03)

10 234 D. Dai et al. / Optics Communications 219 (2003) entrance width and the exit width of the tapered MMI, respectively (see Fig. 1). Light propagation along the tapered structure can be treated by means of the coupled-mode theory with local normal modes. Since the tapering angle is small, coupling between different modes can be negligible. The propagation constants b m for the mth mode can be written as Fig. 1. The geometrical configuration for a tapered MMI. into a twofold image of the input field at the end of the MMI when the length of the MMI is chosen appropriately. The separation of the two image peaks determinates the 3 db passband width of the spectral response of the AWG, and the peak separation can be controlled by the width of the MMI. A flat spectral response can be achieved when one increases the peak separation to a certain value. However, the crosstalk, the insertion loss and the ripple in the spectral response increase when one increases the peak separation. Furthermore, the dispersion characteristic for a conventional MMI-type of flat-top AWG is not good. In the present paper, we connect a tapered MMI (see Fig. 1) at the end of the input waveguide. By optimizing the structure of the tapered MMI, a flattened spectral response with a low ripple, a low crosstalk and a low insertion loss is obtained, as well as a good dispersion characteristic. 2. Theory 2.1. Analysis for the self-imaging in the region of a tapered MMI The width of the tapered MMI is tapered according to W ðzþ ¼W 1 þðw 0 W 1 Þ 1 z ; ð1þ L taper where z is along the propagation direction, L taper is the length of the tapered MMI, W 0, W 1 are the b m k 0 n r ðm þ 1Þ2 pk 4n r Wem 2ðzÞ ; ð2þ where k 0 is the wave number in vacuum, k is the wavelength, n r, n c are the refractive indices of the core and the cladding of the tapered MMI, respectively, and W em ðzþ is the effective width of the tapered MMI. The effective width W em ðzþ for the mth mode is assumed to be approximately the same as the effective width for the fundamental mode, i.e. [8], W em ðzþ ¼W ðzþþc; ð3þ where C ¼ k 2r n c ðn 2 r p n2 c Þð 1=2Þ n r with r ¼ 0 (for the TE case) or 1 (for the TM case). The phase difference D/ m over a length L in the tapered region between the mth mode and the fundamental mode (m ¼ 0) can be given by the following integral: D/ m ¼ Z L 0 ðb 0 b m Þdz: ð4þ Substituting Eqs. (1) (3) into Eq. (4), one obtains the following expression: D/ m ¼ mðm þ 2Þ pk Z Ltaper dz 4n r 0 We 2ðzÞ ¼ mðm þ 2Þ pk L taper 4n r ½W 1 þ CŠðW 0 þ CÞ : ð5þ The above equation can be rewritten as mðm þ 2Þp D/ m ¼ L taper ; ð6þ 3L p eff where p L p eff ¼ ¼ 4n rðw 1 þ CÞðW 0 þ CÞ : ðb 0 b 1 Þ eff 3k 7

11 D. Dai et al. / Optics Communications 219 (2003) According to the self-imaging theory [8] and Eq. (6), an N-fold image will be produced when the length L taper is chosen to be 1 3 L N 4 p eff. In our case, a twofold image is desired and thus we choose N ¼ 2. Therefore, we choose 3 L 8 p eff par as the tapered MMI length in the present paper (except Section 3.6 where the tapered MMI length L taper is adjusted slightly to a better value with a BPM simulation), i.e., L taper ¼ 3 8 L p eff ¼ n r 2k ðw 1 þ CÞðW 0 þ CÞ: ð7þ Furthermore, one has the following geometrical relation (see Fig. 1): W 0 ¼ W 1 2L taper tga; ð8þ where a is the tapering angle. Since the separation of the two image peaks is controlled by the exit width (not the entrance width) of the tapered MMI, we wish to express W 0 and L taper in terms of W 1 and the tapering angle a. From Eqs. (7) and (8), one obtains the following expressions: L taper ¼ n r ðw 1 þ CÞ 2 2k 1 þ n r tgaðw 1 þ CÞ ; ð9þ W 0 ¼ W 1 n r tgaðw 1 þ CÞC : ð10þ 1 þ n r tgaðw 1 þ CÞ In our design, the exit width of the tapered MMI can be determined by the peak separation, which is determined by a required 3 db passband width. We then choose an appropriate value for the tapering angle to obtain an optimal spectral response (the MMI length and the entrance width are given by Eqs. (9) and (10)) 2.2. The spectral response According to the self-image theory, a twofold image can be produced at the end of the tapered MMI if the length is chosen appropriately. The twofold image will have an image at the focusing plane, where the entrances of the output waveguides are located. The spectral response can be obtained by an overlap integral for the field distribution at the AWG focusing plane and the fundamental mode of the output waveguide. All performances of the AWG can then be evaluated from its spectral response. The spectral response T ðdf Þ of the AWG can be calculated by the following overlap integral: Z þ1 2 T ðdf Þ¼ U image ðy DDf ÞU o ðyþdy ; ð11þ 1 where U o ðyþ is the fundamental mode field (normalized for the intensity) for the output waveguide considered. The shift Dy of the focusing point at the focusing plane is proportional to the frequency change Df ¼ f f 0, i.e., Dy ¼ DDf, where D is the dispersion coefficient, f 0 is the central frequency at an output waveguide. If aberrations can be ignored, the AWG can be considered as a perfect 1:1 imaging system for the field distribution U end at the end of the tapered MMI. Thus, the field distribution U image at focusing plane of the AWG can be approximated as U image ¼ U end.in the present paper, we use a beam propagation method (BPM) [9,10] to obtain the field distribution U end at the end of the tapered MMI The dispersion characteristic of the spectral response The dispersion characteristic is another important parameter for an AWG used in a DWDM system. The dispersion characteristic D C ðkþ of an AWG can be calculated by [11] D C ðkþ ¼ os d ok ; ð12þ where s d is the group delay characteristic, which is defined as the frequency derivative of the AWG phase response. The group delay characteristic can be closely approximated by [11] s d k2 0 o/ðkþ 2pc ok ; ð13þ where k 0 is the central wavelength, c is the velocity of the light in vacuum, and /ðkþ is the responded phase of ð R þ1 1 U imageðy DDf ÞU o ðyþdyþ 2 for the AWG. 3. Numerical results and discussions In this section we give an example to demonstrate the main features of a designed AWG such 8

12 236 D. Dai et al. / Optics Communications 219 (2003) Fig. 2. The length L taper of the tapered MMI as the tapering angle a varies when the exit width W 1 is fixed to 16 lm. Fig. 3. The spectral responses when the tapering angle a ¼ 0:8, 0, 0.8, respectively. as the 3 db passband width, the ripple, the crosstalk, the insertion loss, and the dispersion characteristic. As a numerical example, we choose the refractive index n c ¼ 1:46, n r ¼ 1:4675, the channel spacing Df ch ¼ 100 GHz, the width of the input/ output single mode waveguide W ¼ 6 lm. In the example the exit width W 1 is fixed to be 16 lm (the corresponding 3 db passband width is about 80% of the channel spacing). Then the whole structure is determined by the tapering angle a (cf. Eqs. (9) and (10)). The length L taper (given by Eq. (9)) of the tapered multimode waveguide is plotted as the tapering angle a varies (see Fig. 2). Fig. 2 shows that the length L taper can be shortened greatly when the tapering angle a increases. Below we study how the tapering angle a affects the performances (such as the 3 db passband width, the ripple, the crosstalk and the insertion loss) of the flat-top AWG The spectral response By using the procedure described in Section 2.2, the spectral response for the flat-top AWG can be calculated. Fig. 3 gives the spectral responses when the tapering angle a ¼ 0:8, 0, 0.8, respectively. When a ¼ 0 (corresponding to the case of a conventional MMI without tapering), the top of the spectral response (the dash-dotted line in Fig. 3) is not flat and has a depressed shape (which means a large insertion loss at the central wavelength). The spectral response does not have a steep transition and thus there is a high crosstalk between adjacent channels. It is obvious that such a spectral response is not good for use in practice. From Fig. 3 one sees that the spectral response can be improved by adjusting the tapering angle a. When the tapering angle a increases from zero, the depressed depth at the central wavelength decreases and the top of the spectral response becomes flat gradually. When the tapering angle a reaches 0.8, the spectral response is improved greatly in comparison with the case of a ¼ 0. The spectral response has a sharper transition and the crosstalk is reduced to about )40 db. The insertion loss for the case a ¼ 0:8 (about 2 db) is 1 db lower than that for the case a ¼ 0 (about 3 db) The 3 db passband width The 3 db passband width is one of the most important characteristics for an AWG. The 3 db bandwidth is usually given in percentage with respect to the channel spacing. For a typical Gaussian-type AWG, its 3 db passband width is only about 50% of the channel spacing. The narrow passband makes the device sensitive to the wavelength shift, which limits the deviceõs applications in WDM systems. By connecting a tapered MMI at the end of the input waveguide, the passband can be broadened. The level of the broadening can be controlled by 9

13 D. Dai et al. / Optics Communications 219 (2003) Fig. 4. The 3 db passband width as the tapering angle a varies. the exit width W 1 of the tapered MMI. Fig. 4 shows the 3 db passband width for a fixed exit width (W 1 ¼ 16 lm) when the tapering angle a varies from )0.8 to 0.8. From this figure, one sees that the 3 db passband width does not vary significantly for different a values when the exit width W 1 is fixed (the 3 db passband width decreases from 84% to 70% as the tapering angle a increases from )0.8 to 0.8 ). This indicates that the 3 db passband width is determined mainly by the exit width of the tapered MMI. Thus, we can choose the exit width according to the required 3 db passband width when designing a flat-top AWG The ripple The ripple describes that flatness in a passband. Here it is defined as the fluctuation of the spectral response in a window from f 0 ðdf ch =8Þ to f 0 þðdf ch =8Þ. One wishes to reduce the ripple as much as possible. Fig. 5 shows the ripple when the tapering angle a varies. From this figure one sees that the tapering angle a affects the ripple significantly. For a conventional MMI (a ¼ 0), the ripple is about db. The ripple is the smallest (about db) when the tapering angle a is about 0.5 (the ripple is reduced by about 0.27 db as compared to the case of a conventional MMI). Thus, an optimal value for the tapering angle should be searched to obtain a low enough ripple when designing a flat-top AWG. Fig. 5. The ripple as the tapering angle a varies The crosstalk The crosstalk is a key parameter for a DWDM device. For a practical device, a low crosstalk level must be ensured. Usually the crosstalk for a practical device should be lower than )25 db. In order to have a margin for fabrication errors, a design value for the crosstalk should be as low as )30 db. For a flat-top AWG, the crosstalk increases when the spectral response is broadened. Thus, the crosstalk for a flat-top AWG is usually higher than that for a Gaussian type of AWG. Fig. 6 shows the crosstalk as the tapering angle a varies. When the tapering angle increases from )0.8 to 0.8 the crosstalk decreases from about 20 Fig. 6. The crosstalk as the tapering angle a varies. 10

14 238 D. Dai et al. / Optics Communications 219 (2003) to 40 db. The crosstalk for the case of a ¼ 0:8 is reduced by about 11 db as compared to the crosstalk (about 29 db) for the case of a conventional MMI (a ¼ 0). When a ¼ 0:5 (corresponding to the case when the ripple has the lowest level), the crosstalk is about )35.6 db, which is about 6.6 db lower than that for the case a ¼ The insertion loss A low insertion loss is also very important for a practical device. Fig. 7 shows the insertion loss at the central wavelength as the tapering angle a varies. As the tapering angle a increases from zero, the depressed depth at the center wavelength decreases and the top of the spectral response becomes flat gradually, and consequently the insertion loss decreases. Compared to the case of a conventional MMI (a ¼ 0), the insertion loss is reduced by about 1 db when the tapering angle increases to 0.8. When a ¼ 0:5 (corresponding to the case when the ripple has the lowest level), the insertion loss is about 2.35 db, which is about 0.65 db lower than that for the case of a ¼ 0. tapered multimode waveguide. We found that the spectral response can be improved further by modifying the MMI length slightly. Assume that the MMI length is L taper ¼ 3 8 L p eff þ DL taper. For a conventional MMI (a ¼ 0), the dispersion characteristic usually becomes worse when one adjusts the MMI length (the only parameter that can be adjusted) to obtain a flat spectral response. For the present design, we can obtain simultaneously a flat spectral response and a good dispersion characteristic since we can adjust two parameters (DL taper and a). Fig. 8(a) shows the dispersion characteristic D C ðkþ for several different designs of flat-top AWGs. The optimal dispersion characteristic for 3.6. The dispersion characteristic The dispersion characteristic is another important characteristic for an AWG used in a DWDM system. In all the above discussions, the length of the tapered MMI is chosen to be 3 8 L p eff and thus a twofold self-image is formed at the end of the Fig. 7. The insertion loss as the tapering angle a varies. Fig. 8. (a) The dispersion characteristic for several different designs of flat-top AWGs. (b) The corresponding spectral responses. 11

15 D. Dai et al. / Optics Communications 219 (2003) an AWG with a conventional MMI (a ¼ 0) is given by No. 2 line (the optimal value of DL taper is found to be 15 lm by using the BPM simulation). However, the corresponding spectral response is not very flat and has a ripple of about 0.35 db (see No. 2 line in Fig. 8(b)). The crosstalk is about )29 db. The spectral response with the smallest ripple for a flat-top AWG with a conventional MMI (a ¼ 0) is given by No. 3 line in Fig. 8(b) (the optimal value of DL taper is found to be )30 lm). The ripple is lower than 0.05 db. The insertion loss is about db and the crosstalk is about )40 db. The shape of the spectral response is good. However, the dispersion characteristic is bad (see No. 3 line in Fig. 8(a)). The dispersion characteristic is not flat in the 3 db passband and is over 20ps/nm at the central wavelength. When using a tapered MMI, we can obtain simultaneously a flat spectral response and a good dispersion characteristic by choosing DL taper and a appropriately. The dispersion characteristic (almost zero) and the spectral response (with a ripple of only about 0.09 db) for such an optimal design with a ¼ 1:0 and DL taper ¼ 50 lm are shown by No. 1 lines in Figs. 8(a) and (b), respectively. 4. Conclusion In the present paper, a tapered MMI has been used to realize a flat-top AWG with good characteristics. The influences of the tapering angle to the 3 db passband width, the ripple, the crosstalk and the insertion loss of the flat-top AWG have been studied. A flattened spectral response with a virtually zero dispersion characteristic has been obtained by choosing appropriately the tapering angle and the length of the tapered MMI. It has been demonstrated that a tapered MMI can give a much better performance than a conventional MMI for a flat-top AWG. If the 3 db passband width is required to be broadened further, the ending width of the tapered MMI has to be enlarged more, which will increase the insertion loss (this drawback also exists for a flat-top AWG with a conventional MMI). Fortunately, a 3 db passband width of 80% of the channel spacing is sufficient for most of the applications and the corresponding insertion loss (about 2.15 db for our numerical example) is still acceptable. Therefore, this drawback will not limit the application of the present flat-top AWG. Acknowledgements The partial support of the provincial government of Zhejiang Province of China under a major research grant (No ) is gratefully acknowledged. References [1] M.K. Smit, C.V. Dam, IEEE J. Select. Top. Quantum Electron. 2 (2) (1996) 236. [2] M.R. Amersfoort, C.R. de Boer, F.P.G.M. van Ham, M.K. Smit, P. Demeester, J.J.G.M. van der Tol, A. Kuntze, Electron. Lett. 30 (4) (1994) 300. [3] Y.P. Ho, H. Li, Y.J. Chen, IEEE Photo. Tech. Lett. 9 (3) (1997) 342. [4] A. Rigny, A. Bruno, H. Sik, Electron. 33 (20) (1997) [5] K. Okamoto, A. Sugita, Electron. Lett. 32 (18) (1996) [6] J.B.D. Soole, M.R. Amerfoort, H.P. LeBlanc, N.C. Andreadakis, A. Rajhel, C. Caneau, R. Bhat, M.A. Koza, C. Youtsey, I. Adesida, IEEE Photo. Tech. Lett. 8 (10) (1996) [7] C. Dragone, L. Siliver, US patent No. 5,706,377, 2/1995. [8] L.B. Soldano, E.C.M. Pennings, J. Lightwave Tech. 13 (4) (1995) 615. [9] R. Scarmozzino, R.M. Osgood, J. Opt. Soc. Am. A 18 (5) (1991) 724. [10] R. Scarmozzino, A. Gopinath, R. Pregla, S. Helfert, IEEE J. Select. Top. Quantum Electron. Lett. 6 (1) (1996) 150. [11] M.C. Parker, S.D. Walker, Optical Fiber Communication Conference 2 (2000)

16 FIO 22(3) #7574 Fiber and Integrated Optics, 22: , 2003 Copyright 2003 Taylor & Francis /03 $ DOI: / A Flattened AWG Demultiplexer with Low Chromatic Dispersion DAOXIN DAI SHUZHE LIU Centre for Optical and Electromagnetic Research State Key Laboratory of Modern Optical Instrumentation Joint Laboratory of Optical Communications of Zhejiang University Zhejiang University, Yu-Quan Hangzhou, P. R. China SAILING HE Division of Electromagnetic Theory, Alfven Laboratory Royal Institute of Technology Stockholm, Sweden A design method is introduced to obtain a flat-top arrayed-waveguide grating (AWG) demultiplexer with low chromatic dispersion. A multimode interference (MMI) section is connected at the end of the input waveguide, and a tapered waveguide is connected at the entrance of each output waveguide of the AWG demultiplexer. The design procedure is presented. A design example is given and shown to have a much better performance than the conventional flat-top design using only an MMI section. The insertion loss of the designed AWG demultiplexer is also reduced. Keywords AWG, flat-top, chromatic dispersion, flattened spectral response, MMI, taper, insertion loss Introduction Arrayed-waveguide grating (AWG) demultiplexers [1, 2] have been widely used as key components in wavelength division multiplexing (WDM) networks. For a conventional AWG demultiplexer, the shape of the spectral response is of a Gaussian type (the ratio of the 1 db bandwidth to the 20 db bandwidth is small). Therefore, the transmission efficiency is sensitive to a slight wavelength shift (caused by, e.g., the laser quality, temperature change, or the polarization dispersion), and the device is not suitable for high-speed modulation. These drawbacks limit the applications of AWGs of a Gaussian type in WDM systems. An AWG demultiplexer with a flattened spectral response is thus desirable. Received 1 September 2002; accepted 2 December This work is supported by the government of Zhejiang Province (China) under a major research grant (No ). Address correspondence to Sailing He, Division of Electromagnetic Theory, Alfven Laboratory, Royal Institute of Technology, S Stockholm, Sweden. sailing@tet.kth.se

17 142 D. Dai et al. In recent years many methods have been reported for achieving a broadened spectral response of an AWG demultiplexer by using, for example, multimode output waveguides [3], two cascaded grating devices [4], multiple gratings [5], multiple Roland circles [6], a multimode interference (MMI) section [7], or a Y-junction [8]. However, these methods have some drawbacks such as a nonlinear phase response, an increase in the size, or too large an insertion loss of the device. Among these methods, a simple and effective method is to connect an MMI section at the end of the input waveguide of an AWG demultiplexer. One can obtain a flattened spectral response by choosing an appropriate width and length for the MMI section. However, for such a flat-top AWG demultiplexer, a good chromatic dispersion characteristic, which is also important for a practical AWG demultiplexer, is difficult to obtain at the same time. When a very high bit rate of traffic is transmitted in each individual channel, the chromatic dispersion of the AWG demultiplexer is required to be very low. In the present paper we introduce a new design for a flat-top AWG demultiplexer whose chromatic dispersion is low. The new design includes an MMI section (connected at the end of the input waveguide) and tapered waveguides (located at the entrances of the output waveguides). The designed AWG demultiplexer exhibits not only a flattopped passband but also a relatively low chromatic dispersion characteristic. For a given requirement of passband width, we can conveniently design such an AWG demultiplexer with good performance by optimizing the structures of the MMI section and the tapered waveguides. Theory An AWG demultiplexer consists of a waveguide array, input/output waveguides, and two free propagation regions (FPRs). In this paper an MMI section is connected at the end of the input waveguide, and a tapered waveguide is connected at the entrance of each output waveguide (see Figure 1). Figure 1. The schematic layout of the designed flat-top AWG demultiplexer with a low chromatic dispersion characteristic. 14

18 Flattened AWG Demultiplexer 143 When the fundamental mode of the input waveguide is launched into the MMI section, not only the fundamental mode but also higher-order modes of the MMI section are excited since the fundamental mode of the input waveguide does not match the fundamental mode of the MMI section. Since the input is symmetric, only the even modes can be excited. To fulfill the requirement of the insertion loss for the demultiplexer, in this paper we choose the width for the MMI section to be so narrow that only the fundamental and second-order modes can be excited in the MMI section (note that the narrow width of the MMI section is still large enough to fulfill the requirement of the passband width for the weakly confined MMI section considered). After propagating along the MMI section, a phase difference occurs between the fundamental mode and the second-order mode. The MMI section converts its input field into a twofold image of the input field when the phase difference is π. This is the so-called self-image effect [9]. The separation of the two peaks of the twofold image determinates the passband width of the spectral response. The peak separation can be controlled by the width of the MMI section. The Spectral Response According to the self-image theory [9], a twofold image can be formed at the end of the MMI section when the length of the MMI section, L MMI, is chosen appropriately. The twofold image will be reimaged at the focal plane (of the AWG demultiplexer), where the entrances of the tapered waveguides (connected to the output waveguides) are located. The shift y of the focal point at the focal plane is proportional to the frequency change f = f f 0, that is, y = D f, where D is the spatial dispersion coefficient of the AWG demultiplexer, and f 0 is the central frequency for the considered output waveguide. Therefore, the output field at different frequencies can be determined by the following overlap integral of the fundamental mode profile of the tapered waveguide and the field distribution U image at the focal plane of the AWG demultiplexer: T( f)= + U image (y D f ) U 0 (y)dy, (1) where U 0 (y) is the field distribution (normalized for the intensity) of the fundamental mode associated with the entrance width W o of the tapered waveguide (which is tapered very slowly to the single-mode output waveguide). When aberrations can be ignored, the AWG demultiplexer can be considered as a perfect 1:1 imaging system for the field distribution U end at the end of the MMI section. Thus, the field distribution U image at the focal plane of the AWG demultiplexer can be approximated as U image = U end. In this paper we use a finite-difference beam propagation method (FD-BPM) [10, 11] to obtain the field distribution U end at the end of the MMI section. The spectral response of the AWG demultiplexer is then given by T( f) 2. Since the field distribution U image has a shape with two peaks, the spectral response can be certainly broadened according to Equation (1). The Chromatic Dispersion The chromatic dispersion characteristic is another important parameter for an AWG demultiplexer used in a DWDM system. The deleterious effects of the chromatic dispersion become more significant as the bit rate of traffic being transmitted in each individual 15

19 144 D. Dai et al. channel increases. The dispersion characteristic D c (λ) of an AWG can be calculated by [12] D c (λ) = τ d λ, (2) where τ d is the group delay characteristic, which is defined as the frequency derivative of the phase response of the AWG demultiplexer. The group delay characteristic can be closely approximated by τ d λ2 0 φ(λ) 2πc λ, (3) where λ 0 is the central wavelength, c is the velocity of the light in vacuum, and φ(λ) is the responded phase of T( f) for the AWG demultiplexer. A Design Procedure From a given requirement for the 1 db (or 3 db) passband width, we can determine the width of the MMI section first. Obviously the 1 db (or 3 db) passband width increases as the width of the MMI section increases. (However, the insertion loss will also increase at the same time.) Then by optimizing the length of the MMI section and the width of the tapered output waveguide, we can obtain a flat-top AWG demultiplexer with a low dispersion characteristic D c. If the phase distribution of the field U image is flat (i.e., constant) around the focal point, then the phase of the overlap integral T( f)= + U image(y) U o (y + D f )dy will not deviate much from the phase of T(0) = + U image(y) U o (y)dy when the center of the Gaussian function U o moves slightly away from the center point (i.e., the focal point) of the overlapped function U image. Consequently, the chromatic dispersion characteristic D c (λ) will be small around the central wavelength in such a situation according to definitions (2) and (3). Since U image = U end for a 1:1 imaging system, U end with a flat phase distribution is desired. It is well known that the phase distribution of the field changes as the field propagates in the MMI section. According to the selfimaging theory, the phase front is planar at the self-imaging position (i.e., the phase distribution is flat). For a weakly confined MMI section, the phase distribution of the field at the self-imaging position is not perfectly flat (with a nonzero curvature) because of the nonperfect self-imaging. Nevertheless, it is found that the phase distribution at the self-imaging position is still flatter than that at any other position in the MMI region. Therefore, we should choose the twofold self-imaging length for the MMI section in order to make the chromatic dispersion minimal. Usually the self-imaging position is determined approximately according to the selfimaging theory. Let L 0 MMI denote this approximate value (obtained by the self-image theory) for the length of the MMI section. However, this is not accurate enough for the case of weakly confined waveguides such as silica-on-silicon waveguides (which are used in the present design). A more accurate method should be used to obtain a more accurate value for the self-imaging length. In the present paper, the FD-BPM is used. We denote the twofold self-imaging length of the MMI section obtained by the FD-BPM as L MMI. For a conventional flat-top AWG demultiplexer using only an MMI coupler, it is found that the spectral response is usually not flattened optimally when the length of the MMI coupler is chosen to be L MMI. Since the width and length of the MMI section 16

20 Flattened AWG Demultiplexer 145 have already been determined from the required passband width and minimal chromatic dispersion, we need to find another parameter to adjust in order to optimize the spectral response. In this article we connect a tapered waveguide at the entrance of each output waveguide and optimize the entrance width W o of the tapered waveguide to achieve a flat-top spectral response. Numerical Results In this section we illustrate the performance of such an AWG demultiplexer with a design example with the following parameters: n c = 1.46 and n r = for the effective refractive indices of the cladding and the core, respectively, the central wavelength λ 0 = 1.55 μm, the channel spacing f ch = 100 GHz, and the width W = 6.0 μm for the input single-mode waveguide and the ending part of the output waveguide. The length L tp for the tapered part of the output waveguide should be long enough so that the tapering angle is small. In this numerical example we choose L tp = 1,000 μm. The width of the MMI section is chosen to be 16.0 μm so that the 1 db passband width is about 60% of the channel spacing. From the self-image theory, the approximate value for the twofold self-imaging length of the MMI section is determined to be L 0 MMI = μm. Then by using an FD-BPM simulation, a more accurate value L MMI for the twofold self-imaging length of the MMI section is obtained. For the present example, L MMI = (L 0 MMI ) μm, that is, μm. Figure 2 shows the maximal value Dc max of the chromatic dispersion characteristic in the ITU window [ 12.5 GHz, 12.5 GHz] (centered at f 0 ) for such an AWG demultiplexer with a fixed L MMI = μm, however, with different values for the entrance width W o of the tapered output waveguide (in the range of (5.0 μm, 20.0 μm)). From this figure one sees that the maximal dispersion characteristic Dc max Figure 2. The maximal value of the chromatic dispersion Dc max in the ITU window [ 12.5 GHz, 12.5 GHz] as the entrance width W o (for the tapered output waveguide) varies. The length of the MMI section is fixed to the twofold self-imaging length L MMI = μm. 17

21 146 D. Dai et al. does not change much as the width W o varies from 5.0 to 20.0 μm when the length of the MMI section is fixed to L MMI. Thus, the twofold self-imaging length L MMI indeed gives low chromatic dispersion in the passband for any value of W o in a wide range. According to the design procedure described in Section 2.3, the length of the MMI section is fixed to L MMI ( μm) and the width W o is to be optimized to make a flat-top spectral response (i.e., minimal ripple in the passband). The optimal width can be found simply by using a one-dimensional search for W o in the range of (5.0 μm, 20.0 μm). Figure 3 shows the ripple and the insertion loss as W o varies (the length of the MMI section is fixed to L MMI ). From Figure 3 one can see that the ripple (defined as the maximal variance of the spectral response within the ITU window [ 12.5 GHz, 12.5 GHz]) has a minimal value of about db when W o = 9.7 μm. Thus the optimal width is found to be W o = 9.7 μm for the designed flat-top AWG demultiplexer. The corresponding insertion loss is about 2.07 db. Figures 4 and 5 show the chromatic dispersion characteristics and the spectral responses, respectively, for the following three cases: Case (1): W o = 9.7 μm and L MMI = L MMI (= μm). This case corresponds to the optimal design with both properties of flat-top and low chromatic dispersion. Case (2): W o = 6.0 μm and L MMI = L MMI (= μm). This case has a low chromatic dispersion but a large ripple at the center of the spectral response. Case (3): W o = 6.0 μm and L MMI = L MMI 43.0 μm (= μm). This case has a good flat-top shape for the spectral response; however, it also has a quite large chromatic dispersion. Note that cases (2) and (3) are conventional designs for a flat-top AWG demultiplexer with only an MMI coupler (without tapering the output waveguides). From Figure 4 one sees that for cases (1) and (2) (both have L MMI = L MMI ) the dispersion characteristic D c is low (lower than 5 ps/nm) in the passband [ 50 GHz, Figure 3. The ripple (in the spectral response) and the insertion loss as the entrance width W o of the tapered output waveguide varies. The length of the MMI section is fixed to the twofold self-imaging length L MMI = μm. 18

22 Flattened AWG Demultiplexer 147 Figure 4. The dispersion characteristics for the three different cases. Figure 5. The spectral responses for the three different cases. 19

23 148 D. Dai et al. 50 GHz]. And for case (1), D c is even better (as low as 2.1 ps/nm in the passband [ 50 GHz, 50 GHz]). As expected, the chromatic dispersion is quite large for case (3) since the length of the MMI section is quite different from the twofold self-imaging length L MMI. The following analysis can be made from Figure 5. For case (2), the ripple is about 0.3 db. The insertion loss at the central wavelength is about 3.1 db. The 1 db passband width is about 62% of the channel spacing. The 20 db passband width is about 172.2% of the channel spacing. The ratio of the 1 db bandwidth to the 20 db bandwidth is about For case (1) (the optimal case), the ripple is almost 0 db. The insertion loss at the central wavelength is about 2.07 db, which is reduced by about 1 db as compared to case (2). The 1 and 20 db passband widths are about 57% and 170.5% of the channel spacing, respectively. The ratio of the 1 db bandwidth to the 20 db bandwidth is about From the above comparison, one sees that case (1) has a better spectral response than case (2) (the length of the MMI section is fixed to L MMI in both cases). If one adjusts the length of the MMI section, a better spectral response may be obtained. However, its corresponding dispersion characteristic will usually be deteriorated. The dot-dashed lines in Figures 4 and 5 show the dispersion characteristic and the spectral response for case (3) when we fix the width W o = 6.0 μm (i.e., without tapering the output waveguides) and adjust the length L MMI of the MMI section to (L MMI 43.0) μm (for which a flattened spectral response with a good shape is obtained). The insertion loss is about 2.63 db, and the ripple is almost 0 db. The 1 and 20 db passband widths are about 60% and 156% of the channel spacing, respectively. The ratio of the 1 db bandwidth to the 20 db bandwidth is about 0.385, which is larger than those for cases (1) and (2). However, from Figure 4 one can see that at the central wavelength the corresponding chromatic dispersion D c exceeds 20 ps/nm, which is beyond a permissible value in a practical DWDM system. When a very high bit rate of traffic is transmitted in each individual channel, the chromatic dispersion D c is required to be very low. Therefore, the design of case (3), which corresponds to an optimal conventional design for a flat-top AWG demultiplexer using only an MMI coupler, is not good for use, despite its good shape of spectral response. Conclusion In this paper an MMI section (connected at the end of the input waveguide) and tapered waveguides (connected to the output waveguides) have been used to design a flat-top AWG demultiplexer with low chromatic dispersion. A design procedure for such an AWG demultiplexer has been presented. The width of the MMI section can be determined first from a given requirement for the passband width. An accurate twofold self-imaging length L MMI is then chosen for the MMI section by the FD-BPM simulation, which guarantees a low chromatic dispersion for the designed AWG demultiplexer. Finally, we fix this length of the MMI section and adjust the entrance width W o of the tapered output waveguide in order to obtain a flat-top spectral response (with minimal ripple in the passband). Note that the flat-top property is achieved by a combination of the MMI section and a tapered output waveguide, while the low chromatic dispersion is achieved by choosing the twofold self-imaging length for the MMI section. A numerical example has been given, and an AWG demultiplexer with a flattened spectral response and a low chromatic dispersion characteristic has been designed. For a conventional flat-top AWG demultiplexer using only an MMI section, the large insertion loss results from the modal mismatching between the fundamental mode of the output waveguide and the two-peakshaped field distribution at the focal plane. The insertion loss of the present flat-top AWG 20

24 Flattened AWG Demultiplexer 149 demultiplexer is also reduced since the modal size for the tapered waveguide is larger and the modal mismatching is reduced. It has been shown that the present design exhibits a much better performance than the conventional design using only an MMI section for a flat-top AWG demultiplexer. References 1. Smit, M. K., and C. V. Dam Phasar based WDM devices: Principles, design and applications. IEEE J. Select. Topics Quantum Electron. 2(2): Koteles, E. S Integrated planar waveguide demultiplexers for high-density WDM applications. Fiber and Integrated Optics 18(4): Amersfoort, M. R., C. R. de Boer, F. P. G. M. van Ham, M. K. Smit, P. Demeester, J. J. G. M. van der Tol, and A. Kuntze Phased-array wavelength demultiplexer with flattened wavelength response. Electron. Lett. 30(4): Ho, Y. P., H. Li, and Y. J. Chen Flat channel-passband-wavelength multiplexing and demultiplexing devices by multiple-rowland-circle design. IEEE Photo. Technol. Lett. 9(3): Rigny, A., A. Bruno, and H. Sik Multigrating method for flattened spectral response wavelength multi/demultiplexer. Electron. Lett. 33(20): Okamoto, K., and A. Sugita Flat spectral response arrayed-waveguide grating multiplexer with parabolic waveguide horns. Electron. Lett. 32(18): Soole, J. B. D., M. R. Amerfoort, H. P. LeBlanc, N. C. Andreadakis, A. Rajhel, C. Caneau, R. Bhat, M. A. Koza, C. Youtsey, and I. Adesida Use of multimode interference couplers to broaden the passband of wavelength-dispersive integrated WDM filters. IEEE Photo. Technol. Lett. 8(10): Dragone, C., and L. Siliver U.S. patent. No. 5,706,377, February. 9. Soldano, L. B., and E. C. M. Pennings Optical multi-mode interference devices based self-image: Principles and applications. J. Lightwave Technol. 13(4): Scarmozzino, R., and R. M. Osgood Comparison of finite-difference and Fouriertransform solutions of the parabolic wave equation with emphasis on integrated-optics applications. J. Opt. Soc. Am. A. 18(5): Scarmozzino, R., A. Gopinath, R. Pregla, and S. Helfert Numerical techniques for modeling guided-wave photonic devices. IEEE J. Select. Topics Quantum Electron. 6(1): Parker, M. C., and S. D. Walker Adaptive chromatic dispersion controller based on an electro-optically chirped arrayed-waveguide grating. Proceedings of Optical Fiber Communication Conference, Baltimore, Maryland, 2000, 2:257. Biographies Daoxin Dai received his B.Sc. degree at the Department of Optical Engineering of Zhejiang University, China, in Currently, he is a Ph.D. student, and his research activities are in the design, simulation, and fabrication of dense wavelength division multiplexing devices. Shuzhe Liu was born in Currently he is an undergraduate student, and his research activities are in the design of integrated optical waveguide devices. Sailing He received the Licentiate of Technology and Ph.D. degree in electromagnetic theory in 1991 and 1992, respectively, both from the Royal Institute of Technology, Stockholm, Sweden. He has worked at the same institute since then. He is also with the Center for Optical and Electromagnetic Research of Zhejiang University since 1999 as a special professor appointed by the Ministry of Education of China. He has authored one monograph and over 140 papers in refereed international journals. He is also the chief scientist for the Joint Laboratory of Optical Communications of Zhejiang University. 21

25 Optics Communications 262 (2006) Optimal design for a flat-top AWG demultiplexer by using a fast calculation method based on a Gaussian beam approximation Salman Naeem Khan a,b,d, Daoxin Dai a,b,c, Liu Liu a,b,d, Lech Wosinski d, Sailing He a,b,c, * a Centre for Optical and Electromagnetic Research, Zhejiang University, Zijingang, Hangzhou, , China b Joint Research Center of Photonics of the Royal Institute of Technology (Sweden) and Zhejiang University (China), Zijinggang campus, East-5 Building, Zhejiang University, Hangzhou, , China c Division of Electromagnetic Theory, Alfven Laboratory, Royal Institute of Technology, Teknikringen 31, S Stockholm, Sweden d Laboratory of Photonics and Microwave Engineering, Department of Microelectronics and Information Technology, Royal Institute of Technology, S Kista, Sweden Received 16 May 2005; received in revised form 26 October 2005; accepted 23 December 2005 Abstract Passband broadening of an AWG (array waveguide grating) demultiplexer with an MMI (multimode interference) coupler connected at the end of a tapered input waveguide is considered. An explicit formula based on the field propagation of an approximate Hermit Gaussian beam is used to calculate quickly and reliably the spectral response of the AWG demultiplexer. The widths of the input waveguide, the output waveguides and the MMI coupler are optimized. The optimal design is verified with the experimental measurement. Ó 2006 Elsevier B.V. All rights reserved. PACS: Gn; Qb; Et Keywords: Arrayed waveguide grating; Flat top; MMI; Gaussian beam 1. Introduction The explosive growth of internet traffic is pushing the rapid development of dense wavelength division multiplexing (DWDM) systems. An arrayed-waveguide grating demultiplexer [1], which is based on the planar waveguide technology, has played an important role as a key optical component in a DWDM system. A flat-top AWG is insensitive to the laser wavelength shift (due to e.g. temperature change) and is especially desirable in a high speed DWDM system. Several techniques have been proposed to obtain a flattened spectral response, such as using a multimode output waveguide [2], two cascaded grating devices [3] multiple gratings [4], multiple Roland-circles [5], a multimode interference (MMI) coupler [6], and a Y-junction [7]. * Corresponding author. Tel.: ; fax: address: sailing@kth.se (S. He). Putting an MMI section at the end of the input waveguide is a simple and effective way of realizing a flattened spectral response. In the present paper, we connect an MMI section at the end of a tapered input waveguide to broad the spectral response of an AWG demultiplexer. The paper is organized as follows. In Section 2, the basic principle of the AWG demultiplexer with an MMI coupler connected at the end of the input waveguide is discussed, and an explicit formula for the spectral response of an AWG demultiplexer is derived. This formula is efficient for calculating the spectral response of a flat-top AWG demultiplexer. In comparison with some other fast calculation methods (such as 1:1 imaging method [8]) the present formula is more accurate (particularly when the total number of the arrayed waveguides is not large). With such a fast and reliable method, the widths for the MMI section, the input waveguide and the output waveguides are optimized in Section 3. Section 4 gives a comparison of the simulation results and the measured results for a fabricated flat-top AWG demultiplexer /$ - see front matter Ó 2006 Elsevier B.V. All rights reserved. doi: /j.optcom

26 176 S.N. Khan et al. / Optics Communications 262 (2006) Basic principle and formulas The structure of an AWG demultiplexer is shown in Fig. 1(a). An AWG demultiplexer consists of an input waveguide, many output waveguides, two free propagation regions (FPRs), and N arrayed waveguides (AWs) with a constant length difference (DL) between two adjacent waveguides. The input and output waveguides are tapered in this paper. In order to broad the spectral response of an AWG demultiplexer, an MMI coupler is connected at the end of the tapered input waveguide. The input light is radiated to the first FPR and then excites the arrayed waveguides. After traveling through the arrayed waveguides, the light beam interferes constructively at one focal point in the second FPR. The location of the focal point depends on the wavelength [1]. The adiabatically tapered sections for both the input and output waveguides are shown in the enlarged view of Fig. 1(a). Fig. 1(b) shows an enlarged view of the first FPR including the MMI section and the adiabatically tapered section of the input waveguide. Below we give a formula for the flattened spectral response by using the propagation theory for an approximate Gaussian beam. The field propagation of the fundamental mode (of Gaussian beam leaving a waveguide) in an FPR can be described approximately by the following normalized Gaussian field distribution (subscript i is for the first FPR and o for the second FPR) E F ðx; zþ ¼A norm exp j kz tan 1 kz Tapered input px 2 F x 2 1 jk þ ; F ¼ i; o; ð1þ x 2 FðzÞ 2R F Array waveguides Tapered output where A norm ¼ 2 1=4 1 p ffiffiffiffiffiffiffiffiffiffiffi ; p x F ðzþ sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi x F ðzþ ¼x F 1 þ kz 2 ; px 2 F " 2 # R F ðzþ ¼z 1 þ px2 F ; kz where k is the wavelength in the FPR, A norm is the normalized constant, k =2p/k is the wavenumber, x F and x F (z) are the beam waist at z = 0 and the beam width at distance z, respectively, and R F (z) is the wave-front radius of curvature. Note that x F depends on the width w F of the waveguide [1], x F ¼ W wg 2 1 þ 2 ; v pwhere ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi W wg is the width of the waveguide and vð¼ k 0 W wg n 2 eff n2 cþ is the normalized transverse attenuation constant (here k 0 is the wavenumber in vacuum, n eff and n c are the effective refractive index and the refractive index for the cladding, respectively). To broad the spectral response of the AWG demultiplexer, an MMI (1 2) section (with length L MMI ) is connected at the end of the tapered input waveguide. With an appropriately chosen length (L MMI ), the MMI section converts its input field into a two-fold image. The separation Y between the two peaks of this two-fold image determines the 3 db passband width and is directly related to the width W MMI of the MMI [9] 2Y ¼ W e ¼ W MMI þ k 2r n c ðn 2 r p n2 c Þ 1=2 ; ð2þ n r where r = 0 (for TE) and 1 (for TM), and n r and n c are the refractive indices for the core and cladding, respectively. L MMI is related to the effective width W e by the relation [8], L MMI ¼ 4n rw 2 e 3k. ð3þ a MMI 1st FPR Input waveguide 2nd FPR Output waveguides Image plane The two-fold image field distribution at the end of the MMI section is given by [8] ( " # " #) ðx þ Y =2Þ2 ðx Y =2Þ2 E MMI ðxþ ¼CA norm exp þ exp ; x 2 i x 2 i MMI W MMI x L FPR θ l Input aperture z where C ¼ p 1 ffiffiffi 2 1 q ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi. 1 þ exp½ 2Y 2 =ð2w i Þ 2 Š ð4þ Tapered input waveguide b L MMI d g x' Arrayed waveguides Fig. 1. (a) An AWG demultiplexer; (b) enlarged view of the first FPR. The field distribution at the end of the MMI section is shown in Fig. 2 for different values of Y (directly related to the width of the MMI section). Obviously Y = 0 corresponds to the conventional AWG design. The field at the input aperture (E IAP (x)) is given by (see Fig. 1(b)) 23

27 S.N. Khan et al. / Optics Communications 262 (2006) EMMI (x) Y=0 Y= x (μm) Fig. 2. Field at the end of the MMI section as a function of Y. Y X (X l, Z l ) X' L FPR Z' Z X'' X (X im, Z im ) Z'' 2q im ql E IAP ðxþ ¼p 1 ffiffi ½E F ðx þ Y =2; L FPR cos h l Þ 2 þ E F ðx Y =2; L FPR cos h l ÞŠ ; F¼i l ¼ 0; 1; 2;...; N 1; where L FPR is the length of the FPR (same for the first and second FPR) and h l is the angle made by the lth arrayed waveguide with the z axis and N is the total number of the array waveguides. The field at the input aperture is coupled to the arrayed waveguides, and the coupling coefficient (g l ) between the E IAP (x) and the modal field E AW (x 0 ld g ) of the lth arrayed waveguide is evaluated using the following overlap integral g l ¼ Z þ1 1 E IAP ðxþe AW ðx0 ld g Þ dx; where x 0 = L FPR sin h l, d g is the pitch of the array waveguides (i.e., separation between the two consecutive array waveguides) and the superscript (*) denotes the complex conjugate. Note that field E IAP (x) in Eq. (6) is the field at the aperture of waveguide array (instead of a plane perpendicular to the central arrayed waveguide). The field at the image plane is the sum of the far fields from each array waveguide, i.e., E IM ¼ XN 1 g l expð j/ l ÞE F ðx 00 ; Z 00 Þj F¼o ; l¼0 where / l (=/ 0 + l2pn g DL/k) is the phase introduced by the lth arrayed waveguide (/ 0 represents the phase introduced by the shortest array waveguide) and n g is the effective index for the TE or TM mode of the arrayed waveguide. Here E F has the same expression as (1). (X 00,Z 00 ) is actually the value of (X im,z im ) in the coordinate system (X 00,Y 00 ) with origin at (X l,z l ). In (X,Z) coordinate system, one has ðx im ; Z im Þ¼ L FPR 2 ð1 þ cos 2h imþ; L FPR sin 2h im 2 ðx l ; Z l Þ¼ðL FPR ð1 cos h l Þ; L FPR sin h l Þ. And consequently one can obtain the following coordinate transformation (see Fig. 3). ; ð5þ ð6þ ð7þ X 00 ¼ L FPR sin h im cosðh im þ h l Þ; Z 00 ¼ L FPR ½1 sin h im sinðh l þ h im ÞŠ. The coupling (to the output waveguide) coefficient g out is an overlap integral of the E IM (x) and the fundamental modal field (E OW (x)) of the output waveguide, i.e., g out ¼ Z þ1 1 Fig. 3. Transformation of the coordinates. E IM ðxþe OWðxÞ dx. ð8þ The spectral response of the output waveguide is given by g out Design and optimization The AWG is designed and optimized to obtain a flat-top spectral response. Three parameters, namely, the width of the input waveguide (w i ), the width of the output waveguide (w o ) and the width of MMI (W MMI ) are optimized in the flat-top design. The parameters of the designed AWG demultiplexer are listed in Table 1, where m is the diffraction order, Dk ch is the channel spacing and d o is the separation between the two adjacent output waveguides. The refractive indices are chosen according to the measured data of the thin films (deposited with PECVD; see the next section). Figs. 4(a) (c) show the insertion loss, the ripple, and the 1 db pass-bandwidth as Y increases for a particular combination of w i and w o in order to determine the optimal value of Y. This optimized Y is directly related to the width of the MMI section by (2). From Figs. 4(a) and (c), one can easily see that as the width of the input or output waveguide increases, the insertion loss decreases and the 1 db passband width increases for a particular value of Y. Usually the crosstalk will increase as the width of the input/output waveguide increases. However, in the range considered in this figure, the crosstalk is very small. Therefore, we choose w i = w o =8 lm. Table 1 Design parameters for a flat-top AWG demultiplexer m N d g d o L FPR k 0 Dk ch L MMI lm 24.5 lm 5000 lm 1.55 lm 1.6 nm 168 lm 24

28 178 S.N. Khan et al. / Optics Communications 262 (2006) Insertion Loss (db) a Ripple (db) b Δλ 1dB/ Δλ ch wi=6,wo=6 wi=6,wo=8 wi=7,wo=7 wi=8,wo= Y (μm) wi=6,wo=6 wi=6,wo=8 wi=7,wo=7 wi=8,wo= Y (μm) wi=6,wo=6 wi=6,wo=8 wi=7,wo=7 wi=8,wo=8 (Ge) doped silicon dioxide for the core (6 lm), and a layer of undoped silicon dioxide for the upper cladding (13 lm). All these layers were deposited with an equipment of low temperature plasma enhanced chemical vapor deposition (PECVD). Without thermal annealing [10], plasma etching of the core layer was performed using a photoresist mask in an inductively coupled plasma (ICP) source with a gas mixture of C 4 F 8,H 2 and He. The refractive index contrast between the core and the cladding of the buried channel waveguide is D = 0.75%. A broadband ASE (amplified spontaneous emission) light source was used to characterize the fabricated AWG demultiplexer. The light was butt-coupled into the input waveguide passing through a polarizer and a polarization maintenance fiber. This setup was used to get the TE and TM polarized light separately. An optical spectrum analyzer was employed to measure the spectral response of the fabricated AWG demultiplexer. The measured spectral response of a fabricated 16-channel flat-top AWG demultiplexer is shown in Fig. 5 for the TE mode (similar flat-top spectral response has been measured for the TM polarization). The crosstalk level of the device is below 30 db. The insertion loss is about 5.6 db for the central channel. The measured average ripple and 1 db bandwidth (Dk 1dB /Dk ch ) are about 0.25 db and 38.8%, respectively. The corresponding simulated results for the ripple and 1 db bandwidth are 0.04 db and 42%, respectively. c Y (μm) Fig. 4. Simulation results for (a) the insertion loss; (b) the ripple; and (c) the 1 db pass bandwidth. The circles indicate the optimized values. The ripple is defined as the maximal variance of the loss within the ITU (international telecommunication union) passband ( Dk ch /8,Dk ch /8). As Y increases for a particular combination of w i and w o, the spectral response becomes flattened (at the cost of increase in the insertion loss, see Fig. 4(a)) and the ripple decreases first and then increases (see Fig. 4(b)). We choose Y = 9.6 lm (the width of the input/output waveguides is 8 lm), at which the ripple is minimal (and the insertion loss is still acceptable). The corresponding width and length of MMI section is calculated by using Eqs. (2) and (3), i.e., W MMI = 15.2 lm and L MMI = 168 lm. 4. Results and discussion The designed flat-top AWG demultiplexer has been fabricated. The waveguide was formed by a layer of undoped silicon dioxide for the buffer (13 lm), a layer of germanium Fig. 5. Measured spectral response of a 16-channel flat top AWG demultiplexer fabricated according to our optimal design. Power (db) Measurement Simulation Wavelength (nm) Fig. 6. Comparison of the spectral profiles between the simulated and measured results at the central channel. 25

29 S.N. Khan et al. / Optics Communications 262 (2006) Fig. 6 shows a close agreement between the simulated and measured spectral responses of the central channel (the maximal transmission of the simulation is lowered down to the same level as that of the measured result for the comparison of the spectral profiles). The spectral profiles are in good agreement, and the difference in the sidelobe (crosstalk) between the simulated and measured results is mainly due to the fabrication errors. 5. Conclusion A formula based on Gaussian approximation has been given for calculating the spectral response of a flat-top AWG demultiplexer. Using this fast formula, we have optimized the widths of the MMI section (connected to the end of a tapered input waveguide) and the tapered input/output waveguides for achieving a flattened spectral response. The designed AWG demultiplexer has been fabricated. A good agreement between the simulated and measured results has been obtained, and this shows that this approximate formula is reliable for the optimal design of a flat-top AWG demultiplexer. References [1] M.K. Smit, C.V. Dam, IEEE J. Select. Top. Quantum Electron. 2 (2) (1996) 236. [2] M.R. Amersfoort, C.R. de Boer, F.P.G.M. van Ham, M.K. Smit, P. Demeester, J.J.F.M. van der Tol, A. Kuntze, Electron. Lett. 30 (4) (1994) 300. [3] Y.P. Ho, H. Li, Y.J. Chen, IEEE Photon. Technol. Lett. 9 (3) (1997) 342. [4] A. Rigny, A. Bruno, H. Sik, Electronics 33 (20) (1997) [5] K. Okamoto, A. Sugita, Electron. Lett. 32 (18) (1996) [6] D.X. Dai, W. Mei, S. He, Opt. Commun. 219 (2003) 233. [7] C. Dragone, L. Siliver, US Patent , May, [8] D.X. Dai, S.Z. Liu, S. He, Q.C. Zhou, J. Lightwave Technol. 20 (11) (2002) [9] L.B. Soldano, E.C.M. Pennings, J. Lightwave Technol. 13 (4) (1995) 615. [10] L. Wosinski, J.K. Sahu, M. Dainese, H. Fernando, Proc. SPIE 4087 (2000)

30 Analysis of multimode effects in the free-propagation region of a silicon-on-insulator-based arrayed-waveguide grating demultiplexer Daoxin Dai and Sailing He Multimode effects in the free-propagation regions FPRs of an arrayed-waveguide grating AWG demultiplexer based on silicon-on-insulator are considered. Some undesired multimode effects, such as the increase of the insertion loss and the cross talk, are studied by use of a method of three-dimensional guided-mode propagation analysis. It is found that the multimode effects for the edge channels are more serious than those for the central channel. For an AWG demultiplexer with a small channel number, the multimode effects can be minimized by choosing appropriate FPR parameters such as the length and the thickness of the FPR. The coupling coefficient between the FPR and an arrayed waveguide is sensitive to the thickness of the FPR Optical Society of America OCIS codes: , Introduction Arrayed-waveguide grating AWG demultiplexers 1,2 have played important roles as key components in wavelength division multiplexing networks. Various materials such as silica, InP, and polymers 3 5 have been used to implement AWG demultiplexers. For a silicon-on-insulator SOI waveguide, there is a large difference in the refractive indices of silicon approximately and silicon oxide approximately Recently it has been demonstrated experimentally that the propagation loss of a planar and rib waveguide based on SOIs can be lower than 0.1 db cm 6 within the infrared wavelength window ranging from 1.2 to 1.6 m. This offers a tremendous potential for fabricating low-cost wavelength division multiplexing components including AWG demultiplexers. 7 The SOI-based AWG demultiplexers have shown good performance. For an AWG demultiplexer, the channel waveguides and the free-propagation regions FPRs The authors are with the Center for Optical and Electromagnetic Research, State Key Laboratory of Modern Optical Instrumentation, Zhejiang University, Yu-Quan, Hangzhou , China. S. He is also with the Division of Electromagnetic Theory, Alfven Laboratory, Royal Institute of Technology, S Stockholm, Sweden. The address of D. Dai is dxdai@coer.zju.edu.cn. Received 15 February 2003; revised manuscript received 25 May $ Optical Society of America are usually required to be single mode to avoid some undesired effects such as ghost images. A rib SOI waveguide supporting only one mode can be obtained according to the single-mode condition. 8 However, the eigenmode solution for a three-layer planar waveguide indicates that the thickness of the silicon layer should be less than 0.2 m to make the SOI FPR single mode at the infrared wavelength window. To obtain high efficiency in the coupling i.e., to match the spot size of the mode to a standard singlemode fiber, one usually needs the silicon layer in a rib SOI single-mode waveguide to be much thicker than 0.2 m. The thickness of the silicon layer for such a single-mode rib SOI waveguide is usually chosen to be 3 11 m e.g., in Ref. 7 the thickness of the silicon layer is chosen to be 5 m. Thus if one chooses the same thickness of the silicon layer for the FPR of an AWG demultiplexer, the FPR will support more than one mode. For example, there are approximately 20 modes when the thickness of the silicon layer is 5 m. It thus seems difficult to make a single-mode FPR in a SOI-based AWG demultiplexer. For a multimode FPR, some undesirable effects due to the existence of multiple modes may occur. First, the intensity distribution in the multimode FPR oscillates periodically owing to the multimode interference MMI. Therefore the coupling coefficient between the FPR and an arrayed waveguide changes periodically as the length of the FPR increases, and it is sensitive to the fabrication nonreproducibility of the layers. Second, the propagation constants the 4860 APPLIED OPTICS Vol. 42, No August

31 input wavelengths thus the wavelength demultiplexing function is realized. A. Mode Propagation Analysis Method for Light Propagation in the Free-Propagation Region It is well known that a 3D rib SOI waveguide cannot be accurately reduced to a equivalent twodimensional 2D planar waveguide by using an effective-index method. Furthermore, the associated FPR with the same thickness as the rib SOI waveguide is multimode. Therefore the effectiveindex method cannot be applied to the present problem. In the present paper a 3D MPA method is used to analyze the light propagation in the FPR. Because the FPR supports more than one mode, higher-order modes will be excited when the light enters the FPR from a single-mode rib waveguide. An input field profile, E in x, y, can be decomposed into the field distribution u s q y of all modes in the FPR q denotes the order of the guided mode for the FPR slab waveguide, i.e., M 1 E in x, y a q x u s q y, (1) q 0 Fig. 1. Schematic configuration. a The structure of an AWG demultiplexer. b The enlarged 3D view at the interface of the input waveguide and the first FPR. IWG, input waveguide; OWG, output waveguide. effective refractive index are different for different modes of the FPR, and thus the corresponding image centers on the image plane of the AWG demultiplexer will shift particularly for the edge channels. Obviously, this may increase the cross talk the energy of the higher-order modes will be coupled to the adjacent or nonadjacent channels as well as the insertion loss of the AWG demultiplexer. Some analysis for the multimode effects occurring at the arrayed waveguides of InP-based AWG demultiplexers has been given. 9 In the present paper we give a detailed analysis for such multimode effects by using the principles of self-imaging in a MMI section. 10,11 A global simulation for the spectral response of a SOI-based AWG demultiplexer is given by using a numerical method based on threedimensional 3D mode propagation analysis MPA. 2. Theory An AWG demultiplexer consists of a waveguide array, input waveguides, output waveguides, and two FPRs 1,2 see Fig. 1 a. Figure 1 b is a 3D view at the interface of the input waveguide and the first FPR. The coordinate system is chosen as shown in Fig. 1 b with the plane y 0 in the middle of the Si layer of the FPR. Light is launched from the input waveguide and diverges at the first FPR. The light is then coupled into and propagates along the arrayed waveguides. At the second FPR the light transmitted from different arrayed waveguides is focused at an image point, which shifts in space for different where a q x is the excitation coefficient for the qthorder mode and M is the number of the modes supported in the FPR. Usually the input field is the fundamental mode of the input waveguide. The coefficient a q x can be obtained by using the following overlap integral formula: a q x E in x, y u q s y dy. (2) Then the field distribution at point x, y, z can be written as a superposition of all the guided modal fields in the FPR: M 1 E x, y, z a q x, z u s q y. (3) q 0 Here a q x, z can be obtained by using the following 2D Kirchhoff Huygens diffraction formula 12 : j a q x, z 0 n s q 1 2 cos in cos dr 2 a q x 1,0 exp jn s q k 0 r r dx 1, (4) where in is the incident angle and dr is the diffraction angle, r x x 1 2 z 2 1 2, 0 is the wavelength in vacuum, k 0 2 0, and n s q is the effective index for the qth-order guided mode in the FPR. In 20 August 2003 Vol. 42, No. 24 APPLIED OPTICS

32 our case, because cos in and cos dr can be approximated to 1, Eq. 4 can be rewritten as Si layer of the FPR. that Thus it follows from Eq. 11 j a q x, z a 0 n s q 1 2 q x 1,0 exp jn s q k 0 r dx 1. (5) r B. Multimode Interference in the Free-Propagation Region Because the FPR is a 2D MMI along the y direction structure, the MMI in the FPR can be analyzed by using a model of 2D MMI. To obtain a 2D model, one can integrate Eq. 1 along the x direction and obtain M 1 E in y c q u s q y, (6) q 0 where c q a q x dx. Each guided mode u s q y will propagate along the z direction with wave number q for the qth-order guided mode. Thus at z L, one has M 1 E y, L c q u q y exp j t q L, (7) q 0 where exp j t is a time-dependent term. As in the analysis given by Ref. 10, a common factor exp j t 0 z is dropped out, and thus the following equation can be obtained: M 1 E y, L c q u q y exp j 0 q L. (8) q 0 Since a planar SOI waveguide has a high contrast in the refractive index, the propagation constant q can be approximated by q k 0 n 2 q n 2 W e 2, (9) where n 2 is the refractive index of the core layer and W e is the effective width here W e can be approximated to the thickness of the FPR. Thus one has 0 q q q 2 0 q q 2 2, (10) 4n 2 W e 3L where L 0 1 4n 2 W 2 e 3 0. Substituting expression 10 into Eq. 8, one obtains M 1 q q 2 E y, L c q u q y exp j q 0 3L L. (11) In the present case the higher-order mode fields excited in the FPR are much smaller than the fundamental mode field. Thus one can consider only the two lowest-order modes, i.e., the zeroth and the first modes. Consider first the case in which the SOI has a SiO 2 upper cladding. Then the zeroth and the first modes have even and odd symmetries, respectively, in that the plane y 0 is in the middle of the E y, L c 0 u 0 y c 1 u 1 y exp j L L. (12) From the above equation, one can easily see that 1. When L L, one has E y, L E y, 0. This indicates that a mirror image is formed at z L. 2. When L 2L, one has E y, L E y, 0, which means that an identical image is formed at z 2L. For the MMI occurring in the FPR, we use the above formulas instead of those given in Ref. 10 for the general MMI or the restricted interference. When the structure of the arrayed waveguides is the same as that of the input waveguide, one can choose the FPR length as a multiple of 2L to maximize the coupling coefficient between the FPR and an arrayed waveguide when the coupling loss between the FPR and the arrayed waveguides is minimized, the insertion loss of the designed AWG demultiplexer becomes minimal. If the upper cladding of the SOI FPR is air, the even or odd symmetry of the eigenmodes will be broken slightly. Nevertheless, one can still find the optimal FPR length near a multiple of 2L to minimize the coupling loss. Because L is dependent on the thickness h 2 of the FPR, the optimal length varies if the thickness h 2 deviates from the designed value h 0 2 in the fabrication process. For the designed thickness h 0 2, one chooses the following optimal length L opt FPR of the FPR: L FPR opt P 2L 2P 4n 2 h , (13) opt where P is an integer. For the same length L FPR of the FPR, the coupling coefficient is also maximal for a FPR thickness of h 0 2 h 0 where h 0 is the deviation when P 2 4n 2 h P p 2 4n 2 h 0 2 h , (14) where p 1. For a given length of the FPR, the coupling coefficient changes periodically when the thickness of the FPR varies; i.e., it varies from a maximal value to a minimal value and then back to a maximal value again when the thickness deviation increases from 0 to h 0. It thus follows from Eq. 14 that 1 2 P h 0 h P 1. (15) From the above equation, one sees that the period h 0 is very small in that the factor 1 P P approaches zero when P is large which is the case usually. Thus the coupling coefficient is sensitive 4862 APPLIED OPTICS Vol. 42, No August

33 to the thickness of the FPR for a given FPR length. When fabricating such a device, one has to use some approaches such as laser trimming, 13 which can tune slightly the refractive index n 2 of the FPR to compensate the fabrication error h of the designed thickness h 0 2 is attained. One can also use some different structures of SOI AWG demultiplexers such as using different values of thickness for the SOI waveguides and the FPR to reduce the MMI effects. C. Imaging and Spectral Responses of the Higher-Order Modes Because the propagation constants are different for different modes, the corresponding focus points will shift at the image plane of the AWG demultiplexer. Obviously, it may increase the cross talk the energy of the higher-order modes will couple to the adjacent or nonadjacent channels. For the qth-order mode, the corresponding grating equation can be written as n 0 g L n q s d g sin q m, (16) where is the wavelength, m is the diffraction order, d g is the separation of two adjacent arrayed waveguides, L is the length difference between two adjacent arrayed waveguides, n g 0 is the effective refractive index of the fundamental mode for the arrayed waveguides, and q is the diffraction angle for the qth-order mode. From the above equation for the fundamental and the qth-order modes, one can obtain n 0 s d g sin 0 n q s d g sin q 0. (17) Since the diffraction angle q is usually small, a paraxial approximation can be used, i.e., sin q q. Thus one has n 0 s n q s q 0. (18) The angle deviation q between the diffraction angles for the qth-order mode and the fundamental mode can then be written as n s s 0 n q q 0 s. (19) n q From the above equation, one can see that the angle deviation q is proportional to 0 the diffraction angle for the fundamental mode. For the central channel, q 0 0because 0 0. For the Nth channel, one has 0 N ch, where ch is the angle separation between adjacent channels. Thus it follows from Eq. 19 that q N N ch n 0 s n q s n q s. (20) Define a relative angle deviation q N q N ch for the Nth channel. Using expression 10, Eq. 20, and the relation q n s q k 0, one obtains q N 1 2 q q 2 0 N s n q 8n 2 W. (21) 2 e Let us first consider only the two lowest modes. can be approximated with the refractive index n 2 for the core layer cf. expression 9 with q 0or1, and W e can be approximated with the thickness h 2 of the strongly guided FPR. Thus Eq. 21 can be further approximated as n q s q N q q N 2 8n 2 h. (22) 2 2 From the above expression, one sees that the relative angle deviation increases with the channel number N, which means that the multimode effect is more serious for edge channels. One can also see that, when only the first high-order mode is considered, the angle deviation becomes larger when the FPR becomes thinner until the FPR becomes a single-mode planar waveguide. For the first high-order q 1 mode, one can obtain 1 N 3 8 N 2 0 n 2 h 2. (23) From the above formula, one can determine the minimal value of the FPR thickness h 2 for an allowed 1. Now let us consider the higher-order modes. One can determine the total number of the modes supported in the FPR by using the following formula: M INT( n 2 2 n 2 3 k 0 h 2 arctan n 2 3 n 2 1 n 2 2 n 2 3 ), (24) where n 1 is the refractive index of the upper cladding layer and n 3 is the refractive index of the lower cladding. For a SOI planar waveguide, the lower cladding layer is silicon oxide n , and the upper cladding is air n or silicon oxide n Thus arctan n 2 3 n 2 1 n 2 2 n 2 3 is very small as compared with n 2 2 n k 0 h 2 in most situations when h 2 is large enough e.g., h 2 0. Then Eq. 24 can be approximated by M INT n 2 2 n 3 2 k 0 h 2. (25) For the M 1 th-order mode, the relative angle deviation M 1 N can be written as by use of the approximation n q s n 3 for the highest mode, which is close to the cutoff; cf. expression 22 M 1 N M N 8n 2 n 3 h. (26) August 2003 Vol. 42, No. 24 APPLIED OPTICS

34 Fig. 2. Cross section of the rib SOI waveguide. Fig. 3. Field distribution in the cross-sectional plane x 0 starting from z 12,600 m of the FPR. The left part shows the modal field distribution of the input rib SOI waveguide. In that M 2 is usually much larger than 1, M 2 1 can be approximated by M 2. Substituting Eq. 25 into expression 26, one obtains M 1 N n 2 n 3 n 3 n 2 N 2. (27) From the above expression, one sees that the relative angle deviation for the M 1 th-order mode is almost insensitive to the thickness of the FPR. M 1 N is dependent on n 3 and n 2, which are fixed for SOI waveguides. Therefore, unlike 1 N, the relative angle deviation for the highest-order mode cannot be reduced by adjustment of the FPR thickness. Fortunately, the field contributions from the high-order modes are usually small. Thus we can focus on the influences of the first high-order mode in the present paper. 3. Numerical Results and Discussions A. Determination of the Thickness h 2 Expression 23 indicates that one can choose a thick enough FPR to ensure the relative angle deviation to be smaller than an allowed value max, i.e., h 2 0 n 2 3N 8 max 1 2. In the present design of AWG demultiplexers, the multimode effects can be neglected when 10%. Thus we set max 10% as a numerical example. The other parameters are chosen to be m and n , and the total number of the channels is 40 i.e., N 20. Then it is found that h 2 should be larger than 3.89 m if the FPR is multimode. In the present paper we choose the thickness of the FPR as h min the numerical example. The parameters of the single-mode SOI rib waveguide used for the numerical calculation are as follows: w r 4 m, h 2 5 m, h r 2.0 m, n 1 1.0, n , and n The corresponding variables are labeled in Fig. 2. B. Determination of the Length of the Free-Propagation Region In this section we analyze the relation between the insertion loss and the length L FPR of the FPR. Figure 3 is the intensity distribution on the crosssectional plane x 0 in the FPR. The peak of the intensity oscillates, and one sees a periodic variation due to the MMI; cf. Subsection 2.B. Thus the coupling coefficient between the FPR and an arrayed waveguide, i.e., the overlap integral of the field E x, y, L FPR given by Eq. 3 at the end of the FPR and the fundamental mode field, changes periodically as the length of the FPR increases. The period is approximately 2L. In this numerical example, L is approximately 78.8 m. Like in the design of a conventional AWG, an initial value L 0 FPR for the FPR length can be roughly chosen according to the separation of the adjacent array waveguides, channel spacing, etc. It is then adjusted to an optimal value around the initial value L 0 FPR for a maximal coupling efficiency between the FPR and an arrayed waveguide. This value can be found by adjusting the length of the FPR in the range L 0 0 FPR L, L FPR L. The optimal value for the FPR length depends on the fundamental mode field profile for the rib SOI waveguide because the brightest part of the fundamental mode field shifts in the y direction as the height of the rib varies see the left part of Fig. 3. One can optimize the length of the FPR to maximize the coupling coefficient between the FPR and the central arrayed waveguide by a one-dimensional search for L FPR in the range L 0 FPR L, L 0 FPR L. Figure 4 shows the coupling coefficient as the FPR length L FPR varies for three different values of the thickness h 2. From the circles in this figure, one Fig. 4. Coupling coefficient as the length of the FPR varies for three different values of the FPR thickness h APPLIED OPTICS Vol. 42, No August

35 can see that for a FPR thickness of 5.00 m the coupling coefficient reaches its local maximum at the optimal length L opt FPR 12,600 m and reaches its local minimal value at L FPR 12,680 or 12,520 m. The period of the oscillating curve in Fig. 4 is approximately 160 m, which is approximately equal to 2L. In fact, the optimal length L opt FPR 12,600 m is approximately a multiple approximately 80 times of 2L, as expected cf. Subsection 2.B. For this example, the thickness deviation period h 0 predicted by Eq. 15 is approximately 0.03 m. We choose a deviation of 0.02 m to illustrate the sensitivity of the coupling coefficient to the FPR thickness. From the three curves for h , 5.00, and 5.02 m, respectively in Fig. 4, one sees that the coupling coefficient is very sensitive to the thickness of the FPR. When the thickness h 2 deviates from the designed value slightly, the coupling coefficient varies significantly. This indicates that the tolerance of the FPR thickness is smaller than 0.02 m. Therefore one should use some special approaches such as adjusting the refractive index of the FPR by laser trimming to compensate for the fabrication errors in the FPR thickness and obtain a maximal coupling efficiency. To give a further analysis for the dependence of the insertion loss on the FPR length, we compare the results for three values of L FPR, namely, L opt FPR 12,600 m, L opt FPR L 2 12,640 m, and L opt FPR L 12,680 m when the FPR thickness is fixed at 5.00 m. The diffraction fields at the interface between the first FPR and the arrayed waveguides for the three cases are calculated by the method of 3D MPA, and the results are shown in Figs. 5 a 5 c. Here s is the coordinate along the curve of the starting ends of the arrayed waveguides see Fig. 1 a. From these figures, one sees that the brightest part of the intensity distribution moves in the vertical direction from the bottom to the top of the silicon layer when the length of the FPR increases from L opt FPR to L opt FPR L. Figure 6 gives the spectral response for the central channel of the AWG demultiplexer for the above three cases when L FPR L opt FPR, L opt FPR L 2, and L opt FPR L. The other parameters for the designed AWG demultiplexer are as follows: L FPR 12,600 m, m 45, d g 8 m, N WG 280, nm, 2N 40, ch 0.8 nm, and d o m, where N WG is the total number of the arrayed waveguides, ch is the channel spacing, and d o is the separation between two adjacent output waveguides. Because the insertion loss is inverse proportional to the coupling coefficient between the FPR and an arrayed waveguide, a FPR with an optimal length that maximizes will give a minimal insertion loss. From this figure, one can see that the insertion loss is reduced from 3.5 to 1.25 db when the length of the FPR decreases from 12,680 m to the optimal length 12,600 m. Here the MMI effects in both FPRs are considered. Fig. 5. Intensity distribution at the interface between the first FPR and the arrayed waveguides when the length of the FPR increases from L opt FPR to L opt FPR L. a L FPR 12,600 m, b L FPR 12,640 m, and c L FPR 12,680 m. C. Multimode Effects for the Edge Channel Figure 7 shows the spectral response for the edge channel i.e., the 20th channel of the designed AWG demultiplexer with L FPR 12,600 m and h m. The spectral responses for the zeroth-order mode and the first-order mode are indicated by the dashed curve and the dotted dashed curve, respectively. The total spectral response is shown by the solid curve. From this figure, one can see that the spectral response of the zeroth-order mode is slightly different from the total spectral response. However, the difference is not significant. The field intensity of the first-order mode is very small below 30 db. In fact, for this example we have c and c , which show that the higher-order mode fields excited in the FPR are indeed much 20 August 2003 Vol. 42, No. 24 APPLIED OPTICS

36 Fig. 6. Spectral responses for the central channel of the AWG demultiplexer when the length of the FPR decreases from 12,680 m to the optimal length 12,600 m. Fig. 7. Spectral response for the edge channel i.e., the 20th channel of the designed AWG demultiplexer. smaller than the fundamental mode field. The central wavelength of the edge channel for the first-order mode deviates slightly from that for the zeroth-order mode. Figure 7 shows that the multimode effects can be neglected for the designed AWG demultiplexer as discussed in Subsection 3.A. 4. Conclusion In the present paper we have considered a SOI-based AWG demultiplexer with a multimode FPR. The FPR slab waveguide has the same thickness of a silicon core layer as the SOI rib waveguides. The multimode effects in the FPR have been analyzed in detail by using the self-imaging principle for a MMI section and a 3D MPA simulation for the spectral response of the AWG demultiplexer. For the central channel, the existence of the multimode does not much affect the spectral response. However, the impact of the multimode effects on the edge channels is much more serious. The insertion loss is sensitive to the length of the FPR because the intensity distribution at the interface between the first FPR and the arrayed waveguides varies as the FPR length changes. One can optimize the length of the FPR to maximize the coupling coefficient by using a one-dimensional search around an initial design value. The thickness of the FPR is an important parameter that determines the deviation of the imaging positions for the fundamental and the higher-order modes. The coupling coefficient between the FPR and an arrayed waveguide is sensitive to the fabrication nonreproducibility of the FPR thickness, and some approaches such as adjusting the refractive index of the FPR by laser trimming should be used to compensate the fabrication error of the designed FPR thickness is attained. This research is supported by the government of Zhejiang Province, China, under a major research grant References 1. M. K. Smit and C. V. Dam, PHASAR-based WDM-devices: principles, design and applications, IEEE J. Sel. Top. Quantum Electron. 2, M. R. Paiam and R. I. MacDonald, Design of phased-array wavelength division multiplexers using multimode interference couplers, Appl. Opt. 36, C. K. Ndaler, E. K. Wildermuth, M. Lanker, W. Hunziker, and H. Melchior, Polarization insensitive, low-loss, low-crosstalk wavelength multiplexer modules, IEEE J. Sel. Top. Quantum Electron. 5, M. Zirngibl, C. Dragone, and C. H. Joyner, Demonstration of a15 15 arrayed waveguide multiplexer on InP, IEEE Photon. Technol. Lett. 4, Y. Hida, Y. Innoue, and S. Imamura, Polymeric arrayedwaveguide grating multiplexer operating around 1.3 m, Electron. Lett. 30, U. Fischer, T. Zinke, J.-R. Kropp, F. Arndt, and K. Petermann, 0.1 db cm waveguide losses in single-mode SOI rib waveguides, IEEE Photon. Technol. Lett. 8, P. D. Trinh, S. Yegnanarayanan, F. Coppinger, and B. Jalali, Silicon-on-insulator SOI phased-array wavelength multi demultiplexer with extremely low-polarization sensitivity, IEEE Photon. Technol. Lett. 9, S. Lvescan and A. Vonsovici, The single-mode condition for semiconductor rib waveguides with large cross section, J. Lightwave Technol. 16, S. R. Park, B. O, S. G. Lee, and E. H. Lee, Control of multimode effect on an arrayed waveguide grating device, in Optical Fiber and Planar Waveguide Technology II, S. Jian, S. Shen, and K. Okamoto, eds., Proc. SPIE 4904, L. B. Soldano and E. C. M. Pennings, Optical multi-mode interference devices based on self-imaging: principles and applications, J. Lightwave Technol. 13, M. Bachmann, P. A. Besse, and H. Melchior, General selfimaging properties in N N multimode interference couplers including phase relations, Appl. Opt. 33, Z. Shi and S. He, A three-focal-point method for the optimal design of a flat-top planar waveguide demultiplexer, IEEE J. Sel. Top. Quantum Electron. 8, K. Takada, T. Tanaka, M. Abo, T. Yanagisawa, M. Ishii, and K. Okamoto, Beam-adjustment-free crosstalk reduction in 10 GHz-spaced arrayed-waveguide grating via photosensitivity under UV laser irradiation through metal mask, Electron. Lett. 36, APPLIED OPTICS Vol. 42, No August

37 Fast design method for a flat-top arrayed-waveguide-grating demultiplexer using the reciprocity theory Daoxin Dai and Sailing He* Centre for Optical and Electromagnetic Research, State Key Laboratory for Modern Optical Instrumentation, Joint Laboratory of Optical Communications of Zhejiang University, Zhejiang University, Yu-Quan, Hangzhou , China sailing@kth.se Received 25 August 2003; revised manuscript received 24 October 2003 A fast design method, based on the reciprocity theory, is presented for the optimal design of a special input structure (e.g., a parabolic waveguide horn) connected at the end of the input waveguide for flattening the spectral response of an arrayed-waveguide-grating (AWG) demultiplexer. The spectral response is calculated by reversal of the propagation direction of light in the AWG demultiplexer. Light is transmitted from the output waveguide and finally focused at the interface between the first free-propagation region (FPR) and the special input structure. When the special input structure in the optimization is adjusted, the distribution of the focused field (in the first FPR) excited by the modal field of the output waveguide remains unchanged and needs to be calculated only once. The optimal design of a parabolic waveguide horn for a flat-top AWG demultiplexer is given as a numerical example to illustrate the fast design method Optical Society of America OCIS codes: , Introduction The arrayed-waveguide-grating (AWG) demultiplexer [1] has been widely used as a key component in a wavelength-division-multiplexing (WDM) system. The spectral response for a conventional AWG demultiplexer is of Gaussian type. For a Gaussian-type AWG demultiplexer, the ratio of the 1-dB bandwidth to the 20-dB bandwidth is small, and the shape of the passband response is not sufficiently square shaped, which requires strict wavelength control in a network and thus limits the application AWG demultiplexer. A flat-top AWG demultiplexer can relax the requirements on wavelength control for lasers and filters in a WDM system. Thus, an AWG demultiplexer with a flattened spectral response is desirable. To achieve a flattened spectral response for an AWG demultiplexer, several methods have been introduced. Among these, the method of connecting a special structure (such as a standard [2] or tapered [3] multimode interference (MMI) coupler, a parabolic waveguide [4]) at the end of the input waveguide (IW) is simple and effective and thus is considered in the present paper. A flat-top spectral response can be obtained by optimization of the special input structure at the end of the IW. The spectral response of an AWG demultiplexer can be calculated with several methods, such as a 1:1 imaging method [5], a Fourier optics method [6], and a beam-propagation method (BPM) [7]. The 1:1 imaging method is relatively approximate because it assumes perfect imaging. The Fourier optics method and the BPM can give a more accurate spectral response. However, since the special input structure is connected at the end of the IW, light propagating in the whole AWG demultiplexer [from the IW to the 2003 Optical Society of America JON 2924 December 2003 / Vol. 2, No. 12 / JOURNAL OF OPTICAL NETWORKING

38 output waveguide (OW)] should be simulated repeatedly during optimization of the special input structure. This makes computation difficult and lowers the efficiency of optimizing the special input structure. In this paper we present an efficient method based on the reciprocal theory to optimize the special input structure. The reciprocal theory indicates that the transmission of light can be reversed. Therefore we reverse the light-propagation direction when simulating an AWG demultiplexer. The light is transmitted from the (central) OW (instead of the IW), propagates through the second free-propagation region (FPR), through the arrayed waveguides (AWs), and then focuses at the interface between the first FPR and the special input structure. This interface is like the image plane in a standard AWG demultiplexer. We can then obtain the spectral response by overlapping this focused field distribution at this interface and the output field (excited by the fundamental mode of the IW) at the end of the special input structure [which is obtained by application of a beam-propagation method (BPM) in the small area of the special input structure in the present paper]. When adjusting the parameters of the special input structure to achieve the optimal flat-top spectral response, we need to use a numerical method (such as BPM) for repeatedly simulating the light propagation only in the small area of the special input structure (instead of the whole AWG demultiplexer) and for obtaining the output field at the end of the special input structure. Since the size of the special input structure is usually small (as compared with the whole AWG demultiplexer), the computational effort is reduced greatly. 2. Theory In this section we show how the reciprocity theory can be used to calculate the spectral response of an AWG demultiplexer. An AWG demultiplexer consists of AWs, IWs, OWs, and two FPRs [see Fig. 1(a)]. Figs. 1(b) and 1(c) show the enlarged views of the first and second FPR sections, respectively. The input and output apertures of the waveguide array are of Rowland type [1]. The ends of the AWs are located at a circle with a radius R (i.e., the length of the FPR). The ends of the OWs are located at the image circle whose radius is R/2 [see Fig. 1(c)]. Thus the curve equation for the image plane is given by x 2 1 +(z 1 R/2) 2 = (R/2) 2. For AWG demultiplexers based on, e.g., the silica-on-silicon technology, the problem can be simplified to a two-dimensional (2D) one with the effective index method (EIM). We first consider the case in which the field is excited by the fundamental mode of the IW. Using a numerical method (such as BPM), we can easily obtain the input field E in (x 1 )for the first FPR [the field at the end of the special input structure, i.e., the field on plane z = 0 in Fig. 1(b)]. The far field E F (x,z) in the first FPR can then be obtained by use of the following 2D Kirchhoff Huygens diffraction formula [8], ( E F x,z ) i + = E in (x 1 ) exp( in skr) λ/ns r cosθ in + cosθ dr dx 1, (1) 2 where θ in is the incident angle, θ dr is the diffraction angle, r =[(x x 1 ) 2 + z 2 ] 1/2, λ is the wavelength in vacuum, k =2π/λ, and n s is the effective index for the fundamental mode of the TE or TM polarization in the FPR (determined with an EIM for the fundamental mode of the three-layered FPR). When considering the polarization dependence of the AWG demultiplexer, we should use the effective index for the TE or TM polarization modes in the FPR. Since cosθ in and cosθ dr can be approximated to 1 in our case, Eq. (1) can be rewritten as ( E F x,z ) i + = E in (x 1 ) exp( in skr) dx 1. (2) λ/ns r 2003 Optical Society of America JON 2924 December 2003 / Vol. 2, No. 12 / JOURNAL OF OPTICAL NETWORKING

39 Input aperture Output aperture Fig. 1(b) x 1 z AW s z FPR 1 FPR 2 Image plane x 1 Fig. 1(c) IW OW s (a) x 1 z=0 x' x E in(x 1) o d g z IW R FPR 1 L Input aperture (b) x x' z=0 x 1 R R/2 z Output aperture FPR 2 Image plane (c) Fig. 1. Structure of an AWG demultiplexer: (a) layout of an AWG demultiplexer, (b) configuration near the first FPR, (c) configuration near the second FPR Optical Society of America JON 2924 December 2003 / Vol. 2, No. 12 / JOURNAL OF OPTICAL NETWORKING

40 According to the above equation, we can obtain the following far field E IAP (x) at the input aperture with x 2 + z 2 + R 2 [see Fig. 1(b)] of the waveguide array [here x = Ratan(x /z)], E IAP (x)=e F ( x,z ) z= R 2 x 2 i + = E in (x 1 ) exp( in skr) dx 1. (3) λ/ns r z= R 2 x 2 Then the coupling coefficient η l between the field E IAP (x) and the modal field E AW (x) of the lth AW can be calculated by the following overlap integral + η l = E IAP (x)eaw (x ld g )dx, (4) where d g is the separation of the AWs and the superscript * denotes complex conjugate. Substituting Eq. (3) into the above equation, we obtain [ ] + i + η l = E in (x 1 ) EAW (x ld g ) exp( in skr) dx dx 1. (5) λ/ns r The distribution of the transmitted field E EX (x, λ) at the exit of the waveguide array is N 1 E EX (x,λ)= l=0 η l E AW (x ld g )exp( iϕ l ), (6) where N is the number of AWs, ϕ l = ϕ 0 + l2πn g ΔL/λ (here ϕ 0 is the phase introduced by the shortest AW, n g is the effective refractive index for the fundamental mode of the TE or TM polarization of the AW, and ΔL is the length difference between adjacent AWs). The field distribution E IM (x 1, λ) at the image plane [where x 2 1 +(z 1 R/2) 2 =(R/2) 2 ] of the AWG demultiplexer is given by the following 2D Kirchhoff Huygens diffraction formula: i + E IM (x 1,λ)= E EX (x,λ) exp( in skr) dx. (7) λ/ns r By overlapping E IM (x 1, λ) and the fundamental modal field E OW (x 1 ) of an OW (e.g., the central OW), we obtain the following coupling coefficient: + η out (λ)= E IM (x 1,λ)EOW (x 1 )dx 1. (8) The spectral response of the central OW is then given by η out (λ) 2. It is known that each OW of an AWG demultiplexer has a spectral response with a similar shape, since all the OWs usually have the same structure. Therefore one usually optimizes only the spectral response of the central OW in the design of a flat-top AWG demultiplexer. Substituting Eq. (7) into Eq. (8), we obtain η out (λ)= + i + E EX (x,λ) exp( in skr) dxe λ/ns r OW (x 1 )dx 1. (9) In a standard Fourier optics method, the spectral response is calculated by use of the above equation. When we adjust the special input structure in the optimization, the field E in (x 1 ) will change, since the special input structure is connected at the end of the IW. Consequently, E IAP (x), the coupling coefficient η l, the field E EX (x, λ), and the field E IM (x 1, λ) will change. Therefore we have to simulate repeatedly the light propagation in the whole 2003 Optical Society of America JON 2924 December 2003 / Vol. 2, No. 12 / JOURNAL OF OPTICAL NETWORKING

41 AWG demultiplexer (from the IW to the OW) in the optimization. This requires a great computation effort and makes the optimization inefficient. Now we present an efficient design method based on the reciprocity theory. We reverse the light-propagation direction when simulating an AWG demultiplexer. Below we show how the corresponding formula (based on the reciprocity theory) for calculating the spectral response of an AWG demultiplexer can be derived from Eq. (9). First, Eq. (9) is rewritten as where + η out (λ)= E EX (x,λ) = + i + EOW (x 1 ) exp( in skr) dx 1 dx λ/ns r E EX (x,λ)e OAP (x)dx, (10) i + E OAP (x)= EOW (x 1 ) exp( in skr) dx 1 λ/ns r represents the far-field distribution [at the output aperture of the waveguide array; see Fig. 1(c)] excited by the fundamental modal field of the OW. Substituting Eq. (6) into Eq. (10), we obtain Let N 1 η out (λ)= l=0 + η l exp( iϕ l ) [E AW (x ld g )E OAP (x)]dx. (11) + Then Eq. (11) can be rewritten as [E AW (x ld g )E OAP (x)]dx = ξ l. (12) N 1 η out (λ)= l=0 Substituting Eq. (5) into the above equation, we obtain η l ξ l exp( iϕ l ). (13) + i + η out (λ)= E in (x 1 ) λ/ns [ ] N 1 ξ l EAW (x ld g )exp( iϕ l ) l=0 Introduce the following notation, E IM (x 1,λ)= exp( in s kr) r dxdx 1. (14) [ ] i + N 1 λ/ns ξ l E exp( in AW (x ld g )exp( iϕ l ) s kr) dx. (15) l=0 r We then obtain the following useful formula: η out (λ)= + [ Ein (x 1 )E IM (x 1,λ) ] dx 1. (16) From Eq. (15), we see that E IM (x 1, λ) is the field distribution at the interface between the first FPR and the special input structure when light is transmitted from the OW and 2003 Optical Society of America JON 2924 December 2003 / Vol. 2, No. 12 / JOURNAL OF OPTICAL NETWORKING

42 propagates along a reversed direction (as compared with a standard propagation in an AWG demultiplexer). The field distribution E IM (x 1, λ) remains unchanged when the special input structure is adjusted. When the special input structure is being optimized, the field E in (x 1 ) (excited by the fundamental mode of the IW) at the end of the special input structure can be calculated when we apply a BPM just for the small area of the special input structure (instead of the whole AWG demultiplexer). Then the spectral response η out (λ) 2 can be obtained efficiently by use of the overlap integral of Eq. (16). According to the calculated spectral response, we can obtain the key features of a flattop AWG demultiplexer such as the 1-dB bandwidth, the ripple, the cross talk between channels, and the sharpness of the transitions. Usually, the 1-dB bandwidth of a flat-top spectral response is required to be larger than 0.5Δλ ch, where Δλ ch is the channel spacing. The cross talk should be smaller than 30 db. The ripple of the spectral response is defined as the maximal variance of the loss within the ITU window ( Δλ ch /8, Δλ ch /8) for a channel spacing of Δλ ch. The sharpness of the transitions is defined as S =2Δλ 1dB /(Δλ 1dB +Δλ 20dB ), where Δλ 1dB and Δλ 20dB are the 1- and 20-dB bandwidths, respectively. For an AWG demultiplexer, the polarization dependence results mainly from the difference between the effective refractive indices of the TE and TM polarization modes. Thus, when considering the polarization-dependent characteristics, we should choose the corresponding effective refractive index of the TE or TM polarization mode in the relevant formulas. 3. Design As a numerical example we consider a parabolic waveguide horn (see Fig. 2). The width W(z) of the parabolic multimode section along the propagation direction (z axis) can be described by [4] W (z)= ( 2αλ e z +W 2 g ) 1/2, (17) where λ e = λ 0 /n e (λ 0 is the designed central wavelength in vacuum, n e is the effective index in the parabolic waveguide horn), W g is the width of the IW, and α is a constant controlling the shape of the parabolic waveguide horn. x Air slot n c=1.46 d W g n r = z Air slot L p Fig. 2. Special input structure of a parabolic multimode section. The refractive indices for the core and the cladding are n r = and n c = 1.46, respectively. The width of the IW is W g =6μm. The parameters for the AWG demultiplexer 2003 Optical Society of America JON 2924 December 2003 / Vol. 2, No. 12 / JOURNAL OF OPTICAL NETWORKING

43 to be designed are given in Table 1, where m is the diffraction order, N WG is the total number of the AWs, and d o is the separation between two adjacent OWs. Table 1. Parameters for the Designed Flat-Top AWG Demultiplexer m N WG d g d o R λ 0 Δλ ch μm 24.5 μm 5000 μm nm 1.6 nm In the parabolic waveguide horn, many modes are excited, and the field propagation can be calculated with, e.g., the BPM. Usually the cross talk will increase when the spectral response is broadened. To reduce the cross talk between channels, two air slots (with sufficient width, e.g., 2.0 μm) are used. Air slots have been used to reduce the transition loss in a bent rib waveguide [9]. In this paper the air slots are placed around the parabolic waveguide horn connected to the IW (see Fig. 2) to reduce the channel cross talk. The effect of the air slots on the spectral response (including the cross talk) is controlled by the distance d between the air slot and the central axis (x = 0) of the parabolic waveguide horn (see Fig. 2). First, we consider the case without air slots (i.e., d = ) and choose α = 0.8, 1.0, and 1.2. For each chosen α, we increase the length L p of the parabolic horn from 0 to 600 μm and obtain the spectral responses, from which we extract the corresponding features (such as the 1-dB bandwidth, the ripple, the cross talk, and the sharpness of the transitions) as the length L p increases. The 1-dB bandwidth, the ripple, the sharpness, and the cross talk are shown in Figs. 3(a) 3(d), respectively. From Fig. 3(a) we see that a maximal 1-dB bandwidth can be obtained when an appropriate value L p0 is chosen for the length L p. When L p = L p0, the sharpness of the transitions is close to its maximal value [see Fig. 3(c)]. When α increases from 0.8 to 1.2, the maximum values for both the 1-dB bandwidth and the sharpness of the transitions increase, as well as the value of L p0. The ripple of the spectral response is shown in Fig. 3(b). From this figure, we see that the ripple is minimal (almost 0) at two optimal lengths (L 1 and L 2 ) for the parabolic waveguide horn when α is larger than a certain value α 0. We also see that L 1 L p0 L 2. When α decreases, the difference between L 1 and L 2 decreases. When α α 0,wehave L 1 = L 2, and thus only one optimal length with a minimal ripple exists (the optimal length is the same as L p0 in this case). Therefore when α α 0 we can achieve a maximal 1-dB bandwidth, a maximal sharpness, and a minimal ripple if this optimal length is chosen for the length L p. However, when α > α 0, the minimal ripple cannot be obtained when the maximal 1-dB bandwidth is achieved. Fortunately, when L 1 < L p < L 2, the ripple is quite small (e.g., the ripple is smaller than 0.1 db for the case of α = 1). Figure 3(d) shows the cross talk for the cases of α = 0.8, 1.0, and 1.2 as the length of the parabolic waveguide horn increases. From this figure we see that the value of α does not greatly influence the cross talk. When the spectral response is broadened, the cross talk increases to approximately 30 db. If a lower cross talk is desired, we can place two air slots at both sides of the parabolic waveguide horn. The two air slots introduce a strong confinement and reduce the tails of the field in the cladding of the parabolic waveguide horn. Therefore the channel cross talk is greatly reduced. Below we show how the distance d influences the features of the spectral response. We choose α = 1.0 and d = 10.0, 12.5, 15.0, and 20.0 μm. The 1-dB bandwidth, ripples, sharpness of the transitions, and cross talk are shown in Figs. 4(a) 4(d), respectively. From Fig. 4(d) we see that the air slots reduce the cross talk significantly [cf. Fig. 3(d)]. For the cases of d = 10.0 and 12.5 μm, the cross talk is below 50 db when the parabolic 2003 Optical Society of America JON 2924 December 2003 / Vol. 2, No. 12 / JOURNAL OF OPTICAL NETWORKING

44 dB/ ch =0.8 =1.0 =1.2 The Ripple (db) =0.8 =1.0 = L p (μm) (a) L p (μm) (b) S =0.8 =1.0 =1.2 The crosstalk (db) =0.8 =1.0 = L p (μm) (c) L p (μm) (d) Fig. 3. Features of the spectral response flattened by a parabolic input structure: (a) 1-dB bandwidth, (b) ripple, (c) sharpness of the transitions, (d) cross talk. waveguide horn length L p is in the range of [0, 600] (μm). When the distance d increases, the influence of the air slots to the field in the parabolic waveguide horn becomes weaker, and thus the cross talk increases. For the cases of d = 15.0 and 20.0 μm, the cross talk is below 40 db when the length L p is in the range [0, 600] (μm). If we choose L p0 for L p, the cross talk is approximately 45 db. When the distance d approaches infinity, the result is as shown in Fig. 3(d). From Figs. 4(a) to 4(c) we see that when d > 15.0 μm the features of the maximal 1-dB bandwidth, the maximal sharpness of the transitions, and the ripple are similar to those for the case of α = 1.0 shown in Figs. 3(a) 3(c) (where d = ). For example, for both cases the maximal 1-dB bandwidth and the maximal sharpness of the transitions are approximately 0.66 and 0.65, respectively. When the distance d decreases from 15 to 10 μm, the maximal 1-dB bandwidth decreases from 0.66 to When d < 15.0 μm, the ripple differs slightly from the one shown in Fig. 3(b). The values of L 1 and L 2 become smaller when the distance d decreases. If the distance d is too smaller [e.g., d = 10.0 μm as in Fig. 4(b)], the minimal ripple will be larger than 0. These figures show how the features of the spectral response change as the parameters (including the coefficient α, the parabolic waveguide horn length L p, and the distance d) vary. From these figures we can easily choose appropriate values for these parameters (α, 2003 Optical Society of America JON 2924 December 2003 / Vol. 2, No. 12 / JOURNAL OF OPTICAL NETWORKING

45 1dB/ ch D=10.0μm D=12.5μm D=15.0μm D=20.0μm The Ripple (db) D=10.0μm D=12.5μm D=15.0μm D=20.0μm L p (μm) (a) L p (μm) (b) S D=10.0μm D=12.5μm D=15.0μm D=20.0μm L p (μm) (c) The crosstalk (db) L p (μm) (d) D=10.0μm D=12.5μm D=15.0μm D=20.0μm Fig. 4. Features of the spectral response flattened by a parabolic input structure with air slots: (a) 1-dB bandwidth, (b) ripple, (c) sharpness of the transitions, (d) cross talk. L p, and d) to satisfy the requirements for different applications. For example, we choose α = 1.0, d = 12.5 μm, and L p = 300 μm as an optimal design. From Figs. 4(a) 4(d), we obtain the features of the flattened spectral response listed in Table 2. The flattened spectral response and the chromatic dispersion [5] of the central channel (λ 0 = nm) for the designed AWG demultiplexer are shown in Fig. 5. From this figure we see that the spectral response is well flattened and that the chromatic dispersion D c is less than 10 ps/nm in a large passband of [ 1.2 nm, 1.2 nm]. In a conventional design method, we have to calculate the field distribution E IM (x 1, λ) (for different wavelengths) at the image plane of an AWG demultiplexer repeatedly when searching the optimal parameters of the special input structure for a desirable spectral response. Each calculation takes 1 hr on a PC (Pentium IV, 2.0 GHz), and thus one has to spend several tens of hours to obtain a good design with a conventional design method for this numerical example. However, with the present fast design method, only 1 hr suffices, since one applies the BPM repeatedly only in the small area of the parabolic horn waveguide (the BPM simulation in this small area takes only several minutes) and calculates only once the field distribution E IM (x 1, λ) at the interface between the first FPR and the special input structure. The polarization dependence of an AWG demultiplexer is also very important. For an AWG demultiplexer, the polarization dependence results mainly from the difference in the 2003 Optical Society of America JON 2924 December 2003 / Vol. 2, No. 12 / JOURNAL OF OPTICAL NETWORKING

46 Table 2. Features of the Flattened Spectral Response when the Parameters of the Parabolic Input Structure with Air Slots Are Chosen as α = 1.0, d = 12.5 μm, and L p = 300 μm Sharpness of Δλ 1dB /Δλ ch Ripple the Transitions Cross Talk db 0 Power (db) Dc (ps/nm) c (nm) Fig. 5. Flattened spectral response and the chromatic dispersion of a designed AWG demultiplexer with α = 1.0,L p = 300 μm, and d = 12.5 μm. effective refractive index between the TE and TM polarization modes in AWs. Many compensation methods have been developed to reduce the polarization dependence (see, e.g., Ref. [10]). The parabolic waveguide horn used in this paper does not introduce additional polarization dependence [4]. Our simulation results have also shown that the parabolic waveguide horn with air slots is polarization insensitive for flattening the spectral response of an AWG demultiplexer. 4. Conclusion In this paper we have presented an efficient design method to optimize a special input structure (such as a standard or tapered MMI coupler, a parabolic waveguide horn) that is used to flatten the spectral response of an AWG demultiplexer. The present method is based on the reciprocity theory, according to which we reverse the light-propagation direction when calculating the spectral response of an AWG demultiplexer. When adjusting the special input structure in the optimization, we need to apply a numerical simulation method (such as the BPM) repeatedly only for the small area of the special input structure (instead of the whole AWG demultiplexer), since the distribution of the focused field excited by the modal field of the output waveguide (OW) remains unchanged and needs to be calculated only once. Thus the computational effort is reduced greatly, and the design efficiency is improved significantly. By use of the present design method, we can efficiently scan the parameters of the special input structure and observe the changing features of the spectral 2003 Optical Society of America JON 2924 December 2003 / Vol. 2, No. 12 / JOURNAL OF OPTICAL NETWORKING

47 response, from which we can easily choose optimal values for these parameters to satisfy the requirements for different applications. The optimal design of a parabolic waveguide horn has been given as a numerical example to illustrate the present design method. Two air slots have been placed at both sides of the parabolic waveguide horn to reduce the cross talk to a level lower than 45 db. The chromatic dispersion of the designed AWG demultiplexer is also smaller than 10 ps/nm in a large passband. *S. He is also with Division of Electromagnetic Theory, Alfven Laboratory, Royal Institute of Technology, S Stockholm, Sweden. References and Links [1] M. K. Smit and C. V. Dam, Phasar based WDM devices: principles, design and applications, IEEE J. Sel. Top. Quantum Electron. 2, (1996). [2] J. B. D. Soole, M. R. Amerfoort, H. P. LeBlanc, N. C. Andreadakis, A. Rajhel, C. Caneau, R. Bhat, M. A. Koza, C. Youtsey, and I. Adesida, Use of multimode interference couplers to broaden the passband of wavelength-dispersive integrated WDM filters, IEEE Photon. Technol. Lett. 8, (1996). [3] D. Dai and S. He, Use of a tapered MMI coupler to broaden the passband of an AWG, Opt. Commun. 219, (2003). [4] K. Okamoto and A. Sugita, Flat spectral response arrayed-waveguide grating multiplexer with parabolic waveguide horns, Electron. Lett. 32, (1996). [5] D. Dai, S. Liu, S. He, and Q. Zhou, Optimal design of an MMI coupler for broadening the spectral response of an AWG demultiplexer, J. Lightwave Technol. 20, (2002). [6] M. E. Marhic and X. Yi, Calculation of dispersion in arrayed-waveguide grating demultiplexers by using a shifting-image method, IEEE J. Sel. Top. Quantum Electron. 8, (2002). [7] R. Scarmozzino, A. Gopinath, R. Pregla, and S. Helfert, Numerical techniques for modeling guided-wave photonic devices, IEEE J. Sel. Top. Quantum Electron. 6, (1996). [8] Z. Shi and S. He, A three-focal-point method for the optimal design of a flat-top planar waveguide demultiplexer, IEEE J. Sel. Top. Quantum Electron. 8, (2002). [9] C. Seo and J. C. Chen, Low transition losses in bent rib waveguides, J. Lightwave Technol. 14, (1996). [10] J. J. He, B. Lamontangne, and E. S. Koteles, Polarisation dispersion compensated AWG demultiplexer fabricated in single shallow etching step, Electron. Lett. 35, (1999) Optical Society of America JON 2924 December 2003 / Vol. 2, No. 12 / JOURNAL OF OPTICAL NETWORKING

48 Optical and Quantum Electronics 36: , Ó 2004 Kluwer Academic Publishers. Printed in the Netherlands. 967 Calculation of the spectral response of an arrayed-waveguide gating demultiplexer with a wide-angle beam propagation method in a cylindrical coordinate system DAOXIN DAI* AND SAILING HE Centre for Optical and Electromagnetic Research, Joint Research Center of Photonics of the Royal Institute of Technology (Sweden) and Zhejiang University, Zhejiang University, Yu-quan, Hangzhou , China Division of Electromagnetic Theory, Alfven Laboratory, Royal Institute of Technology, S Stockholm, Sweden. (*author for correspondence: dxdai@coer.zju.edu.cn) Received 16 February 2004; accepted 10 August 2004 Abstract. The spectral response of an arrayed-waveguide grating (AWG) demultiplexer is calculated by simulating the field propagation in the output section of an AWG with a wide-angle beam propagation method (BPM) in a cylindrical coordinate system. As in a practical design of an AWG demultiplexer, each output waveguide consists of two straight sections connected by a bending section. The spectral response obtained by the present algorithm is more accurate than those obtained with two popular approximate methods, namely, the conventional overlapped integral method and the standard BPM for radially straight and infinitely long output waveguides. With the present algorithm, the dependence of the spectral response on the parameters of the output section is analyzed. The channel crosstalk and the 3 db passband width of the spectral response depend mainly on the length of the first straight section, the end separation and the angular separation of the output waveguides. The bending section results in an asymmetrical spectral response with remarkable sidelobes which can be reduced by increasing the bending radius. Key words: arrayed-waveguide grating (AWG), beam propagation method (BPM), bending, cylindrical coordinate system (CCS), output waveguide, sidelobe, spectral response 1. Introduction An arrayed-waveguide grating (AWG) demultiplexer (Smit 1991; Smit et al. 1996) is one of the key devices in dense wavelength division multiplexing (DWDM) networks. An AWG demultiplexer consists of arrayed waveguides, input waveguides, output waveguides and two free propagation regions (FPRs). For the design of an AWG demultiplexer, it is very important to accurately calculate the spectral response, from which one can evaluate the specifications such as the sidelobes, the 3 db passband bandwidth and the crosstalk between channels. 45

49 968 D. DAI AND S. HE The spectral response is determined by the focal field at the image plane of the AWG and the structure of the output waveguide. When the input wavelength varies, the position of the focus spot shifts linearly at the image plane. If the waveguide array is optimally designed (e.g. the number of the arrayed waveguides is large enough and the aberration is negligible), an AWG can be considered as a perfect 1:1 imaging system for the input field to the first FPR (from the input waveguide) (see e.g. Dai et al. 2002). Thus, the focal field at the image plane can be approximated as this input field. For a Gaussian AWG demultiplexer, the focal field is the same as the fundamental mode of the input waveguide. For a flat-top AWG demultiplexer (which is desired to relax the requirements on wavelength control for lasers and filters in a DWDM system), the focal field has double-peak in many designs (Okamoto et al. 1996; Soole et al. 1996). To calculate the spectral response, the simplest method is to use an overlapped integral method (OIM) (Smit 1991), i.e., overlap the fundamental modal field of the output waveguide and the focal field at the image plane as the wavelength varies. In the OIM, the spectral response is independent of the structure of the output section except the end separation of the output waveguides (when the parameters of the output waveguides are fixed). From the spectral response obtained by OIM, the 3 db passband bandwidth can be well evaluated. However, the sidelobe and the channel crosstalk are quite rough. To obtain a more accurate result, one should use a beam propagation method (BPM) (Scarmozzino et al. 1991) to simulate the light propagation in the output section for different input wavelengths. Then the spectral response can be obtained according to the field distribution obtained by the BPM. When using a standard BPM, one usually assumes that the output waveguides are straight and infinitely long in the radial direction. With such an assumption, the separation between the output waveguides increases linearly with the propagation distant and thus the obtained spectral response will be symmetric. In this method, the spectral response is determined only by the end separation and the angular separation of the output waveguides. However, in a practical design of an AWG demultiplexer, each output waveguide consists of two straight sections connected by a bending section (see Fig. 3). Due to the bending sections the adjacent waveguides are separated more rapidly. The bending section also makes the output section asymmetrical, which results in an asymmetric spectral response. Thus, the above-mentioned standard BPM algorithm with the assumption of infinitely long and straight output waveguides is not accurate either in calculating the spectral response. Since the standard BPM is not appropriate for a structure with bending sections, we use a wide-angle BPM in a cylindrical coordinate system (CCS) (Hadley 1992; Rivera 1995; Helfert 1998) in the present paper. A global simulation for the propagating of the light in the whole output section (including 46

50 CALCULATION OF THE SPECTRAL RESPONSE OF AN AWG DEMULTIPLEXER 969 the bending section) is carried out with the wide-angle BPM in a CCS and an accurate result for the spectral response is obtained. The dependence of the spectral response on the parameters of the output section is then analyzed. 2. Theory 2.1. CALCULATION OF THE SPECTRAL RESPONSE WITH THE OIM When calculating the spectral response with the OIM, one can use the following formula (Smit 1991) T ðdkþ ¼101g Z þ1 1 2 E f ðx DDkÞE0 ðxþdx ; ð1þ where E 0 ðxþ is the modal field of the output waveguide, E f ðxþ the focal field at the image plane, D the dispersion coefficient of the considered AWG demultiplexer and D ¼ d o =Dk ch (There Dk ch is the channel spacing and d o is the end separation of the output waveguides (see Fig. 1)). In an ideal case, the modal field of the input waveguide is ideally imaged on the focus plane. Thus, the focal field E f ðxþ is the same as the modal field E 0 ðxþ of the output waveguide when the input waveguide is the same as the output one. From the above equation, one sees that the spectral response is determined only by the end separation d o of the output waveguides CALCULATION OF THE SPECTRAL RESPONSE WITH A STANDARD BPM For a standard BPM, one usually considers the structure shown in Fig. 2. The output waveguides are assumed to be straight and infinitely long in the E 0 (x) W g n c n r #1 d o n c n r #0 E f (x) n c Fig. 1. Calculation of the spectral response with the OIM. 47

51 970 D. DAI AND S. HE M #1 L FPR Δ d o #0 FPR N # 1 Output waveguides Fig. 2. Calculation of the spectral response with the standard BPM with the assumption of infinitely long and straight output waveguides. radial direction. One can calculate the field distribution at a plane (e.g. the MN plane in Fig. 2) where the separation of the output waveguides is large enough to neglect the coupling. Then the spectral response can be easily obtained according to the field distribution (at the MN plane) obtained with the standard BPM for different input wavelengths. In this method, the spectral response is determined by two parameters, i.e., the end separation d o and the angular separation Dh of the output waveguides (Dh ¼ d o =L FPR, where L FPR is the length of the FPR) CALCULATION OF THE SPECTRAL RESPONSE WITH THE WIDE-ANGLE BPM IN A CCS A paraxial BPM in a CCS has been introduced and used in some previous work (Rivera 1995; Helfert 1998). In the present paper, we apply the wideangle BPM in a CCS for the calculation of the spectral response of an AWG demultiplexer. For a TE (or TM) mode, one has the following Helmholtz Equation for the 2D scalar electric (or magnetic) field /(x,z) [all the fields are assumed to have the time-harmonic dependence exp()jxt)] r 2 /ðr; hþþk 2 0 n2 ðr; hþ/ðr; hþ ¼0; ð2þ where k 0 is the wave number in vacuum, k 0 ¼ x=c (c is the velocity of light in vacuum). The field is expressed in the following form with the slowly varying envelope approximation: /ðr; hþ ¼Eðr; hþ expðj krhþ; ð3þ 48

52 CALCULATION OF THE SPECTRAL RESPONSE OF AN AWG DEMULTIPLEXER 971 where R is the curvature radius of the cylindrical coordinate axis, k ¼ n k 0 (in which n is the reference refractive index). With the above equation and variable transformations s ¼ Rh and r ¼ R+x, Equation (3) can be ¼ j pffiffiffiffiffiffiffiffiffiffiffi k P þ 1 1 E; ð4þ where the differential operator P ¼ ð1 þ 2 k 2 þ ) k þ k ð1 þ n2 ðxþ ð1 þ jxþ 2 ; ð5þ where j ¼ 1/R. By using a (m, l) Padé approximation (Hadley 1992), Equation (4) is ¼ j k N mðpþ D l ðpþ E; ð6þ where N m ðpþ and D l ðpþ are the polynomials of the operator P, m and l are the highest powers in N m ðpþ and D l ðpþ, respectively. By solving Equation (6), one obtains the field distribution E(x, z) along the propagation direction in a step-by-step way. With the wide-angle BPM in a CCS, one can simulate the light propagation in a complex structure as shown in Fig. 3. Each output waveguide 1 Fig. 3. Calculation of the spectral response with the wide-angle BPM in a CCS for a practical structure of output waveguides. 49

53 972 D. DAI AND S. HE consists of two straight sections and a bending section. With these bending sections, the output waveguides separate rapidly along the propagation direction. Therefore, the length of the first straight section and the bending radius (see Fig. 3) become important parameters influencing the spectral response, besides the end separation and the angular separation of the output waveguides. In our design, we first choose lengths L ½0Š s1 and L½0Š s2 of the first and second straight sections, the bending radius R 0 for the bending sections, and the radial angle a 0 (see Fig. 3) for the central output waveguide (i.e. waveguide #0). For all the output waveguides, the bending sections have the same bending radius R 0. The span angle of the bending section of the i-th ði ¼ N=2;...; N=2Þ output waveguide is given by h ½iŠ c ¼ a 0 idh (i ¼ 0 for the central output waveguide; i>0 for the upper output waveguides; i<0 for the lower output waveguides). The two straight sections are tangent to the bending section at the two junctions for each output waveguide. The parameters of the i-th output waveguide are then determined by the following recursive formula according to the geometric relation shown in Fig. 3: L ½iŠ s1 ¼ 1 n o R½sina 0 sinða 0 2iDhÞŠ=2: R 0 ð1 cosh ½iŠ ½0Š c Þ ðy03 sinða 0 idhþ þid oþ ; ð7þ n o L ½iŠ s2 ¼ R ½ cosða 0 2iDhÞ cos a 0 Š=2 þ L ½iŠ s1 cos h½iš c þ R 0 sin h ½iŠ c þ X 03 ; ð8þ where X 03 ¼ L ½0Š s1 cos a 0 þ R 0 sin a 0 þ L ½0Š s2 ; Y ½0Š 03 ¼ L½0Š s1 sin a 0 R 0 ð1 cos a 0 Þ; D o is the separation of the output waveguides at the facet (see Fig. 3). The length L ½iŠ s2 of the second straight section influences little the spectral response since separation D o is very large (typically 250 lm, in order to connect to a standard fiber-array). In the present paper, the initial field distribution for the BPM simulation is given by the focal field E f (x) at the image plane. 3. Results and discussions In this section, a numerical example is given to show the calculation of the spectral responses. We choose the end separation d g ¼ 10 lm for the arrayed waveguides, the central wavelength k 0 ¼ 1550 nm, the channel spacing 50

54 CALCULATION OF THE SPECTRAL RESPONSE OF AN AWG DEMULTIPLEXER 973 Dk ch ¼ 0:8 nm, the channel number N ¼ 9, the FPR length L FPR ¼ 9915:5 lm, the diffraction order M ¼ 47, and the end separation d o ¼ 25.4 lm for the output waveguides. The width of the input waveguide and output waveguide is W g ¼ 6 lm. The refractive indices for the core and the cladding are n r ¼ 1:4675 and n c ¼ 1:46, respectively. We choose the separation D o ¼ 250 lm and the angle a 0 ¼ 50. First we consider a Gaussian AWG demultiplexer, the focal field is the same as the modal field of the input waveguide in the ideal case. Fig. 4 shows the spectral responses obtained with the three methods mentioned above. Here we choose the bending radius R 0 ¼ 5000 lm for the requirement of the pure bending loss lower than 0.1 dbper 90. The lengths of the first and the second straight sections L ½0Š ¼ 1200 lm and ¼ 1500 lm. From this figure, one sees that the spectral responses are very different when different algorithms are used. When the OIM is used, the obtained spectral response is Gaussian-like (which is well known; OIM is used often in the analyses and designs of an AWG demultiplexer (Smit et al. 1996)). When using the algorithm based on the standard BPM, the obtained spectral response is almost the same as that obtained by the OIM when the normalized passband Dk/Dk ch is in the regions of [)1, 1]. This is because the coupling between adjacent output waveguides is very weak when the separation between output waveguides is large enough (e.g. d o ¼ 25.4 lm in this example). When using the present algorithm (i.e., the wide-angle BPM in a CCS), one obtains a spectral response with large sidelobes. For this numerical example, the sidelobes are about )35 db and much higher than those from the two conventional algorithms. The spectral response calculated with the present algorithm has a deep drop at the adjacent channel wavelengths. The channel crosstalk is still very low, i.e., about )75 db, which is almost the L ½0Š s2 s Power (db) OIM -120 standard BPM present method Δl/Δl ch Fig. 4. Comparison of the spectral responses obtained with three different methods. 51

55 974 D. DAI AND S. HE same as that obtained with the algorithm based on the standard BPM. The drop at the adjacent channel wavelengths is due to the coupling between the output waveguides and can be qualitatively verified with experimental results (see Fig. 9). For the central wavelength of the adjacent channel, light propagates along the corresponding adjacent output waveguide (including the bending section) in a well-confined way since the incident field to the output waveguide is almost the same as the fundamental mode of the output waveguide. Thus, the crosstalk occurs mainly due to the coupling between adjacent output waveguides. However, for the non-central wavelengths of channels, light is transmitted directly into the gap between adjacent output waveguides. Since the direction of the output waveguide alternates due to the bending section, light will impinge the sidewall of the adjacent waveguide and get scattered. The sidelobes are then produced when the scattered light is coupled to the adjacent waveguides. Thus, the two conventional algorithms can be used only for estimating the 3 db passband and the insertion loss (the top of the spectral responses obtained by these three algorithms are almost the same, as shown in Fig. 4). However, the present algorithm should be used in the design of an AWG demultiplexer when an actual spectral response is expected. In practical cases, the distortions caused by the limited number of arrayed waveguides and the phase errors (due to the coupling among arrayed waveguides and fabrication errors), which are all neglected in the present paper, will increase the channel crosstalk greatly and the drop in the spectral response at the adjacent channel wavelengths would not be so deep. The deep sudden reduction of crosstalk (down to )75 db) at adjacent channel wavelengths is due to the assumption that the imaged field at the entrance of the output waveguide is the same as the modal field of the input waveguide (i.e., the ideal 1:1 imaging for the arrayed waveguides is used). The sudden reduction at adjacent channel wavelengths would not be so sharp for a real AWG since the imaged field at the entrance of the output waveguide would not be the same as the modal field of the input waveguide due to the fact that the imaging by the arrayed waveguides is not perfect in practice. Below we analyze how the spectral response is influenced by the parameters of the output section, such as the length L ½0Š s1 of the first straight section and the bending radius R 0. Fig. 5 shows the spectral responses for the designs with different lengths L ½0Š (i.e., L½0Š ¼ 1200; 2000; 4000; and10; 000 lm). Here s1 s1 the bending radius is fixed to R 0 ¼ 5000 lm. From this figure, one sees that the main peak of the spectral response only shift slightly and the channel crosstalks are almost the same (about )75 db) when different lengths L ½0Š s1 are chosen. The sidelobes remain at about )32 db when the length varies. Since the length L ½0Š s1 only influences the spectral response slightly, we choose L ½0Š s1 ¼ 1200 lm to make the output waveguide compact below. Fig. 6 shows the spectral responses for the designs with different angle separations (Dk ¼ rad, rad, respectively). In these two 52

56 CALCULATION OF THE SPECTRAL RESPONSE OF AN AWG DEMULTIPLEXER R o =5000μm q = rad L FPR = μm M=47 Power (db) L [0] s1 =1200μm L [0] s1 =2000μm L [0] s1 =4000μm L [0] s1 =10000μm Δl/Δl ch [0] Fig. 5. The spectral responses for the designs with different values of length L s1 (the bending radius R 0 ¼ 5000 lm) Power (db) q= rad q= rad Δl/Δl ch Fig. 6. The spectral responses for the designs with different values of angle separation Dh. cases, the end separation between the output waveguides are fixed to d o ¼ 25.4 lm.the FPR length and the diffraction order are chosen as (L FPR, M) ¼ ( lm, 47) and ( lm, 90), respectively. From this figure one sees that when the end separation d o is fixed, the spectral responses are almost the same and the crosstalk decreases slightly as the angular separation Dh increases. Fig. 7 shows the spectral responses for the designs of AWG demultiplexers with different bending radii R 0 (the length L ½0Š s2 ¼ 1200 lm). From this figure, one sees that the sidelobes can be reduced noticeably by increasing the bending radius. For example, when the bending radius R 0 increases from lm, the sidelobes decreases from )35 to )48 db. This figure also shows that the other features of the spectral responses for different bending 53

57 976 D. DAI AND S. HE Power (db) R o=5000μm -60 R o =7500μm -70 R o =10000μm R o =15000μm R o=20000μm Δl/Δl ch Fig. 7. The spectral responses for the designs with different values of bending radius R 0 (the length L [0] s1 ¼ 1200 lm). radii, such as the crosstalk (about )75 db in this case) and the 3 db passband width, are almost the same. Therefore, when small sidelobes are desirable, we should use a large enough bending radius in the design of the output waveguides for an AWG demutliplexer. On the other hand, the size for the output waveguide increases as the bending radius increases, which may make the total size of the AWG device too large. One should also note that a remarkable background noise will be introduced inevitably by the phase errors due to a non-perfect fabrication. For a commercial AWG demultiplexer, the background noise is only required to be lower than )30 db. Thus, the bending radius does not need to be too large. For a flat-top AWG demultiplexer, the focus field at the image plane has double-peaks in many designs. In this paper, we consider the method of connecting a MMI section at the end of the input waveguide. The width and length of the designed MMI section are chosen as W MMI ¼ 12.6 lm and L MMI ¼ lm, respectively. Fig. 8 shows the spectral responses (calculated with the present method) for the flat-top AWG demultiplexer with the designed MMI section when R 0 ¼ 5000, 10,000 and 15,000 lm, respectively (the length L ½0Š s2 ¼ 1200 lm is fixed). For comparison the spectral response calculated with the OIM is shown by the dashed curve in the same figure. From this figure, one sees that the spectral responses are almost the same in the passband [)0.5, 0.5] when using the present algorithm and the OIM. This indicates the OIM can also be used to evaluate some characteristics of a flattop spectral response (besides the Gaussian type), such as the 3 db-passband and the insertion loss. However, the present algorithm should be used when a total view of the spectral response is expected. This figure also shows that the sidelobes are reduced when the bending radius increases (which is also true 54

58 CALCULATION OF THE SPECTRAL RESPONSE OF AN AWG DEMULTIPLEXER Power (db) R o =5000μm -80 R o=10000μm R o=150000μm OIM Δl/Δl ch Fig. 8. The spectral responses for a flat-top AWG demultiplexer with different values of bending radius R 0 (the length L s1 [0] ¼ 1200 lm). for the Gaussian spectral responses shown in Fig. 7). The sidelobe level of the flat-top spectral response is almost the same as that of the Gaussian spectral response shown in Fig. 7. For example, the sidelobe is about )32 db when the bending radius R 0 ¼ 5000 lm. If the sidelobe is required to be lower than )40 db, the bending radius should be larger than 10,000 lm. When the end separation d o of the output waveguides becomes smaller, the present method is still applicable even when the coupling between adjacent output waveguides becomes more serious. For example, we choose d o ¼ lm, R 0 ¼ 5000 lm, L ½0Š s2 L½0Š s2 ¼ lm, L½0Š s2 ¼ lm and the other parameters as given in Table 1. We fabricated the designed AWG and measured the spectral response. Fig. 9 shows the simulated and experimental results of the spectral response for channel #-1. For the simulated spectral response, a small shift of central wavelength and an additional insertion loss due to imperfect fabrication have been added in order to make a clear comparison graphically. From this figure one sees that the simulation results obtained by the present method agrees reasonably well with the experimental data. The experimental spectral response has a drop at adjacent wavelengths, as predicted by the numerical simulation based on the present method. Due to the reasons explained before, the crosstalks at adjacent wavelengths do not reach the low values predicted by the present numerical method. Table 1. Parameters for the AWG n r n c m d g k 0 2N Dk ch R a 0 D lm nm nm 5200 lm lm 55

59 978 D. DAI AND S. HE 0-10 numerial experimental -20 Power (db) l (nm) Fig. 9. Comparison between numerical and experimental results. 4. Conclusion In this paper, we have presented an algorithm based on a wide-angle BPM in a CCS to calculate the spectral response of an AWG demultiplexer with the assumption of a 1:1 imaging. The simulation results have been compared with those obtained with two conventional algorithms, namely, the OIM and the standard BPM (with the approximation of radially straight and infinitely long output waveguides). The 3 db passband width of the spectral responses obtained by these three algorithms are almost the same. Thus, the two conventional algorithms can be used when one only wants to estimate the 3 db passband. However, when an actual spectral response is expected, the present algorithm should be used in the design of an AWG demultiplexer. We have shown that the spectral response has a pit at adjacent wavelengths with numerical and experimental results. It has also been shown that the sidelobes can be reduced noticeably by increasing the bending radius. Acknowledgements This work was supported by a research grant (No ) of the provincial government of Zhejiang Province of China, and the National Science Foundation of China (No ). 56

60 CALCULATION OF THE SPECTRAL RESPONSE OF AN AWG DEMULTIPLEXER 979 References Dai, D., S. Liu, S. He and Q. Zhou. J. Lightwave Technol , Hadley, G.R. Opt. Lett , Helfert, S.F. Opt. Quantum Electron , Okamoto, K. and A. Sugita. Electron. Lett ,1996. Rivera, M.J. Lightwave Technol , Scarmozzino R. and R.M.J. Osgood. Opt. Soc. Am. A , Smit, M.K. and C. Van Dam. IEEE J. Sel. Top. Quant. Electron , Smit, M.K. Optical phased arrays in integrated optics in silicon-based aluminum oxide, Ph.D. thesis. Delft University of Technology chapter 6, Soole, J.B.D., M.R. Amerfoort, H.P. LeBlanc, N.C. Andreadakis, C.A.C. Rajhel, R. Bhat, M.A. Koza, C. Youtsey and I. Adesida IEEE Photon. Technol. Lett ,

61 2392 J. Opt. Soc. Am. A/Vol. 21, No. 12/December 2004 D. Dai and S. He Accurate two-dimensional model of an arrayed-waveguide grating demultiplexer and optimal design based on the reciprocity theory Daoxin Dai and Sailing He Centre for Optical and Electromagnetic Research, State Key Laboratory for Modern Optical Instrumentation, Joint Research Center of Photonics of the Royal Institute of Technology, Stockholm, Sweden and Zhejiang University; Zhejiang University, Yu-quan, Hangzhou , China; and Division of Electromagnetic Theory, Alfven Laboratory, Royal Institute of Technology, S Stockholm, Sweden Received January 13, 2004; revised manuscript received June 2, 2004; accepted May 24, 2004 An accurate two-dimensional (2D) model is introduced for the simulation of an arrayed-waveguide grating (AWG) demultiplexer by integrating the field distribution along the vertical direction. The equivalent 2D model has almost the same accuracy as the original three-dimensional model and is more accurate for the AWG considered here than the conventional 2D model based on the effective-index method. To further improve the computational efficiency, the reciprocity theory is applied to the optimal design of a flat-top AWG demultiplexer with a special input structure Optical Society of America OCIS codes: , INTRODUCTION An arrayed-waveguide grating (AWG) demultiplexer 1 has become one of the most essential components in a wavelength-division multiplexing (WDM) system. An efficient and accurate numerical simulation is very important for the design of planar lightwave circuit devices that include AWG demultiplexers. Several common methods have been developed to calculate the spectral response of an AWG demultiplexer, such as a 1:1 imaging method, 2 a Fourier optics method, 3 and a beam propagation method (BPM). 4 The accuracy of the 1:1 imaging method is not good owing to the assumption of perfect imaging. Using the Fourier optics method or the BPM, one can calculate the spectral response more accurately. Since the scale of an AWG demultiplexer is very large (compared with the wavelength), a three-dimensional (3D) model will require tremendous computational time, especially for the optimal design of a structure in an AWG demultiplexer. Usually an effective-index method (EIM) is used to reduce the 3D model to a two-dimensional (2D) model. However, the EIM sometimes may not work well, e.g., in the case of planar lightwave circuit devices based on silicon-on-insulator (SOI) rib waveguides. Thus a more accurate model is desirable for an effective simulation of an AWG demutliplexer. In this paper we reduce the 3D model to a 2D one by integrating the corresponding field distribution in the AWG demultiplexer along the vertical direction under the assumption that the power coupled to higher-order modes in a Free-propagation region (FPR) is negligibly small. The equivalent 2D model greatly improves the computational speed while keeping almost the same accuracy as the original 3D model. A WDM device is required to have a flat-top spectral response in order to relax the requirements on the wavelength control for lasers and filters in a WDM system. To obtain a flat-top spectral response, several methods have been introduced, e.g., the method of multiple gratings, 5 the spatial-phase-modulation method, 6 and the simple and effective method of connecting a special structure (such as a standard 7 or a tapered multimode interference coupler, 8 or a parabolic waveguide horn 9 ) at the end of the input waveguide (IW). The special input structure should be optimized in order to obtain a flat-top spectral response. However, since the special input structure is connected at the end of the IW, light propagating in the whole AWG demultiplexer [from the IW to the output waveguide (OW)] should be simulated repeatedly in a conventional procedure of the optimization of the special input structure. This requires great computation effort and makes the optimization of the special input structure time-consuming, even for a 2D design of an AWG demultiplexer. In this paper the reciprocity theory 10 is also used to improve the efficiency of the optimal design. The reciprocity theory indicates that the transmission of light can be reversed. Therefore, in the optimal design of an AWG demultiplexer in this paper, light is transmitted from the (central) OW (instead of the IW), propagates through the second FPR and the arrayed waveguides (AWs), and then focuses at the interface between the first FPR and the special input structure. Then the spectral response is obtained by overlapping this focused field at this interface and the output field (excited by the fundamental mode of the IW) at the end of the special input structure. In this paper this output field is obtained by applying a 3D BPM in the small area of the special input structure. When adjusting the parameters of the special input structure in order to achieve the optimal flat-top spectral response, one needs only to use a numerical method (such as 3D BPM) to simulate the light propagation repeatedly in the /2004/ $ Optical Society of America 58

62 D. Dai and S. He Vol. 21, No. 12/December 2004/J. Opt. Soc. Am. A 2393 small area of the special input structure (instead of the whole AWG demultiplexer) and obtain the spectral response. Since the size of the special input structure is usually small (as compared with the whole AWG demultiplexer), the computational effort is greatly reduced. 2. THEORY In this section we show how an equivalent 2D model can be obtained from the original 3D model and how the reciprocity theory is applied to the model in the optimal design for the special input section in a flat-top AWG demultiplexer. An AWG demultiplexer consists of AWs, IWs, OWs, and two FPRs [see Fig. 1(a)]. Figures 1(b) and 1(c) show the enlarged views of the first and second FPR sections, respectively. The input and output apertures of the waveguide array are of Rowland type. 1 The ends of the AWs are located on a circle with a radius R (i.e., the length of the FPR). The ends of the OWs are located on the image circle with a radius of R/2 [see Fig. 1(c)]. Thus 2 the curve equation for the image plane is given by x 1 (z 1 R/2) 2 (R/2) 2. First we consider the case in which the field is excited by the fundamental mode of the IW. Using a numerical method (such as 3D BPM), one can easily obtain the input field E in (x 1 ) for the first FPR [the field at the end of the special input structure, i.e., on plane z 0 in Fig. 1(b)]. The input field E in (x 1, y) can be expanded in terms of the orthogonal eigenmodes in the FPR with different weights [similar to the treatment used in a multimode interference coupler], i.e., M 1 E in x 1, y q 0 a q x 1 u q FPR y, (1) where u FPR q ( y) is the field distribution of the qth eigenmode in the FPR, a q (x 1 ) is the excitation coefficient for the qth-order mode, and M is the total number of guided modes supported in the FPR. The qth-order modal field distribution u FPR q ( y) can be obtained by solving the eigenfunction for the FPR slab waveguide. The coefficient a q (x 1 ) is obtained by using the following overlap integral formula: a q x 1 E in x 1, y u q FPR y dy. (2) Then the field distribution at point (x, y, z) can be written as a superposition of all the modal fields in the FPR: M 1 E x, y, z q 0 a q far x, z u q FPR y. (3) Here a q far (x, z) can be obtained by using the following 2D Kirchhoff Huygens diffraction formula, 11 a q far x, z i a q x 1 /nq FPR exp in q FPR kr r cos in cos dr dx 1, 2 where in is the incident angle, dr is the diffraction angle, r (x x 1 ) 2 z 2 1/2, is the wavelength in vacuum, k 2 /, and n FPR q is the effective index for the qthorder guided mode in the FPR. Since cos in and cos dr can be approximated to 1 in our case, Eq. (4) can be rewritten as (4) Fig. 1. Structure of an AWG demultiplexer. (a) layout of an AWG demultiplexer, (b) configuration near the first FPR, (c) configuration near the second FPR. a q far x, z i /nq FPR exp in FPR q kr a q x 1 dx 1. r When the FPR is a single-mode slab waveguide or the coupling coefficient c q a q (x 1 )dx 1 of the higherorder mode is small (i.e., when the power coupled to the higher-order mode is small, which is usually the case), (5) 59

63 2394 J. Opt. Soc. Am. A/Vol. 21, No. 12/December 2004 D. Dai and S. He one needs only to consider the fundamental mode (q 0) in the FPR, and Eq. (1) can be simplified to E in x 1, y a 0 x 1 u 0 FPR y, (6) where a 0 (x 1 ) E in (x 1, y)u FPR 0 ( y)dy. Equation (6) demonstrates a separation of variables. In an EIM, a separation of variables is also used, i.e., E(x, y) X(x)Y( y), where X(x) and Y( y) are the modal fields of equivalent slab waveguides in the x and y directions, respectively. In the present method, u FPR 0 ( y) is the fundamental modal field in the FPR but not the modal field of the equivalent slab waveguide in the y direction. Thus one sees that the present method is different from the separation of variables used in an EIM, especially for a rib waveguide. Consequently, Eq. (3) becomes E x, y, z a 0 far x, z u 0 FPR y. (7) From Eq. (7) one can obtain the following far field E IAP (x, y) at the aperture (with x 2 z 2 R 2 ) of the waveguide array [here x R atan(x /z)]: E IAP x, y E x, y, z z R 2 x 2 u 0 FPR y a 0 far x, z z R 2 x 2. (8) Substituting Eq. (5) into Eq. (8), one obtains i E IAP x, y u FPR 0 y a 0 x 1 /n0 FPR exp in FPR 0 kr r dx 1 z R 2 x 2. (9) where l a i 0 x 1 /n0 FPR A AW * x ld g A AW * x ld g exp in 0 FPR kr r dx dx 1, (12) u FPR 0 y E AW * x ld g, y dy. (13) The field distribution E EX (x, y, ) transmitted from the right exit of the waveguide array is given by N 1 E EX x, y, l 0 l E AW x ld g, y exp i l, (14) where N is the total number of the AW, l 0 l2 n g L/ (here 0 is the phase introduced by the shortest AW, n g is the effective refractive index for the fundamental mode of the AW, and L is the length difference between adjacent AWs). The field distribution E IM (x 1, y, ) at the image plane [where x 2 1 (z 1 R/2) 2 (R/2) 2 in the second FPR] of the AWG demultiplexer is given by the following 2D Kirchhoff Huygens diffraction formula, E IM x 1, y, where 0 A EX far x 1, z, u FPR 0 y z R 2 x 1 R/2 2 1/2, (15) 0 A EX far x 1, z, i /n0 FPR A 0 EX x, Then the coupling coefficient l between the field E IAP (x, y) and the modal field E AW (x, y) (which can be obtained with a finite-difference method 12 (FDM)) of the lth AW is given by and where exp in FPR 0 kr dx, r l E IAP x, y E AW * x ld g, y dxdy, (10) where d g is the separation of the AWs and the superscript* denotes complex conjugation. Substituting Eq. (9) into Eq. (10), one obtains l u i 0 FPR y a 0 x 1 FPR /n0 E AW * x ld g, y Equation (11) can be rewritten as exp in 0 FPR kr r dx dx 1dy. (11) A 0 EX x, E EX x, y, u 0 FPR y dy. (16) Substituting Eq. (14) into Eq. (16), one obtains N 1 A 0 EX x, l 0 l A AW x ld g exp i l. (17) By overlapping E IM (x 1, y) and the fundamental modal field E OW (x 1, y) (which can be obtained with a FDM) of an intended OW, one obtains the following coupling coefficient: out E IM x 1, y, E OW * x 1, y dx 1 dy. (18) Note that the peak position of the fundamental modal field E OW (x 1, y) varies for different OWs. In a design, one usually considers the central OW since the spectral responses of the other channels are very similar to the re- 60

64 D. Dai and S. He Vol. 21, No. 12/December 2004/J. Opt. Soc. Am. A 2395 N 1 A IM x 1, l A AW * x ld g l 0 sponse of the central channel (if the total number of the channels is not very large). Substituting Eq. (15) into Eq. (18), one obtains i /n0 FPR where out A ow x 1 0 A EX far x 1, z, A OW x 1 dx 1, (19) u FPR 0 y E OW * x 1, y dy. (20) The spectral response of the intended OW is then given by out ( ) 2. In a conventional procedure, the spectral response is calculated with Eq. (18). When special structure is adjusted in the optimal design, the field E in (x 1, y) will change since the special input structure is connected at the end of the IW. Consequently, E IAP (x, y), the coupling coefficient l, the field E EX (x, y, ), and the field E IM (x 1, y, ) will change. Therefore one has to repeatedly simulate the light propagation in the whole AWG demultiplexer (from the IW to the OW). This requires great computation effort and makes the optimization time-consuming. In the following part of this section, we present an efficient design method based on the reciprocity theory. We reverse the light propagation direction when simulating an AWG demultiplexer. Equation (19) can be rewritten as where A far OW x out i /n0 FPR A 0 EX x, A far OW x dx, (21) exp in FPR 0 kr A OW x 1 dx 1. r A far OW (x) denotes the far-field distribution (at the right exit of the waveguide array) excited by the fundamental modal field of the OW. Substituting Eq. (17) into Eq. (21), one obtains where N 1 out l 0 l l exp i l, (22) l A AW x ld g A far OW x dx. (23) Substituting Eq. (12) into Eq. (22), one obtains where out a 0 x 1 A IM x 1, dx 1, (24) exp i l exp in 0 FPR kr dx. r (25) Substituting Eq. (2) (for the fundamental mode, i.e., q 0) into Eq. (24), one obtains out E in x 1, y E IM x 1, y, dx 1 dy, where E IM (x 1, y, ) A IM (x 1, )u FPR 0 ( y); i.e., E IM x 1, y, i /n0 FPR exp i l N l 0 (26) l E AW * x ld g, y exp in 0 FPR kr dx. r (27) From Eq. (27) one sees that E IM (x 1, y, ) is the field distribution at the interface between the first FPR and the special input structure when light is transmitted from the OW and propagates along a reversed direction (as compared with the signal propagation in an operating AWG demultiplexer). As shown above, we have simplified the 3D model into an equivalent 2D one in order to reduce the computational complexity. Both Eq. (26) (for the 3D model) and Eq. (24) (for the 2D model) are obtained under the assumption that the power coupled to higher-order modes in a FPR is negligibly small (i.e., approximation 6), whereas Eq. (24) contains only a simple one-dimensional integral. When calculating the spectral response, we use Eq. (24) instead of Eq. (26). The field distribution A IM (x 1, ) remains unchanged when the special input structure is adjusted. The 2D field distributions [e.g., E OW (x 1, y), E AW (x 1, y), which can be obtained with a FDM] are converted to one-dimensional fields A AW (x), A OW (x 1 ) by integrating these fields along the y (vertical) direction as shown in Eqs. (13) and (20). When optimizing the special input structure, one obtains the field a 0 (x 1 ) by integrating the field E in (x 1, y), which is obtained with a 3D BPM. The integral from to in the above equations can be evaluated numerically with a sum of values at discrete points in an integration region large enough to ensure the convergence. According to the calculated spectral response obtained from Eq. (24), one can evaluate the key features of a flattop AWG demultiplexer (with the special input structure) such as the 1-dB bandwidth, the ripple, the channel cross talk, and the sharpness of the transitions. Usually the 1-dB bandwidth is required to be larger than 0.5 ch, where ch is the channel spacing. The cross talk should be smaller than 30 db. The sharpness is defined as S 2 1dB /( 1dB 20 db ), where 1dB and 20 db are the 1-dB bandwidth and the 20-dB bandwidth, respectively. The ripple of the spectral response is defined 61

65 2396 J. Opt. Soc. Am. A/Vol. 21, No. 12/December 2004 D. Dai and S. He Fig. 2. Special input structure of a parabolic multimode section (top view). Fig. 3. Cross section of a SOI rib waveguide. as the maximal variance of the loss within the International Telecommunication Union (ITU) window of ch /8, ch /8. The chromatic dispersion 2 is another important parameter for an AWG. We define a quantity D c max as the maximal absolute value of chromatic dispersion in the ITU window. 3. DESIGN In this section a numerical example is given to compare the present effective model and the conventional 2D EIMbased model. A parabolic waveguide horn (shown in Fig. 2) is used as the special input structure connected at the end of the IW to flatten the spectral response of an AWG demultiplexer. The width W(z) of the parabolic multimode section along the propagation direction z is given by 9 W z 2 e z w r 2 1/2, (28) method and the conventional method (based on EIM) for buried waveguides, which implies the validity of the present method. However, the conventional EIM-based model is not suitable for rib waveguides, and thus we use the present method to design an AWG based on SOI rib waveguides. For the SOI rib waveguide, the total height H and the rib height h r are chosen to be H 5 m and h r 2 m, respectively. The rib width w r 2 m. The refractive indices of the air, silica, and silicon are given as n 1 1.0, n , n , respectively (see Fig. 3). The wavelength c 1550 nm. For the designed AWG demultiplexer, the diffraction order m 45, the separations of the AWs d g 8 m, the separation between two adjacent OWs d o m, the FPR length R 6400 m, the central wavelength nm, the channel spacing ch 0.8 nm, and the number of the AWs N WG 140. To obtain the spectral response, we calculate first the field distribution A IM (x 1, i ) with Eq. (25) at various wavelengths ( i c i ch /80, i 80:80). The obtained field distribution A IM (x 1, 0 ) is shown by the solid curve in Fig. 4, where the field calculated by the conventional 2D EIM is also shown (by the dotted dashed curve). From this figure one sees that there is a large difference between the results (especially the amplitude) obtained with the present method and the EIM-based 2D method. As mentioned in Section 2, we use a 3D BPM to simulate the field propagation in the parabolic horn and obtain the field E in (x 1, y). Then a 0 (x 1 ) is obtained from Eq. (2) with q 0. The parameters of the parabolic horn are chosen as 1.2 and d 10 m. The optimal length of the parabolic horn needs to be determined in the range from 0 to 700 m. The spectral response is obtained from Eq. (24) as the length of the parabolic horn varies. From the obtained spectral responses, we can extract the 1-dB bandwidth, the ripple, the sharpness, the cross talk, the insertion loss, and the chromatic dispersion D c max. In Fig. 5, these characteristics are shown as the length L p of the parabolic horn increases, respectively. When adjusting the length L p of the parabolic horn, with the present method (based on the reciprocity theory) we need only to use a 3D BPM to simulate repeatedly the light propagation in the small area of the parabolic horn (instead of the whole AWG demultiplexer as required in a conventional method) and obtain the spectral response. where e 0 /n e ( 0 is the designed central wavelength in vacuum, n e is the effective index in the parabolic waveguide horn), w r is the width of the IW, and is a constant that controls the shape of the parabolic waveguide horn. Usually the cross talk will increase when the spectral response is broadened. To reduce the cross talk between channels, two air slots are placed at both sides of the parabolic waveguide horn (with a large enough width, e.g., 2.0 m). The effect of the air slots on the spectral response (including the cross talk) is controlled by the distance d between the air slot and the central axis (x 0) of the parabolic waveguide horn. Our simulation results (not included here to save space) have shown good agreement between the present Fig. 4. Field distribution A IM (x 1, 0 ). 62

66 D. Dai and S. He Vol. 21, No. 12/December 2004/J. Opt. Soc. Am. A 2397 Fig. 5. Features of the spectral response of an AWG demultiplexer with a parabolic waveguide horn when its length increases ( 1.2 and d 10.0 m). (a) 1-dB bandwidth, (b) ripple, (c) sharpness of the transitions, (d) cross talk, (e) insertion loss, (f) chromatic dispersion D c max. The results obtained with the present method and the conventional 2D EIM-based model 10 are indicated by the solid curves and the dotted dashed curves, respectively, in Fig. 5. Since the multimode effects in the FPR are considered in the present method, the calculated value for the insertion loss is larger ( 2 db) than that obtained with the conventional method based on EIM [see Fig. 5(e)]. For the other characteristics, the results obtained by the present method also differ greatly from those obtained by the conventional method based on EIM. This is because that EIM is not accurate for a SOI rib waveguide. In this case the present method is preferred for the design of a flat-top AWG based on SOI. In the design for a flat-top AWG, a flat-top spectral response with low chromatic dispersion is desired. From Fig. 5 we choose the optimal length to be L p 504 m. 63

67 2398 J. Opt. Soc. Am. A/Vol. 21, No. 12/December 2004 D. Dai and S. He field distributions along the vertical direction, we have reduced the original 3D model to an equivalent 2D model, which further improves the computational efficiency. Unlike the EIM-based 2D model, the present equivalent 2D model has the same accuracy as the original 3D model. By using the present design method, one can efficiently scan the parameters of the special input structure and observe how the features of the spectral response vary; then one can easily choose appropriate values for the parameters and give an optimal design fulfilling the requirements for different applications. Fig. 6. Flattened spectral response and the chromatic dispersion for the central channel (Ch0) and the 8th channel (Ch8) of a designed AWG demultiplexer with L p 504 m, 1.2, and d 10.0 m. For such a design, the maximal 1-dB bandwidth is more than 60% (0.6) of the channel spacing and the ripple is 0.02 db. At the same time the chromatic dispersion in the ITU passband is also very low ( 10 ps/nm). The flattened spectral response and the chromatic dispersion 2 for the central channel (Ch0) and the 8th channel (Ch8) of the designed AWG demultiplexer are shown in Fig. 6 (the horizontal axis is normalized with the channel spacing). It is well known that the insertion loss of the edge channel of an AWG is slightly larger than that of the central channel (owing to the Gaussian shape of the diffracted far field of an individual arrayed waveguide). 1 This is confirmed in Fig. 6, where one sees that the spectral responses of the central (Ch0) and edge (Ch8) channels are very similar (except for the insertion loss). From Fig. 6 one also sees that the chromatic dispersions are almost the same for the central (Ch0) and edge (Ch8) channels. Therefore one needs only to consider the central channel in the design of a flat-top AWG. 4. CONCLUSION In this paper we have presented an efficient method for the optimal design of an AWG demultiplexer, especially for the optimization of a special input structure used to flatten the spectral response. The present method is based on the reciprocity theory, according to which the light propagation direction can be reversed in the calculation of the spectral response of an AWG demultiplexer. When optimizing the special input structure, one needs only to calculate the output field from the special input structure repeatedly with an accurate numerical method (in this paper the 3D BPM is used), and the focused field at the interface between the first FPR and the special input structure is calculated only once. Thus the computational efficiency is greatly improved. By integrating the Address correspondence to Daoxin Dai, Centre for Optical and Electromagnetic Research, Department of Optical Engineering, Zhejiang University, Yu Quan, Hangzhou , China. , ddxopt@hotmail.com. REFERENCES 1. M. K. Smit and C. V. Dam, Phasar based WDM devices: principles, design and applications, IEEE J. Sel. Top. Quantum Electron. 2, (1996). 2. D. Dai, S. Liu, S. He, and Q. Zhou, Optimal design of an MMI coupler for broadening the spectral response of an AWG demultiplexer, J. Lightwave Technol. 20, (2002). 3. M. E. Marhic and X. Yi, Calculation of dispersion in arrayed-waveguide grating demultiplexers by using a shifting-image method, IEEE J. Sel. Top. Quantum Electron. 8, (2002). 4. R. Scarmozzino, A. Gopinath, R. Pregla, and S. Helfert, Numerical techniques for modeling guided-wave photonic devices, IEEE J. Sel. Top. Quantum Electron. 6, (1996). 5. A. Rigny, A. Bruno, and H. Sik, Multigrating method for flattened spectral response wavelength multi/ demultiplexer, Electron. Lett. 33, (1997). 6. Z. Shi, J. He, and S. He, An analytic method for designing passband flattened DWDM demultiplexers using spatial phase modulation, J. Lightwave Technol. 21, (2003). 7. J. B. D. Soole, M. R. Amerfoort, H. P. LeBlanc, N. C. Andreadakis, A. Rajhel, C. Caneau, R. Bhat, M. A. Koza, C. Youtsey, and I. Adesida, Use of multimode interference couplers to broaden the passband of wavelength-dispersive integrated WDM filters, IEEE Photon. Technol. Lett. 8, (1996). 8. D. Dai, W. Mei, and S. He, Use of a tapered MMI coupler to broaden the passband of an AWG, Opt. Commun. 219, (2003). 9. K. Okamoto and A. Sugita, Flat spectral response arrayedwaveguide grating multiplexer with parabolic waveguide horns, Electron. Lett. 32, (1996). 10. D. Dai and S. He, Fast design method for a flat-top arrayed-waveguide-grating demultiplexer using the reciprocity theory, J. Opt. Netw. 2, (2003), JON D. Dai and S. He, Analysis of multimode effects in the FPR of a SOI-based AWG demulitplexer, Appl. Opt. 42, (2003). 12. N.-N. Feng, G.-R. Zhou, and W. P. Huang, Computation of full-vector modes for bending waveguide using cylindrical perfectly matched layers, J. Lightwave Technol. 20, (2002). 64

68 Optics Communications 247 (2005) Reduction of multimode effects in a SOI-based etched diffraction grating demultiplexer Daoxin Dai *, Sailing He Centre for Optical and Electromagnetic Research, Joint Research Center of Photonics of the Royal Institute of Technology (Sweden) and Centre for Optical and Electromagnetic Research, Department of Optical Engineering, State Key Laboratory of Modern Optical Instrumentation, Zhejiang University, Yu-Quan, Hangzhou, PR China Division of Electromagnetic Theory, Alfven Laboratory, Royal Institute of Technology, S Stockholm, Sweden Received 22 July 2004; received in revised form 4 November 2004; accepted 22 November 2004 Abstract Multimode effects in the free propagation region (FPR) of a silicon-on-insulator (SOI)-based etched diffraction grating (EDG) demultiplexer are analyzed. In a conventional design, the power coupled to the higher order modes is considerable, which introduces a significant excess loss and crosstalk. It is shown that the multimode effects in an SOI EDG demultiplexer are much more detrimental than in an arrayed waveguide grating demultiplexer. Several methods for reducing the multimode effects are discussed. In particular, a laterally tapered structure between the FPR and the input/output waveguides is proposed as a simple and effective method for reducing the power coupled to the higher order modes and consequently reducing the multimode effects. The taper width is optimized to minimize the crosstalk. Ó 2004 Elsevier B.V. All rights reserved. PACS: Dj; m Keywords: Multimode effect; Taper; Silicon-on-insulator; Etched diffraction grating; Insertion loss; Crosstalk; Demultiplexer 1. Introduction Multiplexers/demultiplexers based on the planar light circuit (PLC) technologies have shown a greater potential due to their advanced performances. Arrayed-waveguide gratings (AWGs) [1] * Corresponding author. Tel.: ; fax: address: daoxin@imit.kth.se (D. Dai). and etched diffraction gratings (EDGs) [2 5] are two common types of PLC-based demultiplexers. Many different types of optical waveguide structures for PLCs have been developed, such as buried waveguides, rib waveguides, and strip-loaded waveguides. The propagation loss of a planar and rib waveguide based on silicon-on-insulator (SOI) can be lower than 0.1 db/cm [6] within the infrared wavelength window around 1.5 lm, which offers a tremendous potential for fabricating /$ - see front matter Ó 2004 Elsevier B.V. All rights reserved. doi: /j.optcom

69 282 D. Dai, S. He / Optics Communications 247 (2005) low-cost PLC devices including AWG/EDG demultiplexers. A single mode SOI rib waveguide with a large cross-section [7] is usually used to obtain a high coupling efficiency with a single mode fiber (SMF). The thickness of the silicon layer for such a single mode rib SOI waveguide is usually chosen to be 3 11 lm (e.g. in [8] the thickness of the silicon layer is chosen to be 5 lm). In an AWG/EDG demultiplexer, the free propagation region (FPR) with the same thickness will support more than one mode due to the large difference between the refractive indices of silicon (about 3.455) and silicon oxide (about 1.46). When light is launched from the input waveguide, higher-order modes will be excited at the junction between the FPR and the input/output waveguides due to the mode mismatching between the rib waveguide and the slab (FPR) waveguide. For different modes of the FPR, the corresponding focus positions at the image plane of the AWG/EDG demultiplexer will be separated from one another due to the different propagation constants (the effective refractive indices). Some of the power of the higher-order modes will be coupled to the other channels, which results in an increased channel crosstalk and insertion loss. These multimode effects have been analyzed in detail for a SOI-based AWG demultiplexer in our previous work [9]. For an EDG, the optical path length difference between adjacent grating facets, which determines the properties of the grating, is related to the effective index of the FPR. Thus, a multimode FPR in an EDG will cause more serious problems than that in an AWG. In an EDG, an additional source to excite higher order modes is the non-verticality of grating facets due to fabrication imperfection [10]. In this paper, we only focus on optimizing the waveguide structures to reduce higher order modes excited at the junction between input/output waveguides and the FPR. To compensate for the multimode effects, one can choose an appropriate diffraction order M so that the (M 1)th diffraction angle of the first order mode coincides with the Mth diffraction angle of the fundamental mode [11]. However, the determined diffraction order M in this case is usually very large, which makes the free spectral range too small and limits the channel number for a DWDM system. In the present paper, we give a detailed analysis for the multimode effects in a SOI EDG according to the grating equation for all modes in a FPR. A taper structure between the input/output waveguides and the FPR is proposed and optimized, which can reduce significantly the multimode effects. 2. Theory An EDG consists of a curved grating, an input waveguide, output waveguides and a FPR (see Fig. 1(a)). It is usually based on a Rowland circle construction [4]. Fig. 1(b) is an enlarged view of the Rowland circle in an EDG. The field launched from the end facet of the input waveguide to the FPR is diffracted by each grating facet. It is then refocused on the imaging curve according to the wavelength and guided into different output waveguides Spectral response For a multimode FPR, higher-order modes will be excited when the light enters the FPR from the input rib waveguide. An input field profile E in (x,y,k) (k is the wavelength in vacuum), which is usually the fundamental modal field of the input waveguide, can be decomposed into the field distribution u s q ðyþ of all modes in the FPR (q denotes the order of the guided mode in the FPR slab waveguide) [9], i.e., E in ðx; y; kþ ¼ XQ 1 q¼0 a q ðx; kþu q s ðy; kþ; ð1þ where Q is the total number of the modes supported in the FPR, a q (x,k) is the excitation coefficient for the qth order mode (a q (x,k) can also be regarded as a one-dimensional equivalent field for the input Rfield). If the field u s qðy; kþ is normalized (i.e., þ1 1 uq s ðy; kþuq s ðy; kþ dy ¼ 1), the power c q coupled to the qth mode is given by the following integral: c q ¼ Z þ1 1 a q ðx; kþa qðx; kþ dx; ð2þ 66

70 D. Dai, S. He / Optics Communications 247 (2005) Input waveguide Grating FPR (a) Output waveguides y grating facet (i-th) G(x g, z g ) Input waveguide x I d g_i g_d O g z o P O C R/2 (b) Image plane Fig. 1. Schematic configuration. (a) The structure of an EDG demultiplexer. (b) The enlarged view of the Rowland circle in an EDG. where the superscript Ô*Õ represents the complex conjugate. The multimode effects in an EDG demultiplexer introduce an excess insertion loss L = 10logc 0 for each pass at the junction between the input (or output) waveguide and the FPR. The introduced total excess loss in a SOI-based EDG is double of this amount due to two passes (input/output). The introduced crosstalk depends on not only the coupled power c q but also the focus position of the higher order modes. The coefficient a q (x) can be obtained by using the following overlap integral formula: a q ðx; kþ ¼ Z þ1 1 E in ðx; y; kþu q s ðy; kþ dy: ð3þ Then the field distribution at point P(x p,y p,z p )in the FPR can be written as a superposition of all the guided modal fields in the FPR Eðx p ; y p ; z p ; kþ ¼ XQ 1 a q ðx p ; z p ; kþu q s ðy p; kþ; q¼0 ð4þ where a q (x p,z p,k) is obtained by using the following 2D Kirchhoff Huygens diffraction formula [12]: j a q ðx p,z p,kþ ¼pffiffiffiffiffiffiffiffiffi k=n q s Z þ1 1 cos h i þ cos h d 2 a q ðx,kþ expð jnq s pffiffi krþ r dx, ð5þ where h i and h d are, respectively, the incident angle and the diffraction angle with respect to the normal of a diffracting aperture, r ¼½ðx x p Þ 2 þ z 2 p Š1=2 ; k ¼ 2pk; n q s is the effective index for the qth order guided mode in the FPR. The field distribution at the grating is the diffraction field of the field launched from an input waveguide. Therefore, by using Eqs. (4) and (5) with cosh i = 1, one can easily obtain the field distribution at point G(x g,z g ) of the grating j a q ðx g,z g,kþ ¼pffiffiffiffiffiffiffiffiffi k=n q s Z þ1 1 1 þ cos h IW d 2 a q ðx,kþ expð jnq s pffiffi krþ r dx, ð6þ 67

71 284 D. Dai, S. He / Optics Communications 247 (2005) where h IWd ¼ tan 1 ½ðx g xþ=z g Š. The image field at point (x im,y im,z im ) of the image plane is given by Eðx; y; z; kþj image ¼ XQ 1 u q s ðy; kþa qðx; z; kþj image ; q¼0 where Z j a q ðx,z,kþj image ¼ pffiffiffiffiffiffiffiffiffi k=n q s grating expð jnq s k 0rÞ pffiffi r r g a q ðx g,z g,kþ cos h gi þ cos h gd 2 ð7þ dl, ð8þ and where r g is the reflection coefficient of the grating facet (usually r g 1), h gi and h gd are, respectively, the incident angle and the diffraction angle with respect to the normal of the grating facet. The spectral response g(k) 2 can be obtained by overlapping the image field E(x,y,z,k) image with the fundamental mode field E ow (x,y,z,k) of the output waveguide [3], i.e., Z þ1 Z gðkþ ¼ E ow ðx,y,z,kþeðx,y,z,kþj image dx dy 1 ¼ X Q 1 q¼0 image Z image a ow ðx,z,kþa qðx,z,kþj image dx, ð9þ where a q ow ðx; z; kþ ¼R þ1 1 E ow ðx; y; z; kþuq s ðy; kþ dy. The above equation can be written as follows: gðkþ ¼ XQ 1 g q ðkþ; q¼0 ð10þ where g q ðkþ ¼ R image a ow ðx; z; kþa qðx; z; kþj image dxš and g q (k) 2 represents the spectral response of the qth order mode Imaging of the higher-order modes Since the propagation constants are different for different modes, the corresponding images at the image plane will be separated. Since the energy of the higher-order modes will be coupled to the adjacent/non-adjacent channels, it will introduce some crosstalk in addition to some insertion loss. For the qth order mode, the corresponding grating equation is given by [12] n q s Kðsin h in þ sin h q dr Þ¼Mk; ð11þ where M is the diffraction order, k is the grating period, n q s is the effective index for the qth order guided mode in the FPR, h in and h dr are, respectively, the incident angle and the diffraction angle for the grating. From the above equation for the fundamental (q = 0) and the higher order (q P 1) modes, one obtains sin h q dr ¼ sin h0 dr þ Dnq n q ðsin h in þ sin h 0 dr Þ; ð12þ s where Dn q is the difference between the effective indices of the qth and fundamental modes, i.e., Dn q ¼ n 0 s nq s (Dn q > 0 since n q s < n0 s ). For a strongly confined slab waveguide such as the SOI-based FPR, the effective refractive index of the qth mode can be approximated by [13] n q s n ðq þ 1Þ2 2 8n 2 ðw e =kþ ; 2 ð13þ where n 2 and W e is the refractive index and the effective width of the core layer, respectively. Thus, one obtains Dn q qðq þ 2Þ ¼ 8n 2 ðw e =kþ : ð14þ 2 The coupled powers to higher order modes are dependent on the details of the rib waveguide and the FPR structure and cannot be negligible in some cases [14]. In our case, the power of the higher order mode is very small, which is justified by calculation in Section 3. Thus we consider only the fundamental mode and the first order modes (i.e., q = 0, 1), and ignore the other higher order modes. The diffraction angle h q dr for the first order mode is slightly different from that for the fundamental mode. Let h q dr ¼ h0 dr þ Dhq dr, where Dhq dr is the difference of the diffraction angles between the qth and the fundamental modes. Since Dh q dr (q = 1) is usually small, we have cosðdh q dr Þ1 and sinðdh q dr ÞDhq dr and thus sin h q dr sin h 0 dr þ Dhq dr cos h0 dr. Substituting this equation into Eq. (12), one obtains Dh q dr Dnq n q s sin h in þ sin h 0 dr : ð15þ cos h 0 dr From the above analysis, one sees that the multimode effects depend on two factors. One is the 68

72 D. Dai, S. He / Optics Communications 247 (2005) diffraction angle difference Dh q dr. The other factor is the coupled power c q to the higher order modes. Thus, to reduce the multimode effects, one solution is to modify the angle difference Dh q dr by choosing the FPR thickness appropriately. Another solution is to adjusting the parameters of the input/output waveguides for a fixed FPR to minimize the power c q coupled to higher order modes. First we consider the first solution. Define a relative angle deviation e q ¼ Dh q dr =Dh ch, where Dh ch is the angle separation between the adjacent channels of k and k + Dk ch For the wavelength k + Dk ch one has n 0 s K½sin h in þ sinðh 0 dr þ Dh chþš ¼ Mðk þ Dk ch Þ: ð16þ From the above equation and Eq. (11) with q =0, one obtains the following angle separation Dh ch : Dh ch Dk ch k sin h in þ sin h 0 dr : ð17þ cos h 0 dr In the above equation the approximations of cosðdh ch Þ1 and sinðdh ch ÞDh ch are used since Dh ch 1. From Eqs. (15) and (17), one obtains e q ¼ Dnq n q s Dk ch : ð18þ k Substituting Eq. (14) into the above equation, one obtains qðq þ 2Þ k e q ¼ : 8n q s n 2 ðw e =kþ 2 Dk ch ð19þ For a strongly confined FPR, the effective index n q s (q = 0,1) can be approximated with the refractive index n 2 for the core layer (cf. Eq. (13)), and W e can be approximated with the thickness H of the core layer. Thus, one obtains e q ¼ qðq þ 2Þ 8 k=n 2 H 2 D k ch : ð20þ From the above equation, one sees that the relative angle deviation e q is proportional to the ratio of the channel wavelength k to the channel spacing Dk ch In a DWDM system, the channel spacing Dk ch is usually equal to 0.8 nm (or 1.6 nm), which is much smaller than the channel wavelength k (about 1550 nm). Thus, the ratio (k/dk ch ) is very large and fixed when the channel spacing is determined in the design. The relative angle deviation e q in a SOI-based EDG is much larger than that in a SOI-based AWG since for a SOI-based AWG the relative angle deviation e q is proportional to the channel number [9] (instead of the ratio (k/dk ch )) which is no more than 100 in most cases. Eq. (20) also shows that the relative angle deviation e q is inversely proportional to the square of the thickness H, which is the same as that in a SOI-based AWG. For a SOIbased AWG, one can make the FPR thickness large enough to ensure the relative angle deviation e to be smaller than an allowed value e max and thus the multimode effects is nearly negligible [9]. Similarly, For a SOI-based EDG, one has qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi H > k qðqþ2þ k 1 n 2 8 Dk ch e max from Eq. (20) with the requirement of e < e max. However, if we set e max = 10%, the thickness H has to be larger than 38.3 lm, which is too large for a practical design. Besides, more high-order modes will be excited when the thickness increases. Therefore, this approach is not feasible for a SOI-based EDG. To minimize the influences of the multimode effects on the spectral response, one approach present in [11] for an AWG is to choose an appropriate diffraction order M so that the (M 1)th diffraction angle of the first order mode coincides with the Mth diffraction angle of the fundamental mode, i.e., h 0 dr ¼ h1 dr. With the same idea for an EDG demultiplexer, one has n 1 s Kðsin h in þ sin h 0 drþ¼ðm 1Þk: ð21þ Combining with Eq. (11) for q = 0, one obtains M ¼ n0 s Dn 1 : ð22þ Substituting Eq. (14) with an approximation of W e = H into the above equation, one obtains M 8n2 2 ðh=kþ2 : ð23þ 3 qffiffiffiffiffiffi From this equation, one has H k 3 M n 2. Note 8 that the thickness of the SOI waveguide should be large enough to minimize the coupling loss between the input/output waveguide and the SMFs. Consequently, the diffraction order will be very large according to Eq. (23). Since the maximal 69

73 286 D. Dai, S. He / Optics Communications 247 (2005) number N max of the channels is inversely proportional to the diffraction order, i.e., N < N max ¼ 1 k MDk ch, the number of the available channels is limited. For example, when k = 1.55 lm, n 2 = 3.455, H = lm, and Dk ch = 0.8 nm, one obtains a large diffraction number and a small number of available channels (M = 328 and N max = 6). Furthermore, the fabrication tolerance for this approach is not good and the FPR thickness has to be controlled precisely. Therefore, it is not a good solution to reduce the multimode effects in an EDG. Below we present a more practical solution to reduce multimode effects. Our simulation shows that the power coupled to the higher order modes in FPR can be reduced by optimizing the parameters of the input/output waveguide, thus reducing the multimode effects. Usually the input/output waveguides in an EDG is required to be singlemode. The width and height of the rib should be small enough to satisfy the single mode condition of a SOI rib waveguide [7]. In this paper, we propose to insert a taper between a single mode input/output waveguides and the FPR (see Fig. 2) so that the rib width at the slab interface can be modified freely, while keeping the rib width of the input/output waveguides under the single mode condition. By optimizing the width W tp of the taper structure, the power coupled to the higher order modes can be minimized and thus the multimode effects can be reduced. 3. Numerical results and discussions As a numerical example, we choose the thickness of the SOI waveguide H = 5lm. The refractive indices of the air, silica, and silicon are given as n 1 = 1.0,n 2 = 3.455,n 3 = 1.46, respectively (see Fig. 2). The wavelength k c = 1550 nm. Since the waveguide in a PLC is required to be singemode, we choose the rib height h r =2lm in our design. The taper should be long enough to be adiabatic, and thus we choose the taper length L tp = 1000 lm. Fig. 3 shows the powers (c 0, c 1 and c 2 ) coupled to the fundamental and higher order (q = 1,2) modes as the taper widths W tp varies. The power of the input field E in (x,y,k) is unity, i.e., R þ1 1 E inðx; y; kþe in ðx; y; kþ dx dy ¼ 1. The power coupled to the qth order mode is calculated by using Eq. (2) with q =0,1,2.FromFig. 3, one can see that the coupled power c 2 is much smaller than the coupled power c 1. The sum P c q of the coupled power for all the higher orders (q >1)is also shown in Fig. 3 (see the dotted-dashed curve). This justifies that the cumulative effects of all the higher orders (q > 1) are small enough to neglect compared to the coupled power c 1 in our case. Therefore, in the following part we only consider the powers (c 0 and c 1 ) coupled to the fundamental and first order modes. Since c 0 + c 1 1, the coupled powers c 1 and c 0 vary with opposite trends as shown in Fig. 3. The excess loss becomes max- z y FPR Air:n 1 Taper W tp W r Si:n 2 L tp SiO 2 :n 3 H h r x Fig. 2. Configuration for the taper connecting the input/output waveguide and the FPR. 70

74 D. Dai, S. He / Optics Communications 247 (2005) c H =5μm, h r =2μm c q (q>1) W tp(μm) c 2 c c1, c2 Fig. 3. The coupled powers as the taper width W tp increases for the case of h r =2lm. Power db Ch 0 Ch 6 Crosstalk Wavelength (μm) Fig. 4. The spectral response of the 0th and 6th channels for the case of W tp = 3.0 lm. imal when the coupled power c 0 (c 1 ) reaches the minimum (maximum) value since only the power c 0 coupled to the fundamental mode is received by the intended channel and the coupled power c 1 is received by unintended channels (resulting in crosstalk). From Fig. 3, one sees that when the taper width W tp increases the coupled power P c 0 increases and the cumulative effects cq (q > 1) decreases. For a small taper width (e.g., W tp <8 lm), the coupled power c 0 increases quickly as the width W tp increases. When W tp >8 lm, the coupled power c 0 increases slightly and approaches 1.0. For example, the values of the minimum coupled power c 0 are 0.822, and when W tp = 3, 6, and 14 lm, respectively. It is therefore an effective method of improving the coupled power c 0 (i.e., reducing the multimode effects) by increasing the taper width. In the following numerical example, the following parameters for the EDG demultiplexer are used. The central wavelength k c = 1550 nm, the channel spacing Dk ch = 0.8 nm (i.e., 100 GHz in the frequency domain), the radius of the Rowland circle R = 20,000 lm, the grating angle a = 55.0 (see Fig. 2), the diffraction order m = 36, and the total number of the facets is The distance between neighboring output waveguides is about lm. First we consider the case of W tp = 3.0 lm. Fig. 4 shows the spectral responses for the designed EDG demultiplexer. The shaded regions correspond to the ITU passband [k i Dk ch /8, k i + Dk ch /8], where k i is the central wavelength of the ith channel. This figure shows that the spectral response has two peaks. In addition to the main peak corresponding to the fundamental mode, there is a minor peak corresponding to the first order mode, which is very significant. For the ith channel, a considerable crosstalk is resulted from the (i 6)th and (i 5)th channels in this numerical example. For example, for the central channel (i = 0), the crosstalk due to multimode effects produced by the 6th channel is about 21 db (shown in Fig. 4). From Fig. 3, one sees that c 0 = , c 1 = when W tp = 3.0 lm. Thus the excess loss due to the multimode effect can be determined by L =2 10logc 0 = 1.70 db. The total insertion loss of the spectral response shown in Fig. 4 is about 1.91 db, including the loss due to the power spilling over the reflective grating (the spilling loss L sp is about 0.2 db in this example). From Fig. 3, one sees that when a larger taper width is chosen the coupled power c 0 (c 1 ) will increase (decrease) and thus multimode effects can be depressed. For example, when W tp = 6.0 lm, one has c 0 = and c 1 = Thus, the excess loss is about db, much smaller than that for the case of W tp = 3.0 lm. The spilling loss L sp is almost the same as that for the case of W tp = 3.0 lm, i.e., L sp = 0.2 db. Thus, a predicted total excess loss is about db. 71

75 288 D. Dai, S. He / Optics Communications 247 (2005) The corresponding spectral response for this case is shown in Fig. 5. The crosstalk due to multimode effects (from the 6th channel) is about 38 db, which is reduced greatly compared to the crosstalk for the case of W tp = 3.0 lm. Fig. 6 shows the 3 db passband width Dk 3dB as the taper width varies. From this figure, one sees there is a minimal value for Dk 3 db when W tp = 4.0 lm. When W tp > 4.0 lm, the bandwidth Dk 3dB increases monotonously as the taper width W tp increases. It is well known that a larger 3 db passband width is desirable for a device to be more insensitive to a wavelength change. From this point of view, one should choose a large taper width to obtain a large 3 db passband width. However, increasing the taper width further will result in a larger crosstalk between adjacent channels (as shown in Fig. 7). In Fig. 7, the curve with squares is for the crosstalk due to the coupling between adjacent channels (output waveguides). From this curve one sees that the crosstalk from adjacent channels is minimal when W tp =6 lm. This crosstalk first decreases and then increases as the taper width W tp increases from 3 to 14 lm. This can be explained with Fig. 8 for the field profiles of a 0 (x) at the exit of the taper when 0 Ch 0 Ch -6 Crosstalk from multimode effects Power (db) Crosstalk (db) from adjacent channels Wavelength (μm) Fig. 5. The total spectral response of the 0th and 6th channels for the case of W tp = 6.0 lm W tp (μm) Fig. 7. The crosstalk as the taper width varies dB/ ch (%) a0(x) W tp =3μm W tp =6μm W tp =14μm W tp (μm) Fig. 6. The 3 db passband width as the taper width varies x(μm) Fig. 8. The field profile a 0 (x) at the exit of the taper. 72

76 D. Dai, S. He / Optics Communications 247 (2005) Power (db) Wavelength (μm) W tp = 3, 6 and 14 lm. From this figure one sees that the fields a 0 (x) for W tp = 3 and 14 lm penetrate to the sides deeper (which causes larger crosstalks) than the field for W tp =6lm does. In Fig. 7, the other curve with circles is for the crosstalk due to multimode effects. One sees that the crosstalk due to multimode effects decreases monotonously when the taper width increases. This is consistent with the fact that the coupled power c 1 decreases when the taper width increases (see Fig. 3). The two curves intersect at W tp =11lm. When W tp <11lm, the crosstalk caused by multimode effects is larger than that from adjacent channels. When W tp >11 lm, the crosstalk from adjacent channels is larger than that caused by multimode effects. When W tp =11 lm, the two crosstalks are equal. Thus, we choose the taper width W tp =11lm as an optimal design to minimize the crosstalk. The corresponding spectral response of the central output waveguide is shown in Fig. 9, from which one sees that these two crosstalks are almost the same (about 52 db; the shaded vertical bars in Fig. 9 indicate the positions of various channels). 4. Conclusion Crosstalk (multimode) Crosstalk (adjacent) Fig. 9. The spectral response at the central output waveguide when W tp =11lm. In the present paper, we have considered a SOI-based EDG demultiplexer with a multimode FPR that has the same thickness of silicon core layer as the input/output SOI rib waveguides. The multimode effects in the FPR have been analyzed in detail on the basis of the grating equation for the EDG. We have shown that the multimode effects in an EDG are more serious than that in an AWG demultiplexer. A remarkable excess loss and crosstalk are produced. Our simulation results have shown that the power coupled to the first order mode can be reduced when the width of the input/output waveguide increases. A laterally tapered structure has thus been proposed between the input/output waveguides and the FPR, while the rib width of the input/output waveguides remains small enough to satisfy the single mode condition. The taper width has been optimized to minimize the total crosstalk including the crosstalk caused by multimode effects and the crosstalk due to the coupling of adjacent channels. Acknowledgments This work was supported by a research grant (No. 2004C31G ) of the provincial government of Zhejiang Province of China, and the National Science Foundation of China (No ). References [1] M.K. Smit, C.V. Dam, IEEE J. Sel. Top. Quantum Electron. 2 (2) (1996) 236. [2] J. Song, D. Pang, S. He, Opt. Commun. 227 (2003) 89. [3] J.-J. He, IEEE J. Sel. Top. Quantum Electron. 8 (6) (2002) [4] J.-J. He, B. Lamontagne, A. Delage, L. Erickson, M. Davies, E.S. Koteles, J. Lightwave Technol. 16 (4) (1998) 631. [5] J.-J. He, E.S. Koteles, B. Lamontagne, L. Erickson, A. Delage, M. Davies, IEEE Photon. Technol. Lett. 11 (2) (1999) 224. [6] U. Fischer, T. Zinke, J.-R. Kropp, F. Arndt, K. Petermann, IEEE Photon. Technol. Lett. 8 (5) (1996) [7] S. Lvescan, A. Vonsovici, J. Lightwave Technol. 16 (10) (1998) [8] P.D. Trinh, S. Yegnanarayanan, F. Coppinger, B. Jalali, IEEE Photon. Technol. Lett. 9 (7) (1997) 940. [9] D. Dai, S. He, Appl. Opt. 42 (24) (2003)

77 290 D. Dai, S. He / Optics Communications 247 (2005) [10] S. Janz, A. Balakrishnan, S. Charbonneau, P. Cheben, M. Cloutier, A. Delâge, K. Dossou, L. Erickson, M. Gao, P.A. Krug, B. Lamontagne, M. Packirisamy, M. Pearson, D.-X. Xu, IEEE Photon. Technol. Lett. 16 (2) (2004). [11] S.R. Park, B.H. O, S.G. Lee, E.H. Lee, Proc. SPIE 4904 (2002) 345. [12] Zhimin Shi, Sailing He, IEEE J. Sel. Top. Quantum Electron. 8 (6) (2002) [13] L.B. Soldano, E.C.M. Pennings, J. Lightwave Technol. 13 (4) (1995) 615. [14] M.R.T. Pearson, A. Bezinger, A. Delage, J.W. Fraser, S. Janz, P.E. Jessop, D.-X. Xu, Proc. SPIE 3953 (2000)

78 IEEE JOURNAL OF SELECTED TOPICS IN QUANTUM ELECTRONICS, VOL. 11, NO. 2, MARCH/APRIL Elimination of Multimode Effects in a Silicon-on-Insulator Etched Diffraction Grating Demultiplexer With Bi-Level Taper Structure Daoxin Dai, Jian-Jun He, Senior Member, IEEE, and Sailing He, Senior Member Abstract Multimode effects in the free propagation region (FPR) of an etched diffraction grating (EDG) demultiplexer based on silicon-on-insulator are analyzed. The insertion loss and the crosstalk increase due to these undesired multimode effects. A bi-level taper structure between the FPR and the input/output waveguides is proposed. It is shown that such a taper structure can reduce the multimode effects to an almost negligible level. At the same time, the 3-dB passband width is enlarged by increasing the rib width. No additional fabrication process is needed for an EDG with such a design. Index Terms Air slot, crosstalk, etched diffraction grating (EDG), insertion loss, multimode effect, silicon-on-insulator (SOI), taper. I. INTRODUCTION DENSE wavelength-division multiplexing (DWDM) technology has become an essential part of an optical communication system. Multiplexers/demultiplexers based on the integrated planar lightwave circuit (PLC) technologies have been widely used due to their compactness, high performance, and reliability. Arrayed waveguide gratings (AWGs) [1], [2] and etched diffraction gratings (EDGs) [3] [5] are two common types of planar waveguide demultiplexers. Many kinds of optical waveguide structures for PLCs have been developed, such as buried waveguides, rib waveguides, and strip-loaded waveguides. The most popular materials used for PLCs are Si, SiO, GaAs, InP, etc. Recently, it has been demonstrated experimentally that the propagation loss of a planar and rib waveguide based on silicon-on-insulator (SOI) can be lower than 0.1 db/cm [6] within the infrared wavelength window ranging from 1.2 to 1.6 m. This offers a tremendous potential for fabricating low-cost PLC devices including AWG/EDG demultiplexers [7]. Manuscript received July 15, 2004; revised February 21, This work was supported in part by provincial government of Zhejiang Province of China under Research Grant 2004C31095 and in part by the National Basic Research Program of China under Grant 2004CB D. Dai and S. He are with the Centre for Optical and Electromagnetic Research, State Key Laboratory of Modern Optical Instrumentation, Joint Research Center of Photonics of the Royal Institute of Technology (Sweden) and Zhejiang University, Zhejiang University, Hangzhou, China and also with the Division of Electromagnetic Theory, Alfven Laboratory, Royal Institute of Technology, S Stockholm, Sweden ( daoxin@imit.kth.se; sailing@kth.se). J.-J. He is with Lightip Technologies, Inc., Ottawa, ON K1K 4R8, Canada and also with the Department of Optical Engineering, Zhejiang University, Hangzhou, China ( jj.he@lightip.com). Digital Object Identifier /JSTQE For a SOI-based PLC device, a single mode SOI rib waveguide with a large cross section [8] is usually desirable to obtain a high coupling efficiency with a single mode fiber (SMF). The thickness of the silicon layer for such a singlemode rib SOI waveguide is usually chosen to be 3 11 m. Since there is a large difference in the refractive index between silicon (about 3.455) and silicon oxide (about 1.46), the free propagation region (FPR) will support more than one mode if one chooses the same thickness of the silicon layer for the FPR as for the rib waveguide. Since the propagation constants (the effective refractive indexes) are different for different modes of the FPR, multiple images will be formed at the image plane, each corresponding to a FPR mode. This results in an increased insertion loss and channel crosstalk since the energy of the higher-order modes will be coupled to unintended channels. These multimode effects in a SOI-based AWG demultiplexer have been analyzed in our previous work [9]. For an EDG, the optical path length difference between adjacent grating facets, which determines the properties of the grating, is related to the effective index of the FPR (instead of the rib waveguide as in the case of an AWG). Thus, a multimode FPR in an EDG will cause more serious problems than that in an AWG. One approach to remedy the multimode problem is to choose an appropriate diffraction order so that the th diffraction angle of the first-order mode coincides with the th diffraction angle of the fundamental mode [10]. However, the diffraction order in this case is usually very large, which makes the free spectral range too small, thus, limiting the total number of the channels for a DWDM system. In this paper, we propose a bi-level taper structure between the FPR and the input/output waveguides to reduce the multimode effects. Spectral responses are calculated by taking into account the multimode property of the FPR, and a detailed analysis for such multimode effects is given. II. THEORY An EDG consists of a curved grating, an input waveguide, output waveguides and an FPR [see Fig. 1(a)]. It is usually based on a Rowland circle construction [4]. Fig. 1(c) is an enlarged view of the taper structure at the junction between the input and FPR. The coordinate system is chosen as shown in Fig. 1(c) with plane in the middle of the Si layer of the FPR. The field launched from the end facet of the input waveguide to the FPR is diffracted by each grating facet. It is then refocused on X/$ IEEE 75

79 440 IEEE JOURNAL OF SELECTED TOPICS IN QUANTUM ELECTRONICS, VOL. 11, NO. 2, MARCH/APRIL 2005 where is the excitation coefficient for the th-order mode, is the number of modes supported in the FPR. If the field is normalized (i.e.,, the power coupled to the th-order mode is given by the following integral: where the superscript represents the complex conjugate. For a conventional design, the multimode effects in an EDG demultiplexer introduce an excess insertion loss at the junction between the FPR and the input/output waveguides. The introduced total excess loss in a SOI-based EDG is double of this amount due to the passage of two junctions. The introduced crosstalk depends on not only the coupled power but also on the focus position of the higher order modes. The coefficient can be obtained by using the following overlap integral formula: (2) With the two-dimensional (2 D) Kirchhoff-Huygens diffraction formula [11], one can calculate the field distribution at the image plane. One then obtains the spectral response by using an overlapped integral formula (3) Fig. 1. Schematic configuration. (a) The structure of an EDG demultiplexer. (b) The structure for the top taper. (c) An enlarged view of the taper structure at the junction between the input (or output) and the FPR. the imaging curve and guided into different output waveguides according to the wavelength. Since the FPR supports more than one mode, higher-order modes will be excited when the light enters the FPR from a singlemode rib waveguide. An input field profile, which is usually the fundamental mode of the input waveguide, can be decomposed into the field distribution of all modes in the FPR ( denotes the order of the guided mode for the FPR slab waveguide) [9], i.e., (1) where is fundamental mode field of the output waveguide. If the coupled power or the difference between the propagation constants is small enough, the multimode effects is negligible. However, the difference between the propagation constants is fixed accordingly when the thickness of the FPR is chosen. Thus, the solution is to reduce the coupled power to the higher order modes by adjusting the parameters of the input/output waveguides. Our simulation shows that the power coupled to the higher order modes can be reduced by increasing the width or the height of the rib of the input/output waveguide. However, the input/output waveguides in an EDG is required to be singlemode. The chosen value for the width should be small enough to satisfy the single mode condition of a SOI rib waveguide [8]. In this paper, we propose a bi-level taper structure between a singlemode input (same for output) rib waveguide and the FPR [see Fig. 1(c)]. This bi-level taper includes double-layered tapers at the top and the bottom. One can use a cosine, parabolic, or linear taper. In this paper, a linear taper is used. The width of the input rib waveguide is tapered gradually to a large value (from to ) by the top lateral taper, which is formed by the first etching process [see Fig. 1(b)]. Then, the Si region marked by the dashed lines in Fig. 1(b) is etched through in a second etching process so that the bottom taper structure is formed. Through the bottom taper the shallowly-etched SOI rib waveguide becomes a deeply-etched rectangular waveguide 76

80 DAI et al.: ELIMINATION OF MULTIMODE EFFECTS IN A SOI EDG DEMULITPLEXER WITH BI-LEVEL TAPER STRUCTURE 441 TABLE I PARAMETERS FOR THE SOI RIB WAVEGUIDE with the same depth as that of the connecting slab waveguide of FPR [see Fig. 1(c)]. The Si layer is etched through simultaneously for both the grating and the bottom taper structure, and thus no additional fabrication process is required. The entrance width of the bottom taper should be large enough to minimize the scattering loss near the entrance. The lengths ( and ) of the top and bottom tapers do not need to be the same. However, the tapers should be long enough to make the transformation of the modal field adiabatic. With this design, the power coupled to the higher order modes is reduced greatly and, thus, the multimode effects are almost eliminated. It is also very convenient for the fabrication of an EDG with such a design since no additional fabrication process is needed. III. NUMERICAL RESULTS AND DISCUSSIONS As a numerical example, the parameters of the singlemode input/output SOI rib waveguide are chosen as shown in Table I and the corresponding variables are labeled in Fig. 1. The wavelength nm. The powers coupled to the three lowest order modes are shown in Fig. 2(a) and (b), respectively. Fig. 2(a) and (b), respectively, show the power coupled to the lowest three modes as a function of the taper height for different values of the taper width. The power coupled to the th-order mode is calculated using (2) for. Here, the power of the input field is assumed to be unity, i.e.,. To reduce the multimode effects, one needs to maximize the coupled power and minimize and. From Fig. 2(a), one sees that the coupled power increases monotonously when the taper width increases. For a fixed taper width, the power (coupled to the fundamental mode) first decreases and then increases when the taper height increases. In particular, when the ratio (i.e., the rib height is equal to the total thickness of the silicon layer), the rib waveguide becomes a rectangular waveguide, which results in an input field with a nearly even symmetry in the direction. Since the first-order modal field of the FPR slab waveguide has an odd symmetry, the power (coupled to the first-order mode) is almost zero 10. The power (coupled to the second order mode) is slightly larger than, but still very small. In this case, (the power coupled to the fundamental mode) is very close to 1.0 even for different taper widths. Thus, the multimode effects can be reduced effectively by increasing the taper height. However, in order to keep the input/output waveguides single-mode, the rib waveguides need to be etched shallowly. To satisfy both conditions, we introduce a bi-level taper structure [as shown in Fig. 1(c)] between the FPR and the single mode input/output waveguides to reduce the multimode effects. Fig. 2. Powers coupled to the first three order modes in FPR as the taper height h varies: (a) c ; (b) c and c. In this numerical example, the parameters for the designed EDG demultiplexer are given as follows. The central wavelength nm, the channel spacing nm (i.e., 100 GHz in the frequency domain), the radius of the Rowland circle m, the grating angle, the diffraction order, and the total number of the facets is 1051 (the facets are coated with a reflective metallic thin film). The distance between two neighboring output waveguides is about m. First, we consider the case of m and m. From Fig. 2(a) and (b), one sees that the corresponding coupled powers for this case are, and. For each mode, there is a peak in the spectral response. With the grating equation, the position of the peaks for the first- and second-order modes can be predicted to be and m for the central channel ( m). The spectral response of the designed EDG demultiplexer is shown by the dashed curve in Fig. 3. One sees that the spectral response has three peaks. In addition to the main peak corresponding to the fundamental mode, there are two minor peaks corresponding to 77

81 442 IEEE JOURNAL OF SELECTED TOPICS IN QUANTUM ELECTRONICS, VOL. 11, NO. 2, MARCH/APRIL 2005 Fig. 3. Spectral responses of the central channel for the cases of h =2:0 and 5m when W =3:0 m. Fig. 4. Spectral responses of the central channel for h = 5 m when the taper width W =3, 6, and 10 m. the first and the second order modes. The positions of the minor peaks are almost the same as those predicted by grating equation. For the case of m (which is a conventional design), the minor peak corresponding to the first order mode is very significant (about 15.5 db). The other minor peak corresponds to the second-order mode is much smaller (about 57 db). Consequently, a considerable crosstalk for the th channel is produced from the ( -6)th and ( -5)th channels due to the multimode FPR. For example, for the central channel, the crosstalk caused by the -6th channel m) is about db (shown by the dashed curve in Fig. 3). Furthermore, the excess loss is considerable when m. The excess loss due to the multimode effect is determined by db. The spilling loss (i.e., the loss due to the power spilling over the reflective grating) is about 0.2 db. Thus, the total loss is about 1.6 db (as shown by the dashed curve in Fig. 3). By using the bi-level taper structure with with m, we obtain a greatly improved spectral response (as shown by the solid curve in Fig. 3) with respect to the case m. The side peaks corresponding to the first- and second-order modes disappear and only the major peak for the fundamental mode is observed. Furthermore, the adjacent channel crosstalk is also reduced remarkably (below 80 db). The excess loss due to the multimode effect is reduced to nearly 0 db, which is predicted from the coupled powers shown in Fig. 2. However, the 3-dB passband is also reduced greatly since the size of the modal field in the lateral direction is reduced greatly when the rib height increases from 2 to 5 m. A larger 3-dB passband width is desirable (to relax the strict control of wavelength in the DWDM system). The 3-dB passband increases when the size of the fundamental mode field in the lateral direction is enlarged by increasing the taper end width. Fig. 4 shows the spectral responses of the central channel for different taper end widths with m for three different values of the taper width. When, 6, and 10 m, the 3-dB passband widths are about 11%, 21.2%, and 32.5% of the channel spacing (0.8 nm), respectively. Since the input and output waveguides are tapered in the same fashion, the coupled power (very close to 1.0) is insensitive to the taper end width when m (see Fig. 2). Therefore, the insertion losses are almost the same (nearly 0 db) when the taper end width varies. When the taper end width increases, the crosstalk due to the multimode effects still remains very low. IV. CONCLUSION In this paper, we have investigated a SOI-based EDG demultiplexer with a multimode FPR. The silicon core layer has the same thickness for both the FPR slab waveguide and the SOI rib waveguides. A SOI-based EDG demultiplexer has more serious multimode effects than a SOI-based AWG demultiplexer, and this results in significant excess loss and crosstalk if a conventional designs is used. Our simulation have shown that the power coupled to the higher order slab modes can be reduced by increasing the width and height of the SOI rib waveguide. To reduce the multimode effects (while keeping the input/output rib waveguides singlemode), we have proposed a bi-level taper structure between the FPR and the input/output waveguides. Such a taper structure does not introduce any additional fabrication process since and the deeply etched part of the taper structure is etched through together with the reflective grating. With the present design, the power coupled to the higher order modes has been reduced greatly and, thus, the multimode effects have almost been eliminated. At the same time, the 3-dB passband width has also been enlarged by increasing the taper end width. REFERENCES [1] M. K. Smit and C. V. Dam, Phasar based WDM devices: Principles, design, and applications, IEEE J. Sel. Topics Quantum Electron., vol. 2, no. 2, pp , Mar./Apr [2] M. R. Paiam and R. I. MacDonald, Design of phased-array wavelength division multiplexers using multimode interference couplers, Appl. Opt., vol. 36, no. 21, pp , [3] J.-J. He, Phase-dithered waveguide grating with flat passband and sharp transitions, IEEE J. Sel. Topics Quantum Electron., vol. 8, no. 6, pp , Nov./Dec [4] J.-J. He, B. Lamontagne, A. Delage, L. Erickson, M. Davies, and E. S. Koteles, Monolithic integrated wavelength demultiplexer based on a waveguide Rowland circle grating in InGaAsP/InP, J. Lightw. Technol., vol. 16, no. 4, pp , Apr

82 DAI et al.: ELIMINATION OF MULTIMODE EFFECTS IN A SOI EDG DEMULITPLEXER WITH BI-LEVEL TAPER STRUCTURE 443 [5] J.-J. He et al., Integrated polarization compensator for WDM waveguide demultiplexers, IEEE Photon. Technol. Lett., vol. 11, no. 2, pp , Feb [6] U. Fischer, T. Zinke, J.-R. Kropp, F. Arndt, and K. Petermann, 0.1 db/cm waveguide losses in single-mode SOI rib waveguides, IEEE Photon. Technol. Lett., vol. 8, no. 5, pp , May [7] P. D. Trinh, S. Yegnanarayanan, F. Coppinger, and B. Jalali, Silicon-on-insulator (SOI) phased-array wavelength multi/multiplexer with extremely low-polarization sensitivity, IEEE Photon. Techonol. Lett., vol. 9, no. 7, pp , Jul [8] S. Lvescan and A. vonsovici, The single-mode condition for semiconductor rib waveguides with large cross section, J. Lightw. Technol., vol. 16, no. 10, pp , Oct [9] D. Dai and S. He, Analysis of multimode effects in the FPR of a SOIbased AWG demulitplexer, Appl. Opt., vol. 42, no. 24, pp , [10] S. R. Park, B. O., S. G. Lee, and E. H. Lee, The control of multimode effect on an arrayed waveguide grating-device, in Proc. SPIE, vol. 4904, 2002, pp [11] Z. Shi and S. He, A three-focal-point method for the optimal design of a flat-top planar waveguide demultiplexer, IEEE J. Sel. Topic. Quantum Electron., vol. 8, no. 6, pp , Nov./Dec Jian-Jun He (M 95 SM 03) received the Diplome d Etudes Approfondies and Ph.D. degrees in semiconductor optoelectronics from the University of Paris VI, Paris, France, in 1986 and 1989, respectively. From 1986 to 1989, he was with the Centre National d Etudes des Télécommunications, Bagneux, France, as a Doctoral Fellow on acoustooptical devices and the study of light scattering in semiconductor superlattices. He joined the Technical University of Nova Scotia, Halifax, NS, Canada, as a Research Associate in 1989, where he worked on semiconductor nonlinear optical devices. From 1994 to 2000, he was a Research Officer with the Institute for Microstructural Sciences, National Research Council of Canada, Ottawa, ON, working on semiconductor optoelectronic devices for dense-wavelength-division-multiplexing (DWDM) applications. From 2000 to 2002, he was with MetroPhotonics, Inc., Ottawa, where he was the founding Chief Scientist. He is now a Research Scientist and Consultant with Lightip Technologies, Inc., Ottawa. He has published more than 100 scientific papers and holds 11 U.S. patents with a number of additional patents pending. His research interests include is multifunctional integrated optical components and subsystems for optical communications and biophotonics. Dr. He is a Senior Member of the IEEE Lasers and Electro-Optics Society (LEOS) and Member of the Optical Society of America (OSA). Daoxin Dai received the B.Sc. degree in 2000 from the Department of Optical Engineering, Zhejiang University, Hangzhou, China, where he is currently working toward the Ph.D. degree. His research interests include the design, simulation, and fabrication of dense wavelength-division multiplexing devices. Sailing He (M 92 SM 98) received the Licentiate of Technology and the Ph.D. degree from the Royal Institute of Technology, Stockholm, Sweden, in 1991 and 1992, respectively. Since obtaining the Ph.D. degree, he has been with the Royal Institute of Technology, consecutively, as an Assistant Professor, Associate Professor, and Full Professor. Since 1999, he has also been with Zhejiang University, Hangzhou, China, as a Special Professor appointed by the Ministry of Education of China. He is currently a Chief Scientist for both the Joint Research Center of Photonics, Royal Institute of Technology, and Zhejiang University. He has authored one monograph (Oxford, U.K.: Oxford University Press, 1998), authored/co-authored about 200 papers in refereed international journals, and has been granted a dozen of patents. 79

83 Optics Communications 270 (2007) Three-dimensional hybrid modeling based on a beam propagation method and a diffraction formula for an AWG demultiplexer Daoxin Dai a,b,c, *, Liu Liu a,b,d, Sailing He a,b,c a Centre for Optical and Electromagnetic Research, State Key Laboratory for Modern Optical Instrumentation, Zhejiang University, Hangzhou , China b Joint Research Center of Photonics of the Royal Institute of Technology (Sweden) & Zhejiang University, East Building No. 5, Zijingang Campus, Zhejiang University, Hangzhou , China c Division of Electromagnetic Theory, Alfven Laboratory, Royal Institute of Technology, S Stockholm, Sweden d Laboratory of Photonics and Microwave Engineering, Department of Microelectronics and Information Technology, Royal Institute of Technology, S Kista, Sweden Received 20 February 2006; received in revised form 27 July 2006; accepted 30 August 2006 Abstract An efficient and accurate three-dimensional (3D) hybrid modeling, which combines a 3D beam propagation method (BPM) and the two-dimensional (2D) Kirchhoff Huygens diffraction formula, is developed to simulate the field propagation in an arrayed waveguide grating (AWG) demultiplexer. The 2D Kirchhoff Huygens diffraction formula is used for the simulation of the light propagation in the free propagation regions (FPRs). A 3D BPM in a polar coordinate system is used to simulate the light propagation in the transition region between the input FPR and the arrayed waveguides so that the coupling coefficients for the arrayed waveguides are calculated conveniently and accurately. For the simulation in the transition region between the arrayed waveguides and the output FPR, only the central arrayed waveguide and several adjacent ones are needed in the computational window of a standard BPM and thus the computation efficiency is improved. Finally, a flat-top AWG is designed and fabricated to verify the reliability of the present simulation method. The calculated and measured spectral responses are in a good agreement. Ó 2006 Elsevier B.V. All rights reserved. PACS: Gn; Sz Keywords: Arrayed waveguide grating; Hybrid method; Kirchhoff Huygens diffraction; Beam propagation method; Polar coordinate; Flat-top 1. Introduction Arrayed-waveguide grating (AWG) demultiplexers [1] have played a very important role in a wavelength division multiplexing (WDM) system. A good design for an AWG depends on an effective simulation tool and method. There have been several common methods developed to estimate * Corresponding author. Address: Centre for Optical and Electromagnetic Research, State Key Laboratory for Modern Optical Instrumentation, Zhejiang University, Hangzhou , China. Tel.: x215; fax: address: ddxopt@yahoo.com.cn (D. Dai). the performances of an AWG demultiplexer, such as the 1:1 imaging method [2], the Fourier optics method [3 5], and the beam propagation method (BPM) [6]. The accuracy of the 1:1 imaging method is not good due to the assumption of perfect imaging. When the Fourier optics method is used, the coupling coefficient for each arrayed waveguide (i.e., each waveguide in the array) is obtained by overlapping the far field (at the entrance of the waveguide array) in the free propagation region (FPR) and the fundamental modal field of an arrayed waveguide [7]. However, the overlapping method (using the fundamental modal field of a single waveguide) is not accurate when the separation between two adjacent arrayed waveguides /$ - see front matter Ó 2006 Elsevier B.V. All rights reserved. doi: /j.optcom

84 196 D. Dai et al. / Optics Communications 270 (2007) is not large enough (e.g., comparable to the diameter of the modal spotsize) to ignore the evanescent coupling between them. BPM is an accurate and popular tool for simulating the light propagation in a planar lightwave circuit (PLC). A three-dimensional (3D) BPM simulation for an AWG demultiplexer requires a tremendous computational effort due to the very large scale (compared with the wavelength). Therefore, few 3D-BPM simulation results for an AWG have been reported [8,9]. Furthermore, one can only obtain the field distribution at planes perpendicular to the propagation direction when using a standard BPM. Since the arrayed waveguides are along the radical direction at the two ends, only one arrayed waveguide (usually the central one) can be parallel to the propagation direction and consequently all the other arrayed waveguides are tilted. For the other arrayed waveguides (which are tilted), it is not convenient to get the corresponding coupling coefficients since the field distributions of the fundamental mode for arrayed waveguides with different tilted angles are different in the coordinate system used for the BPM simulation. The tilting of the arrayed waveguides causes the same inconveniences when the initial field is constructed for the BPM simulation in the output FPR. Therefore, one sees that a standard BPM is not good for obtaining the coupling coefficients for the arrayed waveguides. In this paper, we present a hybrid simulation method which combines a 3D BPM [8] and a two-dimensional (2D) Kirchhoff Huygens diffraction formula. The BPM is used for the simulation of the light propagation in the transition region between the FPRs and the input/output/arrayed waveguides. After a field decomposition [7], the 2D Kirchhoff Huygens diffraction formula is used to obtain the far field in the input/output FPR. To avoid the inconvenience of the tilted arrayed waveguides mentioned above, a 3D BPM in a polar coordinate system [10] is used for the simulation of the light propagation in the transition region between the input FPR and the starting straight sections of the arrayed waveguides (see Fig. 1). Consequently, the coupling coefficient for each arrayed waveguide is calculated conveniently and accurately. Meanwhile, the coupling between the arrayed waveguides is included in the simulation. The phase induced by the bent sections of the arrayed waveguides can be either estimated approximately through the waveguide length or calculated with an accurate method (see e.g. [11]). In the output FPR, the total far field is the sum of the far field radiating from each arrayed waveguide and thus we can consider the arrayed waveguides individually. We choose a coordinate system whose z-axis (the propagation direction of the standard BPM) is parallel to the arrayed waveguide considered. Since the arrayed waveguides are arranged uniformly along the Rowland circle, the field (calculated with BPM in the chosen coordinate system) at a plane (near the exit of the waveguide array) in the FPR is the same for different arrayed waveguides when a normalized initial field is launched [9]. Therefore, one only needs to carry out the BPM simulation once. Then the BPM-calculated field is modulated by the coupling coefficient (obtained previously for the input FPR) and the phase delay for the arrayed waveguide considered. From the modulated field, one can calculate the corresponding far field in the output FPR by using a 2D Kirchhoff Huygens diffraction formula. Using this procedure, one obtains the field distribution at the image plane or a plane perpendicular to the direction of the output waveguide considered. Then this field can be used as the initial field in the BPM simulation for the output section to obtain the output power from the output waveguide. If no special structure (e.g., a taper) is connected at the end of the output waveguide, one can obtain the output power from each output waveguide by simply overlapping the field at the image plane and the fundamental field of the output waveguide. Finally the spectral response can be obtained by scanning the wavelength. 2. Theory y x θ L z A P(x, y, z) R' L FPR B x' C An AWG demultiplexer consists of arrayed waveguides, input waveguides, output waveguides and two FPRs. The input and output apertures of the waveguide array are of Rowland type [1]. The ends of the arrayed waveguides are located uniformly at a circle (with the FPR length as its radius). The present simulation method for an AWG demultiplexer is divided into three parts, i.e., the part for the input FPR, the part for the decoupled arrayed waveguides, and the part for the output FPR. The part for the decoupled arrayed waveguides introduces only a linearly modulating phase and is very simple to treat. Therefore, in the rest part of this section, we focus on the simulation of the light propagation in the parts for the input and output FPRs. D l=n d' g l=1 Fig. 1. Schematic configuration and the polar coordinate system for the field propagation in the part for the input FPR. r z 81

85 D. Dai et al. / Optics Communications 270 (2007) The part for the input FPR A given input field E in (x, y) (at plane z = 0) from an input waveguide can be decomposed into the field distributions u FPR q ðyþ of all modes in the FPR (q denotes the order of a guided mode for the FPR slab waveguide), i.e., E in ðx; yþ ¼ XQ 1 q¼0 a q ðxþu FPR q ðyþ; ð1þ where a q (x) is the excitation coefficient for the qth order mode, Q is the total number of the guided modes supported in the FPR. Then the field distribution at point P(x, y, z) can be written as a superposition of all the modal fields in the FPR, E far ðx; y; zþ ¼ XQ 1 q¼0 a far q ðx; zþufpr q ðyþ; ð2þ where the far field a far q ðx; zþ is given by the following 2D Kirchhoff Huygens diffraction formula [7]: q ðx;zþ¼ i qffiffiffiffiffiffiffiffiffiffiffiffiffiffi a far k=n FPR q Z þx =2 X =2 a q ðx 1 Þ expð infpr q krþ pffiffi r cosh in þ cosh dr dx 1 ; 2 where X is the width of the input field, h in is the incident angle, h dr is the diffraction angle and h dr =tan 1 [(x x 1 ]/z], r =[(x2x 1 ) 2 1z 2 ] 1/2, k is the wavelength in vacuum, k = 2p/k, and n FPR q is the effective index for the qth order guided mode in the FPR. In our case, cos h in = 1 (see Fig. 1) and consequently one has q ðx; zþ ¼ i qffiffiffiffiffiffiffiffiffiffiffiffiffiffi a far k=n FPR q Z þx =2 X =2 1 þ cos h dr dx 1 : 2 a q ðx 1 Þ expð infpr q krþ pffiffi r Let (x S, y, z S ) denote the x and z coordinates for point S(R 0, y, h) at arc AB shown in Fig. 1. The one has x S ¼ R 0 sin h; ð5þ z S ¼ R 0 cos h; where R 0 is the radius of arc AB. Therefore, the field distribution at point S is given by E AB ðr 0 ; y; hþ ¼E far ðx S ; y; z S Þ: ð6þ This field distribution is used as the initial field for the BPM simulation (in the polar coordinate system) in the arrayedwaveguide section to obtain the field distribution E CD (h, y) at arc CD (r = L z ). Here length L z is chosen to be long enough so that the arc separation d 0 g (at arc CD) between two adjacent arrayed waveguides is large enough to ignore the coupling between them. From the geometrical configuration shown in Fig. 1, one has d 0 g ¼ d gl z =L FPR. Since arc CD is perpendicular to all arrayed waveguides, one can easily obtain the coupling coefficient g l for the lth arrayed waveguide from the BPM-calculated field as follows: ð3þ ð4þ g l ¼ Z þ1 Z ld 0 g þd 0 g =2 1 ld 0 g d0 g =2 E CD ðx 0 =L z ; yþe AW ðx0 ld 0 g ; yþdx0 dy; ð7þ where E AW (x, y) is the modal field of the lth arrayed waveguide The part for the output FPR In the xz coordinate system shown in Fig. 2, one obtains the field E ðcþ MN ðx; yþ at the plane M cn c by launching a normalized field into the central arrayed waveguide. Since the arrayed waveguides are arranged uniformly along the Rowland circle, the field distribution at plane M l N l in the x 00 z 00 coordinate system will be E ðcþ MN ðx00 ; yþ if a normalized field is launched into the lth arrayed waveguide. Therefore, by modulating E ðcþ MN ðx00 ; yþ with the corresponding amplitude g l and phase / l, one obtains the following field at plane M l N l : E ðlþ MN ðx00 ; yþ ¼g l E ðcþ MN ðx00 ; yþ expð i/ l Þ; ð8þ where / l = / 0 + l2pn g DL/k (where / 0 is the phase introduced by the shortest arrayed waveguide, n g is the effective y x N l x x' x'' M l M c N c z' z o θ dr z θ l R' Image plane S P Q y z z'' Fig. 2. Schematic configuration for the field propagation in the part of the output FPR: (a) the structure for the BPM simulation; (b) the structure for the calculation with a 2D Kirchhoff Huygens diffraction formula. 82

86 198 D. Dai et al. / Optics Communications 270 (2007) refractive index for the fundamental mode of the arrayed waveguide, DL is the length difference between two adjacent arrayed waveguides). Note that one can also calculate phase / l with an accurate method (see e.g. [11]). The transformation relations between the xz and x 00 z 00 coordinate systems is given by the following formulas: x 00 ¼ðx x l Þ cos h l þðz z l Þ sin h l ; ð9aþ z 00 ¼ ðx x l Þ sin h l þðz z l Þ cos h l ; x ¼ x 00 cos h l z 00 sin h l þ x l ; ð9bþ z ¼ x 00 sin h l þ z 00 cos h l þ z l ; where x l ¼ R 0 sin h l ; ð10þ z l ¼ R 0 ð1 cos h l Þ: The obtained field E ðlþ MN ðx0 ; yþ is then decomposed into the field distribution u FPR q ðyþ of all modes in the FPR, i.e., E ðlþ MN ðx00 ; y 00 Þ¼ XQ 1 q¼0 a ðlþ q ðx00 Þu FPR q ðyþ; ð11þ where a ðlþ q ðx00 Þ is the excitation coefficient for the qth order mode. The coefficient a ðlþ q ðx00 Þ can be obtained by using the following overlap integral formula: a ðlþ q ðx00 Þ¼ Z þx =2 E ðlþ X =2 ¼ g l expð i/ l Þ MN ðx00 ; yþu FPR ðyþ dy q Z þx =2 X =2 ¼ g l expð i/ l Þa q ðx 00 Þ; where a q ðx 00 Þ¼ R þx =2 X =2 E ðlþ MN ðx00 ; yþ is given by E ðlþ EðcÞ E ðcþ MN ðx00 ; y 00 Þu FPR q ðyþ dy ð12þ MN ðx00 ; yþu FPR ðyþdy. Then the field MN ðx00 ; y 00 Þ¼g l expð i/ l Þ XQ 1 a q ðx 00 Þu s q ðyþ: q¼0 q ð13þ The field distribution at point (x 00, y, z 00 ) can be written as a superposition of all the modal fields in the FPR, E ðlþ far ðx00 ; y; z 00 Þ¼g l expð i/ l Þ XQ 1 q¼0 a far q ðx00 ; z 00 Þu FPR q ðyþ: ð14þ Here a far q ðx00 ; z 00 Þ can be obtained by using the 2D Kirchhoff Huygens diffraction formula (3) with h in = 0. Therefore, the excited field at plane PQ for the lth arrayed waveguide is given by E ðlþ PQðx; y; zþ ¼EðlÞ far ðx00 S ; y; z00 S Þ ¼ g l expð i/ l Þ XQ 1 q¼0 a far q ðx00 S ; z00 S ÞuFPR q ðyþ; ð15þ where ðx 00 S ; z00 SÞ is the coordinate for an arbitrary point S at plane PQ in thex 00 z 00 coordinate system. The transformation relation between (x, z) and ðx 00 S ; z00 SÞ is given by Eq. (9a). The total field at plane PQ is given by the following sum: N E PQ ðx; y; zþ ¼ X WG 1 E ðlþ PQðx; y; zþ; ð16þ l¼0 where N WG is the total number of the arrayed waveguides. If a BPM is used for the simulation of the light propagation in the output section of an AWG, the initial field needs to be determined first. In this case, the wavelength-dependent field at plane PQ with z = z o is calculated by using Eqs. (15) and (16) with the following transformation relation: x 00 S ¼ðx x lþ cos h l þðz o z l Þ sin h l ; z 00 S ¼ ðx x lþ sin h l þðz o z l Þ cos h l : From the BPM simulation, one can obtain the output power from each output waveguide. By scanning the wavelength, one obtains the spectral response (i.e., the dependence of the output power on the wavelength). When the separation between tow adjacent output waveguides are large enough to ignore the coupling between them, one can also estimate the output power from each output waveguide by overlapping the wavelength-dependent field at the image plane and the fundamental modal field of the output waveguide. For the image plane with z =[(R/2) 2 x 2 ] 1/2 +(R 0 R/2) (where R = L FPR ), the field distribution is calculated by using Eqs. (15) and (16) with ( x 00 S ¼ðx x lþcosh l þ f½ðr=2þ 2 x 2 Š 1=2 þðr 0 R=2Þ z l gsinh l ; z 00 S ¼ ðx x lþsinh l þ f½ðr=2þ 2 x 2 Š 1=2 þðr 0 R=2Þ z l gcosh l : Since the terms (except/ l ) in Eq. (16) are almost insensitive to P the wavelength in most cases, one only needs to calculate Q 1 g l q¼0 afar q ðx00 S ; z00 S ÞuFPR q ðyþ in Eq. (16) once (instead of repeatedly) when scanning the wavelength. This saves much time and thus improves the computational efficiency. 3. Simulation In the present paper, SiO 2 -on-si buried waveguides are chosen as the channel waveguides (input/output/arrayed waveguides). For the channel waveguide, the width is chosen to be 6 lm. The refractive indices for the core and cladding layers are n co = and n cl = , respectively. For the designed AWG demultiplexer, the diffraction order m = 45, the separations of the arrayed waveguides d g =10lm (or 20 lm), the separation between two adjacent output waveguides d o = lm, the FPR length R = 5000 lm (or 10,000 lm), the central wavelength k 0 = nm, the channel spacing Dk ch = 1.6 nm, and the total number of the arrayed waveguides N WG = 130. Since a flat-top AWG is desirable for a high-speed communication system, we design and fabricate an AWG with a flattened spectral response (see Fig. 3). The input part includes an MMI section and a taper, which is connected at the end of the input waveguide (see Fig. 3(a)). The output part contains a taper inserted between the output FPR and the output waveguide (see Fig. 3(b)). A MMI section 83

87 D. Dai et al. / Optics Communications 270 (2007) taper MMI section C oupling coefficient, l d g =10 m d g =20 m Input waveguide W i W MMI FPR Series number of the arrayed waveguide, l L tp FPR2 W o L tp L MMI taper Output wavegu P hase of l d g =10 m -4 d g =20 m Series number of the arrayed waveguide, l Fig. 4. The coupling coefficient g l when d g =10lm and 20 lm: (a) the amplitude distribution; (b) the phase distribution. Fig. 3. The input/output structures for flattening the spectral response: (a) the input structure between the input waveguide and the input FPR; (b) the output structure between the output FPR and the output waveguide. connected at the end of the input waveguide was used for flattening the spectral response [12]. An explicit analysis based on Fourier transform method was given for a flattop AWG with an MMI section [13]. In this paper, we use a 3D BPM for the simulation of the light propagation in the input part (including an MMI section and a taper, shown in Fig. 3(a)) and obtain the field distribution E in (x, y) (at plane z = 0). In our design the width and the length of the taper are chosen to be 8 lm and 400 lm, respectively. In order to give a comparison, two different MMI designs are considered, i.e., (1) W MMI = 17.8 lm, L MMI = 212 lm; and (2) W MMI = 15.2 lm, L MMI =168 lm. Here the length of the MMI section is chosen so that a twofold image is formed at the end of the MMI section. Fig. 4 shows the amplitude and phase of the coupling coefficient g l for the first MMI design (i.e., W MMI = 17.8 lm, L MMI = 212 lm) when d g =10lm and 20 lm. Here, a linear taper with a length of 400 lm is connected at the end of each arrayed waveguide to reduce the insertion loss due to the gaps between the arrayed waveguides at the ends. The width of the taper is chosen to be 7 lm and 17 lm, respectively, so that the gap between two adjacent arrayed waveguides is larger than 3 lm (the minimal gap is limited by the fabrication process). When the separation is smaller, the coupling between two adjacent arrayed waveguides becomes stronger. Due to this coupling, the coupling coefficient (including the amplitude and phase) changes for different separations as shown in Fig. 4. It is well known that the spectral response is not so sensitive to the amplitude distribution of the coupling coefficient, however, sensitive to the phase distribution. Fortunately, the phase distortion due to the coupling is very small (<0.02 rad). Therefore, as shown in Fig. 5 there is little difference between the field distributions at the image plane for the two different values of d g. Consequently, the spectral responses are almost the same (see Fig. 6(a)). It takes less than 90 min on a PC (Pentium IV, 3.0 GHz) to calculate the spectral responses of all 16 channels. However, when a conventional model based on a 3D BPM is used to calculate the spectral response for the same AWG, it takes more than 10 h. This shows that the present method is much more efficient than the 3D conventional modeling. Fig. 6(b) shows the calculated and measured spectral responses. In order to give a clear comparison, the insertion loss and central wavelength of the simulated spectral response are set at the same values as those of the measured spectral response. The measured insertion loss shown in this figure is about 45 db, which includes the loss of the whole light propagation. The peak of the spectral response of the used ASE light source is about 16 db m. The other loss introduced by the optical components (such as collimation lens, etc.) used in the measurement system is about 23 db. Therefore, the insertion loss of the AWG chip is about 6 db. From Fig. 6 one sees that the present simu- 84

88 200 D. Dai et al. / Optics Communications 270 (2007) Amplitude One sees from Fig. 6 that there is a valley at the top of the spectral response, which indicates the width of the MMI is too large. Therefore, we reduce the MMI width and obtain an optimal design with W MMI = 15.2 lm and L MMI = 168 lm. We fabricate the optimally designed flattop AWG demultiplexer with a standard fabrication process. First a buffer layer (13 lm) and core layer (6 lm) are deposited. The SiO 2 films are deposited with a plasma enhanced chemical vapor deposition (PECVD) technology and the refractive index contrast D = 0.75% (which is realized by Germanium-doping). The core layer with a photoresist mask is etched by using an ICP (inductively coupled plasma) etcher with a gas mixture of C 4 F 8,H 2 and He. An upper cladding (13 lm) is then deposited on the etched core layer. The dimension of the waveguide core is about 6 lm 6 lm. For the measurement of the fabricated AWG chip, we use a broadband ASE (amplified spontaneous emission) light source and the light is butt-coupled to from the light source to the chip. The simulated and measured spectral responses of all channels for the optimal flattop AWG demultiplexer are shown in Fig. 7(a). Here we have removed the loss due to the other components, which is obtained by measuring the received power when the input fiber is directly connected to the output fiber (without the AWG chip). From this figure, one sees that the measured insertion loss of the central channel of the AWG chip is about 6 db. Since the propagation loss of the waveguides and the coupling loss between the single mode fibers and the input/output waveguides are not taken into account in our simulation, the measured insertion loss is larger than the simulated value (as expected). It is well known that the edge channel has a larger insertion loss than the central one in an AWG demultiplexer and consequently non-uniformity is introduced, which is shown clearly in Fig. 7(a). From this figure, one sees that the measured uniformity is slightly different from the simulated results. Fig. 7(b) shows an enlarged view for the spectral responses of the central channel and the two edge channels (in order to give a clear comparison the simulated value is set to have the same top level as the measured value). The shapes of the simulated and measured spectral responses shown in Fig. 7(b) agree well. From this figure, one can also see that the measured spectral responses have much larger sidelobes than the simulation results. This is because the phase error due to non-perfect fabrication is not considered in our simulation. Fig. 7(c) shows the top of the spectral response for the central channel. The result from a 2D model based on a 2D-BPM simulation is also shown in this figure to give a comparison. For the 2D model, an effective index method (EIM) is used to make a 3D structure equivalent to a 2D one first. Then a 2D BPM is used to simulate the light propagation in the path including a singlemode input waveguide, the taper and the MMI section (as shown in Fig. 3), the input FPR, the waveguides in the array, the output FPR, and finally the output waveguide. It takes less than 1 h to calculate the spectral response of one channel by using this 2D simulation (Peny (μ m ) y=0 d g=20μm x (μm) d g=10μm d g=10μm d g=20μm x (μm) Fig. 5. The field distribution at the image plane: (a) the 2D field distribution; (b) the field distribution at y = 0. lation method is accurate and agrees with the experimental result very well, particularly the 1 db passband width and the ripple. (db) Power (db) Power d g=10μm d g =20μm Wavelength (nm) d g=10μm simulation experiment Wavelength (nm) Fig. 6. The spectral response when W MMI = 17.8 lm and L MMI = 212 lm. (a) The simulation results when d g =10lm and 20 lm; (b) the comparison between the simulated and measured results when d g =10lm. 85

89 D. Dai et al. / Optics Communications 270 (2007) a 0-5 simulated measured simulation experiment Spectrum (db) Spectrum (db) Wavelength (nm) Edgechannel Central channel Edgechannel Wavelength (nm) c Spectrum (db) D simulated 3D simulated Measured 1552 Wavelength (nm) 1553 Fig. 7. The comparison between the simulated and measured results for the case of d g =10lm when W MMI = 15.2 lm and L MMI = 168 lm. (a) All the channels; (b) the edge and central channels; (c) enlarged view of the spectral response for the central channel. tium IV, 3.0 GHz). The computational efficiency of the 2D model is higher than the present 3D hybrid model. However, from Fig. 7(c), one sees that the 2D simulation gives a non-flat spectral response, which is not agreeable with the results from the present 3D model and the measured result. Therefore, the present 3D model gives a more reliable simulation result than a 2D model. 4. Conclusion An efficient and accurate 3D hybrid simulation method has been developed in this paper. The 2D Kirchhoff Huygens diffraction formula has been used for the light propagation in the FPRs. The coupling coefficient for each arrayed waveguide has been calculated conveniently and accurately by using a 3D BPM in polar coordinate system. A standard BPM with a small computational window including only several adjacent arrayed waveguides has been used for the simulation in the region connecting the arrayed waveguides and the output FPR. Finally, the reliability of the present hybrid simulation method has been verified by the excellent agreement between the simulated and measured spectral responses for some designed flattop AWG demultiplexers. Acknowledgement This project was supported by China Postdoctoral Science Foundation (No ) and research grants (No , R104154) of the provincial government of Zhejiang Province of China, the National Science Foundation of China (No ). References [1] M.K. Smit, C.V. Dam, IEEE J. Sel. Top. Quantum Electron. 2 (1996) 236. [2] D. Dai, S. Liu, S. He, Q. Zhou, J. Lightwave Technol. 20 (2002) [3] C. Dragonne, J. Lightwave Technol. 7 (1989) 479. [4] C. Dragonne, IEEE Photon. Technol. Lett. 3 (1991) 812. [5] M.E. Marhic, X. Yi, IEEE J. Sel. Top. Quantum Electron. 8 (2002) [6] R. Scarmozzino, A. Gopinath, R. Pregla, S. Helfert, IEEE J. Sel. Top. Quantum Electron. 6 (1996) 150. [7] D. Dai, S. He, J. Opt. Soc. Am. A 21 (12) (2004)

90 202 D. Dai et al. / Optics Communications 270 (2007) [8] R. Scarmozzino, R.M. Osgood Jr., in: Lasers and Electro-Optics Society Annual Meeting (November 10 13, 1997), IEEE Conference Proceedings, vol. 1, 1997, p [9] J.C. Chen,C. Dragone, IEEEPhoton. Technol.Lett. 15(10)(1997)1895. [10] Z. Zhou, D. Wang, S. Lu, Y. Yan, G. Jin, E.Y.B. Pun, Proc. SPIE Int. Soc. Opt. Eng (2001) 101. [11] W.W. Lui, C.-L. Xu, T. Hirono, K. Yokoyama, W.-P. Huang, J. Lightwave Technol. 16 (1998) 910. [12] J.B.D. Soole, M.R. Amerfoort, H.P. LeBlanc, N.C. Andreadakis, A. Rajhel, C. Caneau, R. Bhat, M.A. Koza, C. Youtsey, I. Adesida, IEEE Photon. Technol. Lett. 8 (1996) [13] P. Muñoz, D. Pastor, J. Capmany, Opt. Exp. 9 (2000)

91 Design and fabrication of ultra-small overlapped AWG demultiplexer based on a-si nanowire waveguides D. Dai, L. Liu, L. Wosinski and S. He A novel layout for an ultra-compact arrayed-waveguide grating (AWG) demultiplexer is presented. The present layout has two overlapped free propagation regions, and is more compact than a conventional layout. Using asi-on-sio 2 nanowire waveguides, an ultra-small 4 4AWG (about mm 2 ) with channel spacing of 11 nm is fabricated and characterised. Introduction: Because of their excellent performances and suitability for mass production, photonic integrated devices based on the planar lightwave circuit (PLC) technology are becoming increasingly attractive. The SiO 2 buried rectangular waveguide is one of the most popular waveguides. However, the bending radius of a SiO 2 -based waveguide has to be large (usually several millimetres), even its refractive index contrast increases to a very high value (e.g. D ¼ 2.5%) [1], and this limits the integration density of SiO 2 -based PLCs. The large difference between the refractive indices of Si and SiO 2 (or air) makes silicon-on-insulator (SOI) waveguides a good choice for realising ultra-small photonic integrated devices with a high integration density [2, 3]. An arrayed-waveguide grating (AWG) (de)multiplexer is a most important component in many wavelength division multiplexing (WDM) modules and systems. It is becoming more important to reduce the total size of an AWG for monolithic integration with many other devices. A horseshoe-shaped AWG with very small size (about mm 2 ) has been presented [4], which shows the possibility of realising an ultra-small AWG with Si nanowire waveguides. The size of the AWG chip is mainly determined by the total number of the waveguides and the separation between adjacent arrayed waveguides. In fact the decoupled separation (i.e. the separation required for a negligible coupling) is very small (2 mm) for Si nanowire waveguides [5]. However, when a conventional layout is used [6], separation between arrayed waveguides is usually much larger than the decoupled separation in order to obtain a large length difference (i.e. a large diffraction order) between two adjacent arrayed waveguides for the case of dense WDM. In this Letter we present a novel layout with two overlapped free propagation regions (FPRs) for an AWG based on Si nanowire waveguides. This novel layout introduces more flexibility for the design, and separation between two adjacent arrayed waveguides can be much smaller than in a standard layout and consequently a very compact AWG is achieved. The performance of such an ultra-compact AWG strongly depends on not only an optimal design but also a fabrication process of high quality [2]. In our experiments, we use a structure of asi-on-sio 2 instead of commercially available SOI wafers. The layers of SiO 2 and a-si are deposited in sequence with the technology of plasma enhanced chemical vapour deposition (PECVD). This technology is more versatile since thickness and refractive indices can be adjusted in some range to fit some special requirements and designs. The fabrication process is optimised to obtain high quality and high precision. Finally, the fabricated ultra-small AWG is characterised. fabrication [5, 7]). A 4 4 (four inputs and four outputs) AWG with channel spacing of 11 nm is designed. The constant length difference between adjacent arrayed waveguides is about 7.2 mm, which corresponds to a diffraction order of 12. The separation between output waveguides is about 1.8 mm. The width of the input and output waveguides was tapered to 2 mm for better in=out-coupling of light. 40 mm 50 mm Fig. 1 Mask layout of our ultra-compact AWG demultiplexer In our experiments, pure silane gas is used as precursor for the deposition of the a-si film and the other key parameters are chosen as follows: RF power P ¼ 5 W (13.56 MHz), temperature T ¼ 250 C and process pressure p ¼ 270 mtorr. Under this condition, excessive polymerisation of silane radicals in the gas phase is prevented and a very low deposition rate (about 10 nm=min) is obtained. Such a low deposition rate is beneficial to control the deposited thickness of a very thin a-si film. The refractive index of the deposited a-si is 3.63 (at 1.55 mm), which is measured with a spectroscopic ellipsometry. The SiO 2 buffer layer and a-si core layer are subsequently deposited on a silicon wafer using the PECVD technology. The AWG pattern is formed using an electron beam lithography system (Raith 150) with an acceleration voltage of 25 kv. The followed etching process is accomplished using the ICP-RIE equipment with a gas mixture of SF 6 and C 4 F 8. Fig. 2 shows the cross-section of a fabricated waveguide. The size of the fabricated a-si nanowire waveguide is nm 2. The propagation loss of such a waveguide is about 4 db=mm, which is estimated with the cut-back method. Although this loss is about one order of magnitude larger than some recent reported results based on commercial SOI wafers, such a level of loss is still acceptable for the present ultra-compact AWG (about several hundred micrometres). Design and fabrication: To obtain a more compact AWG than the one with a conventional layout, we introduce a novel layout (Fig. 1), where the two FPRs are overlapped. Each half of an arrayed waveguide includes three subsections of straight waveguides which are connected smoothly by two subsections of bending waveguides in sequences. The separation between two adjacent arrayed waveguides is much smaller than in a conventional layout. The total length L l of the lth arrayed waveguide is the sum of the lengths of all the subsections, i.e. L l =2 ¼ S 1l þ R 1l ðp=2 a l ÞþS 2l þ R 2l p=2 þ S 3l where S 1l, S 2l and S 3l are the lengths of the first, second and third straight subsections, R 1l and R 2l are the curvature radii of the first and second bending sub-sections. In our design, we choose the bending radius R l ¼ 10 mm to ensure small bending loss (actually the bending radius can be reduced to 2 3 mm in the case of an ideal Fig. 2 Cross-sectional view of fabricated waveguide Fig. 3 shows SEM pictures of a fabricated AWG. The total size for the part of the waveguide array is very small (about mm 2 ). We use an amplified spontaneous emission (ASE) source with a spectrum range of nm to characterise the device. The polarised light is butt-coupled to the input waveguide through a focusing GRIN (gradient index) lens. The output light is collected with an objective lens, and guided to an optical spectrum analyser (OSA) with a multimode fibre. Fig. 4 shows the measured spectral responses for ELECTRONICS LETTERS 30th March 2006 Vol. 42 No. 7 88

92 the TE-polarisation light (coupling loss to fibres is excluded). The channel spacing is about 11 nm, which agrees well with the design value. The crosstalk between adjacent channels is about 10 db. The large crosstalk is mainly due to the large scattering loss of a-si nanowire waveguides, the phase errors and the coupling between output waveguides, and can be reduced by optimising the fabrication process. The spectral response for the TM-polarisation is similar but shifts towards the shorter wavelength by 35 nm (see Fig. 4b). This is because the effective index of the TM-polarisation is much smaller than that of the TE-polarisation. This shows that in general an AWG based on Si nanowire waveguides is highly polarisation-sensitive. Therefore, some special consideration or method for the polarisation compensation is required a Fig. 3 SEM pictures of fabricated 4 4AWG a Top view b Enlarged view for arrayed waveguides power, db b TE TM l, nm l, nm a b Fig. 4 Measured spectral responses of fabricated AWG a Four channels for TE-polarisation b Channel 3 for TE- and TM-polarisations power, db nm Conclusion: We present a novel design for an ultra-compact AWG demultiplexer based on a-si nanowire waveguides. The novel layout includes two overlapped FPRs and each half of an arrayed waveguide includes three straight waveguides which are connected smoothly by two bending waveguides. A 4 4 overlapped AWG demultiplexer with an ultra-small size of mm 2 has been fabricated and characterised. The results also show that an AWG based on Si nanowire waveguides is highly polarisation-sensitive. Acknowledgment: The partial support of the provincial government of the Zhejiang Province of China (grant nos and R ) is gratefully acknowledged. # IEE February 2006 Electronics Letters online no: doi: /el: D. Dai, L. Liu and S. He (Centre for Optical and Electromagnetic Research, Zhejiang University, Zijingang, Hangzhou, , People s Republic of China) dxdai@coer.zju.edu.cn L. Wosinski (Joint Research Center of Photonics of the Royal Institute of Technology, Sweden) L. Liu: Also wih Joint Research Center of Photonics of the Royal Institute of Technology, Sweden and Zhejiang University, Zijingang, Hangzhou, People s Republic of China L. Wosinski: Also with Department of Microelectronics and Information Technology, Royal Institute of Technology (KTH), Electrum 229, S Kista, Sweden and Division of Electromagnetic Theory, Alfven Laboratory, Royal Institute of Technology, S Stockholm, Sweden S. He: Also with Joint Research Center of Photonics of the Royal Institute of Technology, Sweden and Division of Electromagnetic Theory, Alfven Laboratory, Royal Institute of Technology, S Stockholm, Sweden References 1 Hibino, Y.: Recent advances in high-density and large-scale AWG multi=demultiplexers with higher index-contrast silica-based PLCs, IEEE J. Sel. Top. Quantum Electron., 2002, 8, (6), pp Sparcin, D.K., Spector, S.J., and Kimerling, L.C.: Silicon waveguide sidewall smoothing by wet chemical oxidation, J. Lightwave Technol., 2005, 23, (8), pp Bogaerts, W., Baets, R., Dumon, P., Wiaux, V., Beckx, S., Taillaert, D., Luyssaert, B., Van Campenhout, J., Bienstman, P., and Van Thourhout, D.: Nanophotonic waveguides in silicon-on-insulator fabricated with CMOS technology, J. Lightwave Technol., 2005, 23, (1), pp Sasaki, K., Ohno, F., Motegi, A., and Baba, T.: Arrayed waveguide grating of mm 2 size based on Si photonic wire waveguides, Electron. Lett., 2005, 41, (14), pp Dai, D., and He, S.: Characteristic analysis of nano silicon rectangular waveguides for planar lightwave circuits of high integration, Appl. Opt., 2006 (to be published) 6 Kaneko, A., Goh, T., Yamada, H., Tanaka, T., and Ogawa, I.: Design and applications of silica-based planar lightwave circuits, IEEE J. Sel. Top. Quantum Electron., 1999, 5, (5), pp Vlasor, Y.A., and McNab, S.J.: Losses in single-mode siliconon-insulator strip waveguides and bends, Opt. Express, 2004, 12, pp ELECTRONICS LETTERS 30th March 2006 Vol. 42 No. 7 89

93 1988 OPTICS LETTERS / Vol. 31, No. 13 / July 1, 2006 Design of a polarization-insensitive arrayed waveguide grating demultiplexer based on silicon photonic wires Daoxin Dai and Sailing He Centre for Optical and Electromagnetic Research, State Key Laboratory for Modern Optical Instrumentation, and Joint Research Center of Photonics of the Royal Institute of Technology (Sweden) and Zhejiang University, East Building No. 5, Zijingang Campus, Zhejiang University, Hangzhou , China Received January 4, 2006; revised March 10, 2006; accepted March 12, 2006; posted April 12, 2006 (Doc. ID 66809) The polarization dependence of an arrayed waveguide grating demultiplexer based on Si photonic wires is analyzed. The height and width of the arrayed waveguides are optimized to make the channel spacing polarization insensitive. To make the central wavelength polarization insensitive, different diffraction orders are chosen for TE and TM polarizations, and the remaining polarization-dependent wavelength is compensated with a noncentral input. A detailed design procedure is presented and numerical simulation results are given Optical Society of America OCIS codes: , , , , , Because of the large index contrast, it is possible to realize Si photonic nanowires and very compact planar lightwave circuit (PLC) devices. 1 4 A polarization-insensitive arrayed waveguide grating (AWG) demultiplexer is one of the most important devices in a dense WDM system. One can use a square Si photonic wire to obtain a polarization-insensitive wavelength for the central channel in an AWG. However, a nanoslab waveguide [like the free propagation region (FPR) in an AWG] is always polarizationdependent n TE n TM, which usually makes the channel spacing polarization dependent. Therefore the polarization compensation methods for an AWG based on micrometric waveguides, 5 which can only compensate the polarization sensitivity of the central channel wavelength, are not suitable for an AWG based on Si photonic wires. The polarization diversity approach is one of the most efficient methods. 6 To avoid polarization splitters and combiners, we try to optimize the cross section of the arrayed waveguides to obtain a polarization-insensitive AWG. For an AWG demultiplexer, the channel spacing ch is given by ch = ch d g /L FPR n s 0 / N g L, 7 where d g is the end separation of the arrayed waveguides, L FPR is the FPR length, L is the constant length difference between adjacent arrayed waveguides, x ch is the separation between adjacent output waveguides, n s is the effective index for the FPR (slab waveguide) at the wavelength, and the group effective index N g is given by N g =n g 0 D g (here n g is the effective index of the arrayed waveguide, and the dispersion coefficient D g =dn g /d. When the free spectral range (FSR) is very large, one should consider the dependence of the dispersion coefficient on the wavelength. In this Letter the dispersion coefficient is approximated by a constant, since a relative small FSR is used. For an AWG based on micrometer-sized waveguides, the polarization dependence of the channel spacing is usually very small. However, it becomes significant for the case of Si photonic wires. To cancel this polarization dependence, one should have s = g, where s =n s TE /n s TM and g =N g TE /N g TM. When s = g 1+ (here is a small deviation), the difference ch = ch TE ch TM between the channel spacings of the TE and TM polarizations is given by ch / ch TM =. The channel spacing difference ch will be large if the waveguide cross section is not appropriately designed. For example, if one chooses w co =h co =300 nm, one obtains 0.17 (i.e., the difference ch is about 17% of ch ). For the edge channel, the deviation can be estimated by edge = N ch /2 ch, where N ch is the total channel number. If edge ch /20 is required, one should make 1/ 10N ch, which can be realized by optimizing the arrayed waveguides. The Si photonic wire with an air cladding is considered in this Letter, and the cross section is shown in the inset of Fig. 1. With the material dispersions of SiO 2 and Si, 8,9 we use a fullvectorial finite-difference method to calculate the effective index as the wavelength varies and thus obtain D g and N g for TE and TM polarizations. Figure 2 shows that the ratio g decreases to a minimal value first and then increases as the height h co increases for a fixed core width. The curve of the ratio s is also shown by the thick solid curve, and we can obtain two cross points (h co1 and h co2 ) between the curves of s and g. At these cross points, s = g, which gives the design with a polarizationinsensitive channel spacing. We note that h co1 is very small, e.g., h co1 =263 nm when w co =320 nm (h co1 is even smaller for other widths w co ). If one chooses such a design, the mode confinement is not good. More important, the slope of g curves at this point h co =h co1 is large, which indicates a small fabrication tolerance of the core height. Therefore we focus on cross point h co2, where the slope is much smaller. Figure 3 shows the optimal height h co2 as w co increases. One sees that there is a minimal point where w co =297 nm and h co =362 nm. If one chooses such a design, a maximal fabrication tolerance for the core /06/ /$ Optical Society of America 90

94 July 1, 2006 / Vol. 31, No. 13 / OPTICS LETTERS 1989 Fig. 1. (Color online) Schematic configuration for an AWG demultiplexer. Fig. 2. (Color online) Ratio g as h co increases for different core widths w co. width is obtained. When h co 362 nm one can obtain two widths to realize a polarization-insensitive channel spacing. We also found there is a maximal value g _max as w co increases when h co is fixed. Figure 4 shows the maximal value g _max for different h co. One sees that g _max is always smaller than s when 262 nm h co 362 nm. In this case it is impossible to obtain g = s for the polarization-independent channel spacing. In the other ranges (h co 262 nm or h co 362 nm), there are two points for s = g, which can be seen from Fig. 3 clearly. As we mentioned before, the design for s = g when h co 262 nm is not good because of the weak confinement and small fabrication tolerance. Therefore we choose w co =297 nm and h co =362 nm for a maximal fabrication tolerance. This design also satisfies the single-mode condition. 10 From the grating equation for an AWG, 7 the wavelength 0 for the central channel x o =0 is given by for TE and TM polarizations was used for an AWG demultiplexer based on InP micrometric waveguides. 11 This method limits the FSR, and thus it is not suitable for an AWG (de)multiplexer with many channels. In this Letter we choose N ch =4 as an example. The term n g 0 TM /n g 0 TE m TE may be nonintegral, and thus one should choose a round integer as the diffraction order for the TM polarization; i.e., m TM =int n g 0 TM /n g 0 TE m TE. The residual is given by m= n g 0 TM /n g 0 TE m TE m TM. In this case, for the central channel, PD = m/m TM 0 TE. For the requirement of PD ch /20, the residual should satisfy the following inequality: m m TM / 0 TE ch /20. 2 To minimize m, here we choose an appropriate diffraction order for the TE polarization in the range of m / N ch ch. To compensate the minimized residual m, we use a simple method of choosing a noncentral input. In this case, the polarizationdependent effective index in the FPR can introduce polarization-dependent shifts of wavelength. The grating equation shows that an input position shift introduces almost the same wavelength shifts for the central and edge channels. Therefore this can compensate the PD for both the central and edge channels (see Fig. 5). From Eq. (1), one obtains the following formula for x i to make PD =0: Fig. 3. (Color online) Relation between h co and w co when s = g. 0 TE/TM = n g 0 TE/TM L n s 0 TE/TM d g x i /L FPR /m TE/TM, 1 where x i is the position of the input waveguide. Usually one chooses a central input, i.e., x i =0, and thus one has 0 TE/TM =n g 0 TE/TM L/m TE/TM. To eliminate the polarization-dependent wavelength PD = 0 TE 0 TE, one should choose m TM = n g 0 TM /n g 0 TE m TE. The polarization compensation method of choosing adjacent diffraction orders Fig. 4. (Color online) Maximal value g _max as the core height h co increases. 91

95 1990 OPTICS LETTERS / Vol. 31, No. 13 / July 1, 2006 Fig. 5. (Color online) (a) Simulated spectral responses (TE and TM polarizations) of the designed polarizationinsensitive AWG for the central and edge channels; (b) enlarged view. x i = 1/ 1 m TM / m +1 m TE 0 TE / n s 0 TE d g i /L FPRi, 3 where = n g 0 TE /n g 0 TM n s 0 TM /n s 0 TE. To design a polarization-insensitive AWG demultiplexer, we use the following procedure: (1) determine w co and h co to make s = g so that ch TE = ch TM ; (2) choose an appropriate m TE to minimize m and use Eq. (3) to calculate the required x i. For example, we choose parameters L FPR =36 m, d g =1.6 m, ch =1.6 nm, N ch =4, and thus 1 10N ch = As we mentioned before, we choose the optimal parameters: w co =297 nm and h co =362 nm. One has n g 0 TE =1.7171, n g 0 TM =1.7991, D g TE = / m and D g TM = / m. The fabrication tolerances for w co and h co are estimated to be ±8 and ±15 nm, respectively. We scan the diffraction order in the range 60 m TE 100 and obtain m TE =61 m TM =72 with a minimal m= This residual does not satisfy the requirement of m [from inequality (2)]. By using Eq. (3), we obtain x i =1.102 m. With this design, the separation of the output waveguide is about 2.12 m. Our designed polarization-insensitive AWG demultiplexer has 34 arrayed waveguides and a footprint of 316 m 216 m =0.068 mm 2. This size is larger than that of the design in Ref. 3 simply because our channel spacing is much smaller. In comparison with the design in Ref. 4, the present design has a similar size but includes much more arrayed waveguides. Furthermore, only TE polarization was considered in Refs. 3 and 4. The simulated spectral responses are shown in Fig. 5(a), from which one sees that the peaks of the spectral responses for the TE and TM polarizations are almost the same. This indicates that both the channel spacing and channel wavelengths are polarization insensitive, as predicted. On the other hand, to reduce the polarization-dependent coupling loss between the FPRs and the arrayed waveguides, we introduce some linear tapers at the ends of the arrayed waveguides. We choose the entrance width and length of the taper as 1.6 and 10 m, respectively. From Fig. 5 one sees that the losses for TE and TM polarizations are about 1.12 and 1.4 db, respectively, and a relatively low polarization-dependent loss 0.5 db is obtained [as shown in Fig. 5(b)]. In summary, we have optimized the height and width of the arrayed waveguides to obtain a polarization-insensitive channel spacing with a relative large fabrication tolerance. To reduce PD, we have chosen different diffraction orders for the TE and TM polarizations. A noncentral input has been used to eliminate PD. Numerical simulation results have shown that the present design can indeed give excellent performance of polarization insensitivity. When the difference in diffraction orders for TE and TM modes is large, a large difference in FSR and a large polarization-dependent channel nonuniformity may appear in the case of a large channel number. This method limits the FSR and thus it is not suitable for an AWG (de)multiplexer with many channels. To extend the present design to the case of a large channel number, a method of cascading two stages of AWGs can be used (such an interleaver cascaded by two AWG demultiplexers). This project was supported by China Postdoctoral Science Foundation and research grants ( and R104154) of the provincial government of Zhejiang Province of China. D. Dai s address is ddxopt@yahoo.com. References 1. W. Bogaerts, R. Baets, P. Dumon, V. Wiaux, S. Beckx, D. Taillaert, B. Luyssaert, J. Van Campenhout, P. Bienstman, and D. Van Thourhout, J. Lightwave Technol. 23, 401 (2005). 2. T. Tsuchizawa, K. Yamada, H. Fukuda, T. Watanabe, J. Takahashi, M. Takahashi, T. Shoji, E. Tamechika, S. Itabashi, and H. Morita, IEEE J. Quantum Electron. 11, 232 (2005). 3. K. Sasaki, F. Ohno, A. Motegi, and T. Baba, Electron. Lett. 41, 801 (2005). 4. P. Dumon, W. Bogaerts, D. Van Thourhout, D. Taillaert, R. Baets, J. Wouters, S. Beckx, and P. Jaenen, Opt. Express 14, 664 (2006). 5. Y. Inoue, Y. Ohmori, M. Kawachi, S. Ando, T. Sawada, and H. Takahashi, IEEE Photon. Technol. Lett. 6, 626 (1994). 6. M. K. Smit and C. van Dam, IEEE J. Quantum Electron. 2, 236 (1996). 7. A. Kaneko, T. Goh, H. Yamada, T. Tanaka, and I. Ogawa, IEEE J. Quantum Electron. 5, 1227 (1999). 8. C. Wu, Optical Waveguide Theory (Tsinghua University, 2000). 9. H. Wei, J. Zhong, L. Liu, X. Zhang, W. Shi, and C. Fang, J. Lightwave Technol. 19, 739 (2001). 10. D. Dai and S. He, Characteristic analysis of nano silicon rectangular waveguides for planar lightwave circuits of high integration, Appl. Opt. (to be published). 11. M. Zimgibl, C. H. Joyner, L. W. Stulz, Th. Gaiffe, and C. Dragone, Electron. Lett. 29, 201 (1993). 92

96 Novel ultracompact Si-nanowire-based arrayedwaveguide grating with microbends Daoxin Dai 1 and Sailing He 1, 2 1. Centre for Optical and Electromagnetic Research, State Key Laboratory for Modern Optical Instrumentation, Zhejiang University; Joint Research Center of Photonics of KTH (the Royal Institute of Technology, Sweden) & Zhejiang University, East Building No.5, Zijingang Campus, Zhejiang University, Hangzhou , China. 2. Division of Electromagnetic Engineering, School of Electrical Engineering, Royal Institute of Technology, S Stockholm, Sweden. dxdai@coer.zju.edu.cn Abstract: A novel layout is presented to minimize the size of an arrayedwaveguide grating (AWG) demultiplexer based on Si nanowire waveguides, in particular when a high diffraction order is required. A series of microbends are inserted in the middle of arrayed waveguides to increase the lightpath difference while keeping small separation between arrayed waveguides. A designed ultrasmall AWG with a narrow channel spacing of 0.8nm has a total size of only about 0.505mm 0.333mm (0.165mm 2 ) Optical Society of America OCIS codes: ( ) Integrated optics devices; ( ) Multiplexing. References and links 1. W. Bogaerts, R. Baets, P. Dumon, V. Wiaux, S. Beckx, D. Taillaert, B. Luyssaert, J. Van Campenhout, P. Bienstman, and D. Van Thourhout, Nanophotonic waveguides in silicon-on-insulator fabricated with CMOS technology, J. Lightwave Technol. 23, (2005). 2. T. Tsuchizawa, K. Yamada, H. Fukuda, T. Watanabe, J. Takahashi, M. Takahashi, T. Shoji, E. Tamechika, S. Itabashi, and H. Morita, Microphotonics devices based on silicon microfabrication technology, IEEE J. Select. Top. Quantum Electron. 11, (2005). 3. D. Dai, and S. He, Characteristic analysis of nano silicon rectangular waveguides for planar lightwave circuits of high integration, Appl. Opt. 45 (2006). 4. Y. Hibino, Recent advances in high-density and large-scale AWG multi/demultiplexers with higher indexcontrast silica-based PLCs, IEEE J. Select. Top. Quantum Electron. 8, (2002). 5. K. Sasaki, F. Ohno, A. Motegi and T. Baba, Arrayed waveguide grating of µm 2 size based on Si photonic wire waveguides, Electron. Lett. 41, (2005). 6. D. Dai, L. Liu, L. Wosinski and S. He, Design and fabrication of an ultra-small overlapped awg demultiplexer based on α-si nanowire waveguides, Electron. Lett. 42, (2006). 7. P. Dumon, W. Bogaerts, D. Van Thourhout, D. Taillaert, R. Baets, J. Wouters, S. Beckx, and P. Jaenen, Compact wavelength router based on a Silicon-on-insulator arrayed waveguide grating pigtailed to a fiber array, Opt. Express. 14, (2006). 8. N.-N. Feng, G.-R. Zhou, C. Xu, and W.-P. Huang, Computation of full-vector modes for bending waveguide using cylindrical perfectly matched layers, J. Lightwave Technol. 20, , (2002). 9. D. Dai and S. He, Design of a polarization-insensitive arrayed waveguide grating demultiplexer based on silicon nanowire waveguides, Opt. Lett., 31 (2006). 1. Introduction In recent years, Si nanowire waveguides have become very attractive since the large difference between the refractive indices of the core (Si) and the cladding/insulator (air or SiO2) makes it possible to realize ultra-small photonic integrated devices [1-3]. An arrayed waveguide grating (AWG) (de)multiplexer, which can realize various functionalities, is one of the mot important components in a dense wavelength division multiplexing (DWDM) system [4]. It is very attractive to develop a Si-nanowire-waveguide-based AWG (de)multiplexer, which has an ultra-small size [5-7]. In some papers published earlier, the channel spacing λch is relatively large, e.g., λch=11nm in [5, 6]. Recently a compact wavelength router with a smaller channel spacing of 2nm has been presented [7]. When a high diffraction order m is (C) 2006 OSA 12 June 2006 / Vol. 14, No. 12 / OPTICS EXPRESS

97 desired in e.g. a dense AWG (de)multiplexer or wavelength router with a narrow channel spacing, a large path difference (several tens of microns) between two adjacent arrayed waveguides is required. In order to achieve the required large path difference, the separation between two adjacent arrayed waveguides will be much larger than the decoupling separation (~2µm) for Si nanowire waveguides when a standard layout is used (This can be seen clearly from the design shown in [7]). In this case, the size of an AWG is determined by the separation of arrayed waveguides instead of the bending radius. Therefore, a conventional design will not be suitable to minimize the size of an AWG based on Si nanowire waveguides. In this paper we present a novel layout for a very compact AWG including arrayed waveguides with a series of microbends, which enable a large lightpath difference in a small occupied area (with a small separation), and consequently minimize the total size. 2. Layout Our novel layout is shown in Fig. 1, where the two FPRs (free propagation regions) are overlapped and a series of microbends are inserted at the middle of arrayed waveguides. Y l L SB R 3l, θ 3l R 2l, θ 2l S 3l Xl S 2l y S 1l R 1l, θ 1l O α l L io x O Fig. 1. Schematic configuration for our present AWG with microbends. For an AWG, a constant lightpath difference between two adjacent optical paths (instead of geometrical length) is required, i.e. P l c Pl 1 = mλ ΔP, (1) where P l is the lightpath of the l-th arrayed waveguide, m is the diffraction order, λc is the central wavelength. It is well known that there is a difference between the effective indices of the straight and bending sections ([8]; also see Fig. 3 below). This is considered in our design since a very small bending radius (~5µm) is usually chosen for Si nanowire waveguides. The lightpath P l is given as follows (see Fig. 1): P l / 2 = nss1 l + nb1r1 lθ 1l + nss 2l + nb2r2lθ 2l + nss 3l + nb3(4r3lθ3l ) Ql, (2) where n S, n B1, n B2 and n B3 are the effective indices in the straight and bending sections, R 3l, θ3l, and Q l are the bending radius, the arc angle, and the total number of the microbends, respectively, S 1l, S 2l and S 3l are the lengths of straight waveguides, R 1l and R 2l are the curvature radii of the bending sections, θ1l and θ2l are the corresponding arc angles, θ1l=π/2 αl (here αl is the radial angle), and θ2l=π/2 (see Fig. 1). The radial angle αl is given by αl=α0 l α, where α0 is the radial angle for the shortest (l=0) arrayed waveguide, α=d g /L FPR (here d g is the end separation between two adjacent arrayed waveguides, L FPR is the FPR length). One can rewrite Eq. (2) as follows: P l /( 2nS ) = S1 l + η 1R1lθ 1l + S 2l + η2r2lθ 2l + S3l + η3(4r3lθ 3l ) Ql, (3) where η1=n B1 /n S, η2=n B2 /n S, η3=n B3 /n S. In this paper, we use a full-vectorial finite-difference method (FV-FDM) [8] to calculate the effective index n B of a bent Si nanowire and obtain a (C) 2006 OSA 12 June 2006 / Vol. 14, No. 12 / OPTICS EXPRESS

98 fitting function η=f(r) to give the relation between the ratio η(=n B /n S ) and the radius R, which makes the design convenient especially when one chooses different bending radii for different arrayed waveguides. From Fig. 1, one also has the following relations: Y l = ( S1 l + LFPR )sinα l + R1 l sinθ1 l + S2l + R2l = Yl 1 X l = ( S1 l + LFPR)cosαl + R1 l (1 cosθ1 l ) = X l 1 + ΔYl, (4) + ΔX l, (5) L io / 2 = X l R2l S3l (4R3l sinθ3l ) Ql, (6) where L io is the distance between the vertexes (O and ( O of two FPRs, X l is the position for the second straight waveguide in x direction, Y l is the height of the third straight waveguide, X l =X l X l 1 and Y l =Y l Y l 1. We choose X l = Y l = xy and then obtain the following formulas where b S1 l = ( b + d) /( a + c), (7) S3l = b as1 l, (8) S 2l = ( Pl / ns )/ 2 [ η1r1 lθ1l + η2r2lπ / 2 + η3(4r3 lθ3l ) Ql ] ( S1 l + S3l ), (9) c = cosα, a = 1 sinαl + cosα, l l ( P / ) / 2 + (sin cos ) + (sin 1 + cos ) + (1 FPR / 2) 3 (4 3 3 ) ( l ns L α l α l R l θ l θ l η θ l R l η π η R lθ l Ql Yl 1 X 1), = l d = Lio / 2 LFPR cosα l R1 l (1 cosθ1 l ) + R2l + (4R3l sinθ3l ) Ql. In order to avoid any geometrical cross between arrayed waveguides, we add a constraint that each period of microbend has the same stretch L MB(l) in the x direction, i.e., L MB(l) =4R 3l sinθ3l=l MB(l 1). Then one can obtain the geometrical parameters for the l-th arrayed waveguide from those for the (l 1)-th arrayed waveguide. From Eq. (3)-(6), we have the following relevant equations for the shortest arrayed waveguide (l=0), which will be used as the initial in the recursion., P0 /( 2nS ) = S10 + η 1R10θ10 + S20 + η2r20θ 20 + S30 + η3(4r30θ 30) Q0, (10a) Y = ( θ + S + R 0 S10 + LFPR )sinα 0 + R10 sin X , (10b) = ( S10 + LFPR ) cosα 0 + R10(1 cos 10), (10c) 0 θ Lio / 2 = X 0 R20 S30 (4R30 sinθ30) Q0. (10d) From the above equations, one sees that parameters (S 10, S 20, S 30, R 10, R 20, α0, L FPR, R 30, θ30, and Q 0 ) should be chosen first in a design, and the whole structure of the AWG is then determined accordingly. The initial value of the bending radii for the l-th arrayed waveguides are chosen (according to the allowable bending loss) with a constant R min, i.e., R 1l =R 2l =R 3l =R min. R 3l and θ3l will be adjusted below in order to avoid negative value for S 3l. First, we preset Q l =Q l 1 for the calculation of S 1l, S 2l and S 3l. If S 3l >L MB(l), we let Q l =Q l 1 +1 and recalculate all the parameters for the l-th arrayed waveguide. When S 3l <0, we adjust R 3l to a new value R 3l =(1+γ)R 3l (where γ is a small quantity), and consequently θ 3l =sin 1 [L MB 4R )/ 3l )], 3 η f(r = 3l ). Generally speaking, the calculated bending radii R 3l will be different from R 30 for a few arrayed waveguides according to the chart flow of Fig. 2. (C) 2006 OSA 12 June 2006 / Vol. 14, No. 12 / OPTICS EXPRESS

99 waveguide parameters: w, h, n co, n cl ; fitting function: η=f(r); AWG parameters: L FPR, m, S 10, S 20, S 30, α0, R 10, R 20, R 30, θ30, Q 0 =0 Eq. (10a) L 0 ; Eq. (10b) X 0 ; Eq. (10c) Y 0 ; Eq. (10d) L io ; R 1l =R 2l =R 3l =R min ; Eq. (1) L l ; Q l =Q l 1 ; R 3l =(1+γ)R 30, θ3l=sin 1 [L MB /(4R 3l )] η 3 =f(r 3l ) Y Eqs. (7), (8), (9) S 1l, S 2l, S 3l S 3l >L MB(l)? Y N S 3l <0? N Eq. (4), (5) X l ; Y l Q l = Q l 1 +1 l< N WG? END Fig. 2. The flow chart for the layout design of the present AWG. 3. Design example Here we give a design example to demonstrate the size minimization of an AWG with a small channel spacing ( λch=0.8nm) when the present layout is used. We choose a 500nm 300nm Si nanowire waveguide with an air cladding. The refractive indices for the core and insulator layers are and 1.460, respectively. The other parameters are given as follows: λc= nm, m=80, L FPR =50µm, d g =1.0µm, the total channel number N ch =8, and the total number of arrayed waveguides N WG =34. For this design, the free spectral range is about 19nm. We calculate the effective index n B of a bent Si nanowire by using a FV-FDM. Fig. 3 shows the ratio η(=n B /n S ) for different core widths, which is fitted numerically with a power function of η=f(r)= r ( ). From this figure, one sees that the change of η due to the variation of the core width is small and thus the performance of the AWG will not degrade much when the width of the fabricated microbends deviates slightly from the designed value. N Y η η= r w co =490nm w co =500nm w co =510nm R (µm) Fig. 3. The ratio η(=n B /n S ) as the bending radius R increases. We choose S 10 =6µm, S 20 =6µm, S 30 =10µm, R 10 =R 20 =R 30 =5µm, and α0=55.48º for the shortest waveguide. Since the diffraction order is large, we choose the arc-angle θ 30 =80º. According to the flow chart shown in Fig. 2, the parameters for all the arrayed waveguides are obtained and shown in Fig. 4. From Fig. 4(a), one sees that the total period number (2Q l ) of the microbends in the l-th arrayed waveguide does not increase linearly (they are obtained automatically from the algorithm shown in Fig. 2). Nevertheless, the lightpaths of the arrayed waveguides (each arrayed waveguide consists of many microbends and six straight (C) 2006 OSA 12 June 2006 / Vol. 14, No. 12 / OPTICS EXPRESS

100 waveguides) increase linearly [see Eq. (1)], as the basic principle of an AWG for (de)multiplexing. The calculated bending radius R 3l and arc-angle θ 3l are shown in Fig. 4(b), from which one sees that the bending radius and arc-angle for most microbends are the same as the initial value, i.e., R min =5µm and θ 3l =80º. Fig. 4(c) shows the distance xy (in x or y direction) between the arrayed waveguides. One sees the separation is smaller than 10µm and the smallest separation is larger than 4µm. This minimizes the total size and in the mean time makes the coupling negligible between arrayed waveguides Q l m) R 3l (µ l(º) θ m) xy (µ 8 (a) l (b) l 60 (c) l Fig. 4. The parameters for different arrayed waveguides in the designed AWG. (a) total period number (2Q l ) of the microbends; (b) bending radius R 3l and arc angle θ 3l ; (c) distance xy. The designed AWG with the present layout is shown in Fig. 5(a). One sees that with the present novel design the device size is only about 0.165mm 2. For this layout, the minimal distance xy is about 4.0µm [see Fig. 4(c)] and the corresponding minimal separation between arrayed waveguides is about 1.35µm, which is large enough for a negligible coupling between arrayed waveguides [3]. In order to check this, we use a FDTD to simulate the light propagation in the microbends of the arrayed waveguides [see Fig. 5(b)]. From this figure one sees that the coupling between arrayed waveguides is negligible and will introduce little phase error. In fact, the coupling is still very small even when the distance xy is reduced to 3µm mm Power (db) mm Wavelength(nm) (a) (b) (c) Fig. 5. (a) The present AWG layout; (b) light propagation in the microbends simulated with a FDTD; (c) the calculated spectral response. Fig. 5(c) shows the calculated spectral response (which does not include the coupling loss between the input/output waveguides and the fibers). In a sharply bending section the hybrid modes exhibit varying scattering losses for different initial polarizations and this introduces a polarization-dependent loss (PDL). In our cases, the calculated PDL is small (as the bending radius R=5µm is large enough) [3]. From Fig. 5(c), one sees that the calculated crosstalk is smaller than 30dB. The excess loss due to the inserted microbends in the arrayed waveguides is very small when the bending radius is large enough (e.g., 5µm in our design). Generally speaking, an AWG based on Si nanowire waveguides is highly polarization-sensitive [6] and consequently one should use some polarization-compensation method, e.g., optimize the height and width of the core [9] (this does not increase the total size of an AWG). Therefore, theoretically speaking, our design can give good performances while keeping the total size very small. (C) 2006 OSA 12 June 2006 / Vol. 14, No. 12 / OPTICS EXPRESS

101 We also give a design of an AWG with the same parameters as the AWG presented in Ref. [7] for comparison. In this example, the diffraction order is very large (m=113) and thus the separation between two adjacent arrayed waveguides will be much larger than the decoupling separation when a conventional layout is used (e.g., the separation is about 30µm in Ref. [7]. Fig. 6 shows our designed AWG with the present layout and the size is about 0.2mm 0.144mm, which is smaller than half of the size of the AWG presented in Ref. [7]. For this layout, the minimal distance xy is about 6.5µm and the corresponding minimal separation between arrayed waveguides (see position P in Fig. 6) is about 1.4µm (the coupling between arrayed waveguides is negligible). From the above example, one sees that the proposed layout is preferred for a reduction of the total size, especially when the diffraction order is quite high. P 0.144mm mm Fig. 6. Our Layout of an AWG with the same parameters as the AWG presented in [7]. 4. Conclusion In this paper, we have proposed a novel layout design for an ultra-small AWG demultiplexer based on Si nanowire waveguide especially when a high diffraction order is required. The arrayed waveguides with a series of microbends have been introduced to reduce the separation between arrayed waveguides, which minimizes the total size of the AWG. The difference between the effective indices of the straight and bending sections of waveguides has been considered. As an example, an ultrasmall AWG with a narrow channel spacing ( λch=0.8nm) has been designed and the total size is only about 0.505mm 0.333mm=0.165mm 2. Acknowledgment This project was supported by China Postdoctoral Science Foundation and research grants (No and R104154) of the provincial government of Zhejiang Province of China (C) 2006 OSA 12 June 2006 / Vol. 14, No. 12 / OPTICS EXPRESS

102 IEEE JOURNAL OF SELECTED TOPICS IN QUANTUM ELECTRONICS, VOL. 12, NO. 6, NOVEMBER/DECEMBER Ultrasmall Overlapped Arrayed-Waveguide Grating Based on Si Nanowire Waveguides for Dense Wavelength Division Demultiplexing Daoxin Dai and Sailing He, Senior Member, IEEE Abstract A novel design for an ultrasmall arrayed-waveguide grating (AWG) demultiplexer based on a Si nanowire waveguide is presented. The two free propagation regions (FPRs) are overlapped so that the structure becomes more compact than the layout of a conventional design. Each half of an arrayed waveguide includes three straight sections and two bending sections, and all these sections are connected smoothly in sequence. Some recursive formulas for determining the geometrical parameters of the novel layout are derived. Numerical simulation results are given. Index Terms Arrayed-waveguide grating (AWG), nanowire, overlapped, silicon, ultrasmall, waveguide. I. INTRODUCTION THE planar-lightwave-circuit (PLC)-based devices are attractive due to their excellent performance and small size. There are many materials and structures for optical waveguides, and SiO 2 -buried rectangular waveguides are the most popular. For a SiO 2 -based waveguide, however, the bending radius has to be very large (e.g., of the order of several millimeters) even for the case with a super-high refractive index contrast (Δ = 2.5%) [1]. This limits the integration density of SiO 2 -based PLCs. Recently, silicon-on-insulator (SOI) waveguides [2], [3] have become popular for PLC devices due to their potential to integrate with complimentary metal-oxidesemiconductors (CMOS). The investigations in the past several years were focused on SOI rib waveguides with a large cross section [in order to obtain a high coupling efficiency to a standard single-mode fiber (SMF)]. Due to the large difference between the refractive indices of the core (Si) and the cladding/insulator (air or SiO 2 ), it is possible to realize ultrasmall photonic integrated devices. Some results on Si nanowire (instead of rib) Manuscript received October 5, 2005; revised June 5, This work was supported in part by the China Postdoctoral Science Foundation under Grant , in part by the provincial government of Zhejiang Province of China under Grant and Grant R104154, and in part by the National Science Foundation of China under Grant D. Dai is with the Centre for Optical and Electromagnetic Research, State Key Laboratory for Modern Optical Instrumentation, Zhejiang University, Hangzhou , China, and also with the Joint Research Center of Photonics of the Royal Institute of Technology (Sweden) and Zhejiang University, Hangzhou , China ( dxdai@zju.edu.cn). S. He is with the Centre for Optical and Electromagnetic Research, State Key Laboratory for Modern Optical Instrumentation, Zhejiang University, Hangzhou , China, and also with the Joint Research Center of Photonics of the Royal Institute of Technology (Sweden) and Zhejiang University, Hangzhou , China, and also with the Division of Electromagnetic Theory, Alfven Laboratory, Royal Institute of Technology, S Stockholm, Sweden ( sailing@zju.edu.cn). Digital Object Identifier /JSTQE waveguide have been reported [4] [8]. For a Si nanowire waveguide, the scattering loss (per unit of length) due to the roughness of the sidewall is much larger than that for a conventional micrometric waveguide [7], [8]. Meanwhile, the reduction of the total size of PLC devices based on Si nanowire waveguides compensates the large scattering loss in terms of the total loss per device. The total loss in a PLC device based on Si nanowire waveguides can be low enough for practical uses. Therefore, it is attractive to develop ultrasmall PLC devices based on Si nanowire waveguides. The authors of [11] and [12] presented a horseshoe-shaped arrayed-waveguide grating (AWG) with a large channel spacing, e.g., 6 or 11 nm, which is for coarse wavelength-division multiplexing. A dense wavelength division demultiplexing (DWDM) based on Si nanowire waveguides is very attractive. For a dense AWG multiplexer, a high diffraction order is usually desirable, which corresponds to a large path difference (several tens of micrometers). In order to achieve the required large path difference, the separation between adjacent arrayed waveguides will be much larger than the decoupling separation ( 2 μm) for Si nanowire waveguides when a standard layout [10] is used. In the case of Si nanowire waveguides, the size of an AWG is determined by the separation of arrayed waveguides instead of the bending radius. Therefore, a conventional design will not be suitable for the realization of a compact AWG based on Si nanowire waveguides. In this paper, we present a novel layout for AWGs based on Si nanowire waveguides, and a very compact AWG with a narrow channel spacing (e.g., 0.8 nm) is realized. For the presented layout, each half of an arrayed waveguide includes three straight parts and two bending parts (instead of two straight parts and one bending part in a standard AWG layout). This introduces more flexibility for the design of the layout and thus it is easier to design an AWG with more requirements. The separation between two adjacent arrayed waveguides is uniform and smaller than that for an AWG with a standard layout. Furthermore, the two free propagation regions (FPRs) in the present layout are overlapped to make the AWG more compact. The recursive formulas for determining the novel layout are derived and a design example is given. II. LAYOUT First, we review the design of a standard layout for a conventional AWG demultiplexer as shown in Fig. 1. L s is the distance between the vertexes (O and O ) of two FPRs, L FPR is the FPR length, S 1l and S 2l are the lengths of the first and second straight X/$ IEEE 99

103 1302 IEEE JOURNAL OF SELECTED TOPICS IN QUANTUM ELECTRONICS, VOL. 12, NO. 6, NOVEMBER/DECEMBER 2006 Fig. 1. Schematic configuration for a conventional AWG. waveguides in the first half of the lth arrayed waveguide, R l is the bending radius, α l and H l are the tilting angle and the height for the lth arrayed waveguide, respectively. For the shortest arrayed waveguide, one has the following relations: L s /2=(L FPR + S 10 ) cos α 0 + R 0 sin α 0 + S 20 L 0 /2=S 10 + R 0 α 0 + S 12. (1) H 0 =(L FPR + S 10 )sinα 0 + R 0 (1 cos α 0 ) For the lth arrayed waveguide, one has the following relations: (S 1l + L FPR )sinα l + R l (1 cos α l )=H l S 2l = 1 2 L s (S 1l + L FPR ) cos α l R l sin α l. Consequently, one has S 1l = H l L FPR R l tan α l (2) sin α l 2 S 2l = 1 2 L s H l R l tan α l tan α l 2. (3) The constant difference between the optical paths of two adjacent arrayed waveguides is mλ c, where m is the diffraction order and λ c is the central wavelength for the central channel. Then, one has 1 2 n g(l)l l = n g(l) (S 1l + R l α l + S 2l )= 1 2 n g(0)l 0 + l mλ c 2 where n g(l) and L l are the effective index and the total length of the lth arrayed waveguide. Substituting (2) and (3) into the above equation, one obtains (4), shown at the bottom of the page. For a conventional AWG, all the arrayed waveguides have the same cross section, i.e., n g(l) = n g(0) n g. It then follows from (4) that R l = L 0/2+lmλ c /(2n g ) H l tan(α l /2) L s /2+L FPR. α l 2tan(α l /2) (5) Fig. 2. Schematic configuration for the overlapped AWG. In a conventional AWG layout, the height H l of the lth arrayed waveguide is given by H l = H l 1 +ΔH (6) where ΔH is a fixed constant for the separation (at the middle) between two adjacent arrayed waveguides. To achieve a large path difference for the required high diffraction order, the separation ΔH should be much larger than the decoupling separation ( 2 μm) for Si nanowire waveguides. This is disadvantageous for reducing the size of an AWG based on Si nanowire waveguides. To reduce the size of an AWG, further we introduce a novel layout as shown in Fig. 2, where the two FPRs are overlapped so that the structure becomes more compact. Each half of an arrayed waveguide includes three straight waveguides that are connected smoothly by two bending waveguides in sequences. For the present novel design, we let the effective index of arrayed waveguide increase as l increases by increasing the waveguide width so that the geometrical length difference (L l L l 1 ) can be reduced. Meanwhile, a constant difference between the two adjacent optical paths (instead of geometrical length) is introduced. One has L l = n g(l 1) L l 1 + mλ c. (7) n g(l) n g(l) From the above recursion relation, the length L l is determined once the length L 0 is chosen. The total length L l of the lth arrayed waveguide is the sum of the lengths of all the subsections, i.e., L l /2=S 1l + R 1l (π/2 α l )+S 2l + R 2l π/2+s 3l (8) R l = [n g(0)/n g(l) ]L 0 /2+lmλ c /[2n g(l) ] H l tan(α l /2) L s /2+L FPR α l 2tan(α l /2) (4) 100

104 DAI AND HE: ULTRASMALL OVERLAPPED AWGs BASED Si NANOWIRE WAVEGUIDES 1303 where S 1l,S 2l, and S 3l are the lengths of the first, second, and third straight waveguides, and R 1l and R 2l are the curvature radii of the first and second bending sections. The radial angle α l is given by α l = α 0 lδα (9) where α 0 is the tilting angle for the shortest (l =0)arrayed waveguide, Δα is the angle separation between two adjacent arrayed waveguides, and Δα = d g /L FPR (where d g is the arc separation between the two adjacent arrayed waveguides). In Fig. 2, it is shown that X l =(L FPR + S 1l ) cos α l + R 1l (1 sin α l ) (10) Y l =(L FPR + S 1l )sinα l + R 1l cos α l + S 2l + R 2l (11) L s 2 = X l R 2l S 3l (12) where X l is the position for the second straight waveguide in the x-direction, and Y l is the height of the lth arrayed waveguide. Consequently, one has the following formulas: S 1l = X l / cos α l R 1l (1 sin α l )/ cos α l L FPR (13) S 2l = Y l X l tan α l + R 1l (1 sin α l ) tan α l R 1l cos α l R 2l (14) S 3l = X l R 2l L s 2. (15) Substituting (13) (15) into (8), one obtains R 1l [π/2 α l +2(sinα l 1)/ cos α l ]+ R 2l (π/2 2) = L l /2+L FPR + X l (tan α l 1 1/ cos α l )+L s /2 Y l. (16) To determine the parameters uniquely, we add some additional conditions, e.g., Consequently, one obtains R 1l = R 2l R l. (17) R l = L l/2 Y l + L s /2+L FPR X l (1/ cos α l +1 tan α l ). π α l 2+2tanα l 2/ cos α l (18) Let { Xl = X l 1 +ΔX l Y l = Y l 1 +ΔY l (19) where ΔX l and ΔY l are the separations in the x- and y- directions between the straight sections of the lth and (l 1)th arrayed waveguides, respectively. Then, one has a l ΔX l +ΔY l = L l 2 + L s 2 + L FPR a l X l 1 Y l 1 b l R l (20) where { al =1/ cos α l +1 tan α l b l = π α l 2+2tanα l 2/ cos α l. In our design, we set ΔX l =ΔY l. Denoting c l = L l 2 + L s 2 + L FPR a l X l 1 Y l 1 (21) one obtains ΔX l =ΔY l = c l b l R l a l +1. (22) To ensure that the bending radii for all the arrayed waveguides are larger than a minimal value R min, we choose the bending radius R l = R max l(r max R min )/(N WG 1) (where l =0,...,N WG 1). Once the bending radius R l is chosen, the value for ΔX l (ΔY l ) is consequently determined by (22). Therefore, the recursive relations (7), (9), and (19) between the lth and (l 1)th arrayed waveguides and (13) (15) can be used to determine the length for each section of the lth arrayed waveguide. In the following section, we construct the relevant equations for the shortest (0th) arrayed waveguide, which will be used as the initial for the above recursion. From the geometrical relation of the shortest (0th) arrayed waveguide, one obtains the following relations for X 0,L s,y 0, and L 0 from (8), (10), (12), and (14) L 0 2 = S 10 + R 10 (π/2 α 0 )+S 20 + R 20 π/2+s 30 (23a) X 0 =(L FPR + S 10 ) cos α 0 + R 10 (1 sin α 0 ) (23b) Y 0 =(L FPR + S 10 )sinα 0 + R 10 cos α 0 + S 20 + R 20 (23c) L s 2 = X 0 R 20 S 30. (23d) From the above equations, it can be seen that parameters (S 10,S 20,S 30,R 10,R 20,α 0,L FPR ) should be chosen first in a design, and the whole structure of the AWG should then be determined accordingly. As a summarization, the flowchart for the design procedure is shown in Fig. 3. III. DESIGN As a numerical example, we choose a rectangular Si waveguide with a cross section of 500 nm 300 nm. The refractive indices for the core and cladding layers are and 1.46 at the wavelength of 1.55 μm. Following a procedure similar to that for a conventional AWG, we determine the central wavelength λ c = nm, the channel spacing Δλ ch =0.8 nm, the channel number N ch =8, the diffraction order m =80,the FPR length L FPR =50μm, the separation d g =1μm, and the total number of arrayed waveguides N WG =34. First, the design with a conventional layout with a constant ΔH is given for comparison (shown in Fig. 4). In this case, the separation ΔH =26.5 μm, which is much larger than the decoupling separation (as mentioned earlier). The total size of the AWG demultiplexer is about 1.27mm 2. The design of the present layout of the overlapped AWG is shown in Fig. 4(b). For this design, we choose the bending radius R l =5μm. Fig. 5 shows the lengths S 1j,S 2j, and S 3j for all the arrayed waveguides. Comparing Fig. 4(a) and (b), one 101

105 1304 IEEE JOURNAL OF SELECTED TOPICS IN QUANTUM ELECTRONICS, VOL. 12, NO. 6, NOVEMBER/DECEMBER 2006 Fig. 5. Lengths for the straight sections for all the AWGs. Fig. 6. Simulated spectral response. Fig. 3. Flowchart for the design of the present overlapped AWG. Fig. 4. Layout for the designed AWG. (a) Conventional design with a constant ΔH (26.5 μ m). (b) The present overlapped AWG. sees that with the present novel design the device size has been successfully reduced from 1.27 to mm 2.TheAWGsize with the present overlapped structure is only about one-sixth the size in a conventional layout. We use a hybrid method (which combines the beam propagation method and the Kirchhoff Huygens diffraction formula) to calculate the spectral response (see Fig. 6). One sees that the theoretical results are quite good. This spectral response does not include the coupling loss between the input/output waveguides and the SMFs. This coupling loss can be reduced by using, e.g., some modal converters [13]. The crosstalk for the two leftmost channels is about 26 db, as shown in Fig. 6, which is relatively large in comparison with that for a SiO 2 -on-si AWG demultiplexer ( 30 db) [10]. Theoretically speaking, this can be improved by increasing the total number of arrayed waveguides. For example, the crosstalk can be reduced to 30 db when one chooses N WG =40in our present design. However, this will result in an increase in the total size of the AWG chip. It is more difficult to achieve good performances for a large chip due to the nonuniformity of the thicknesses and refractive indices of the thin film. Therefore, for an AWG based on Si nanowire waveguides, the total number of arrayed waveguides is usually not large, e.g., N WG =10was chosen and the crosstalk is relatively large (about 15 db) in a recent publication [14]. In comparison with the design in [14], the present 102

106 DAI AND HE: ULTRASMALL OVERLAPPED AWGs BASED Si NANOWIRE WAVEGUIDES 1305 design gives a smaller channel spacing and includes much more arrayed waveguides. Due to the strong light confinement in Si nanowire waveguides, SOI-based wavelength filters are rather sensitive to temperature. The change of temperature introduces a variation of the refractive index and consequently some shift of the channel wavelengths. Since the thermo-optical constant of Si is about K 1 [15], the estimated wavelength shift Δλ is about 0.1nm/KbyusingΔλ =(Δn eff /n eff )λ c, where Δn eff is the variation of the effective refractive index n eff. To obtain an athermal SOI-based wavelength filter, one can use, e.g., a temperature controller (in packaging) to achieve a stable temperature for the chip and thus eliminate the influence of the temperature. IV. CONCLUSION In this paper, we have proposed a novel layout design for an AWG demultiplexer based on Si nanowire waveguides. In this novel layout, the two FPRs are overlapped and each half of the arrayed waveguides includes three straight sections and two bending sections. With such a design, the size of the AWG has been reduced significantly, and is only about one fifth of the size in a conventional layout. REFERENCES [1] Y. Hibino, Recent advances in high-density and large-scale AWG multi/demultiplexers with higher index-contrast silica-based PLCs, IEEE J. Sel. Topics Quantum Electron., vol. 8, no. 6, pp , Nov. Dec [2] D. Dai and S. He, Analysis of the birefringence of a silicon-on-insulator rib waveguide, Appl. Opt., vol. 43, no. 5, pp , [3], Analysis for characteristics of bent rib waveguides, J. Opt. Soc. Amer. A, vol. 21, no. 1, pp , [4] K. K. Lee, D. R. Lim, D. Pan, C. Hoepfner, W.-Y. Oh, K. Wada, L. C. Kimerling, K. P. Yap, and M. T. Doan, Mode transformer for miniaturized optical circuits, Opt. Lett., vol. 30, no. 5, pp , [5] V. R. Almeida, Q. Xu, C. A. Barrios, and M. Lipson, Guiding and confining light in void nanostructure, Opt. Lett., vol.29,no.11,pp , [6] Q. Xu, V. R. Almeida, R. R. Panepucci, and M. Lipson, Experimental demonstration of guiding and confining light in nanometer-size lowrefractive-index material, Opt. Lett., vol. 29, no. 14, pp , [7] J. H. Jang, W. Zhao, J. W. Bae, D. Selvanathan, S. L. Rommel, and I. Adesida, Direct measurement of nanoscale sidewall roughness of optical waveguides using an atomic force microscope, Appl. Phys. Lett., vol. 83, no. 20, pp , [8] F. Grillot, L. Vivien, S. Laval, D. Pascal, and E. Cassan, Size influence on the propagation loss induced by sidewall roughness in ultrasmall SOI waveguides, IEEE Photon. Technol. Lett., vol. 16,no.7,pp , Jul [9] Y. Barbarin, X. J. M. Leijtens, E. A. J. M. Bente, C. M. Louzao, J. R. Kooiman, and M. K. Smit, Extremely small AWG demultiplexer fabricated on InP by using a double-etch process, IEEE Photon. Technol. Lett., vol. 16, no. 11, pp , Nov [10] A. Kaneko, T. Goh, H. Yamada, T. Tanaka, and I. Ogawa, Design and applications of silica-based planar lightwave circuits, IEEE J. Sel. Topics Quantum Electron., vol. 5, no. 5, pp , Sep. Oct [11] T. Fukazawa, F. Ohno, and T. Baba, Very compact arrayed-waveguide grating demultiplexer using Si photonic wire waveguides, Jpn. J. Appl. Phys., vol. 43, no. 5B, pp , [12] K. Sasaki, F. Ohno, A. Motegi, and T. Baba, Arrayed waveguide grating of 70 60μm 2 size based on Si photonic wire waveguides, Electron. Lett., vol. 41, no. 14, pp , [13] K. K. Lee, D. R. Lim, D. Pan, C. Hoepfner, W.-Y. Oh, K. Wada, L. C. Kimerling, K. P. Yap, and M. T. Doan, Mode transformer for miniaturized optical circuits, Opt. Lett., vol. 30, no. 5, pp , [14] P. Dumon, W. Bogaerts, D. Van Thourhout, D. Taillaert, R. Baets, J. Wouters, S. Beckx, and P. Jaenen, Compact wavelength router based on a silicon-on-insulator arrayed waveguide grating pigtailed to a fiber array, Opt. Express, vol. 14, no. 2, pp , [15] T. Baehr-Jones, M. Hochberg, C. Walker, E. Chan, D. Koshinz, W. Krug, and A. Scherer, Analysis of the tuning sensitivity of silicon-on-insulator optical ring resonators, J. Lightw. Technol., vol. 23, no. 12, pp , Dec Daoxin Dai was born in Jiangxi, China, in He received the B.Eng. and Ph.D. degrees from the Department of Optical Engineering at Zhejiang University, Hangzhou, China, in 2000 and 2005, respectively. Currently, he is a Postdoctoral Fellow at Zhejiang University. He is also associated with the Joint Research Center of Photonics at the Royal Institute of Technology, Sweden, and Zhejiang University, Hangzhou, China. He has first-authored more than 20 papers in refereed international journals. He holds five patents in the area of optical waveguide devices. His research interests include modeling and fabrication of integrated microphotonic and nanophotonic devices. Sailing He (M 92 SM 98) received the Licentiate of Technology and Ph.D. degrees in electromagnetic theory from the Royal Institute of Technology, Stockholm, Sweden, in 1991 and 1992, respectively. Since 1992, he has been a member of the faculty of at the Royal Institute of Technology. Since 1999, he has also been with the Centre for Optical and Electromagnetic Research, Zhejiang University, Hangzhou, China, as a Special Changjiang Professor appointed by the Ministry of Education of China. He is also a Chief Scientist for the Joint Research Center of Photonics of the Royal Institute of Technology (Sweden) and Zhejiang University, Hangzhou, China. He is the author of one monograph (Oxford University Press) and has authored/coauthored more than 200 papers published in refereed international journals. He is the holder of 12 patents in the area of optical communications. 103

107 JOURNAL OF LIGHTWAVE TECHNOLOGY, VOL. 25, NO. 10, OCTOBER Improve Channel Uniformity of an Si-Nanowire AWG Demultiplexer by Using Dual-Tapered Auxiliary Waveguides Zhen Sheng, Daoxin Dai, Member, IEEE, and Sailing He, Senior Member, IEEE Abstract Dual-tapered auxiliary waveguides at the exit of the waveguide array are introduced to improve the channel uniformity of an Si-nanowire-based arrayed waveguide grating (AWG) demultiplexer. By using a hybrid simulation method, the dualtapered auxiliary waveguides of the AWG demultiplexer are optimized reliably and efficiently. A 12-channel AWG demultiplexer is designed as an example, and a small nonuniformity (< 0.5 db) is achieved. Index Terms Arrayed waveguide grating (AWG), auxiliary waveguide, dual-tapered, nanowire, nonuniformity, silicon. I. INTRODUCTION AN ARRAYED waveguide grating (AWG) demultiplexer [1], [2] is one of the essential important components in wavelength-division-multiplexing systems. AWG demultiplexers based on silica buried waveguides have been in commercial use for several years. However, a silica-based AWG demultiplexer usually has a very large size of several square centimeters. Recently, ultracompact photonic integrated circuits, such as AWG demultiplexers, have been realized by using Si nanowires [3] [5]. For AWG demultiplexers, it is very important to have good uniformity of channels in some system applications, such as receivers and add/drop scenarios [6]. Otherwise, the signal-to-noise ratio will be degraded for the channel with a large insertion loss after a long-distance transmission. Nonuniformity L u of an AWG is defined as L u = 10 lg(i m /I c ) (in decibels) [1], where I m and I c are the intensities of the marginal channel and the central channel, respectively. It is well known that the focal field distributions for all of the wavelengths at the image plane of an AWG demultiplexer have an envelope, which is determined by the far fields of the field distributions at the end of the arrayed waveguides [1]. The spectral responses of all channels have a similar envelope. Manuscript received March 5, 2007; revised July 1, This work was supported by the provincial government of the Zhejiang Province of China under Research Grant and Research Grant R and in part by the National Science Foundation of China under Grant and Grant The authors are with the Centre for Optical and Electromagnetic Research, State Key Laboratory of Modern Optical Instrumentation, Zhejiang University, Hangzhou , China, and also with the Joint Research Center of Photonics, Royal Institute of Technology and Zhejiang University, Hangzhou , China ( dxdai@zju.edu.cn). Color versions of one or more of the figures in this paper are available online at Digital Object Identifier /JLT This envelope is of quasi-gaussian shape due to the quasi- Gaussian far field from an individual arrayed waveguide in a conventional AWG demultiplexer. In this case, the marginal channel has a larger insertion loss than the central one, which indicates a fairly large nonuniformity L u. For example, a 16-channel AWG demultiplexer based on silica or polymer may have a nonuniformity of more than 2 db [7] [9]. The situation is even worse for AWG demultiplexers based on Si nanowires, even if the total number of channels is not large. For example, the nonuniformity of a nine-channel Si-nanowire AWG exceeds 3 db [10]. Usually, one can reduce the channel nonuniformity L u by increasing the length of the free propagation region (FPR). However, this significantly increases the AWG size. To improve the channel uniformity without any increase of the FPR length, Dragone et al. introduced some special structures (such as Y-branches and auxiliary waveguides) at the end of waveguide array for silica-based AWG [6], [11]. In this paper, we consider the improvement of the channel uniformity for a Si-nanowire AWG demultiplexer, which has an ultrasmall size and is becoming more and more attractive for large-scale optical integrations. Here, we use the method of introducing auxiliary waveguides between adjacent arrayed waveguides. However, due to the strong confinement and the submicrometer size of Si nanowires, the situation (e.g., the coupling between auxiliary waveguides and arrayed waveguides) is quite different. When using Si nanowires, one cannot achieve a result that is as good as that using conventional single-tapered auxiliary waveguides that are presented in [6] (which will be shown in Section III). Therefore, in this paper, we use dualtapered auxiliary waveguides (which are different from those that are used in [6]). The dual-tapered auxiliary waveguides are optimized by using a hybrid simulation method that was given in our previous work [12]. In the succeeding sections, we present the optimal design of a 12-channel AWG demultiplexer as an example. II. THEORY An AWG demultiplexer consists of input/output waveguides, two FPRs, and a set of arrayed waveguides, as shown in Fig. 1(a). There is a constant length difference between adjacent arrayed waveguides. As mentioned earlier, the nonuniformity L u of channels for an AWG demultiplexer can be estimated from the far field at the image plane. In a conventional AWG demultiplexer, the end of each arrayed waveguide is simply a tapered straight waveguide, and the far field at the image /$ IEEE 104

108 3002 JOURNAL OF LIGHTWAVE TECHNOLOGY, VOL. 25, NO. 10, OCTOBER 2007 Fig. 1. (a) Schematic configuration of an AWG demultiplexer. (b) Conventional auxiliary waveguides. (c) Present dual-tapered auxiliary waveguides, where the length l tp1 and starting width w tp1 of taper I are fixed at 10 and 0.1 μm, respectively. plane is of quasi-gaussian shape. In this case, one has a large nonuniformity when the total number of channels is large. To reduce the nonuniformity, a flat-top far field is desirable (actually a rectangular farfield is ideal). To obtain such a far field, Chen et al. [6] used a waveguide array with auxiliary waveguides, as shown in Fig. 1(b), where auxiliary waveguides are tapered to maintain a constant gap width between the auxiliary and neighboring arrayed waveguides. However, for an AWG demultiplexer based on Si nanowires, which has a high index contrast, this structure does not work as well as it does in an SiO 2 AWG demultiplexer (see the results that are given in Section III). Therefore, we modify the conventional single-tapered structure and introduce the dual-tapered auxiliary waveguide, which includes two inverse tapers, as shown in Fig. 1(c). In this way, it is easy to optimize the structure for good channel uniformity. We note that the facets of the auxiliary waveguides may introduce some reflections. Therefore, the small tip width w tp1 should be beneficial to reduce the light reflection at the facet (cladding core) in some cases. For the present case, fortunately, our finite-difference time-domain (FDTD) simulations have shown that both the reflections for the cases with single-tapered [Fig. 1(b)] and Fig. 2. Cross section of a Si-nanowire waveguide. dual-tapered [Fig. 1(c)] auxiliary waveguides are quite small because light is tightly confined in the silicon core. For the simulation, our focus is to achieve the far field from an individual arrayed waveguide and estimate the nonuniformity of channels from this far field. So, our simulation region is chosen to include the auxiliary waveguides and the output FPR. In other words, we consider the light propagating in sequence along the output end of the arrayed waveguides (including the auxiliary waveguides) and the second FPR and finally reach the image plane, which is at the end of the second FPR. One can get an accurate calculation of the far field by using a 3-D-FDTD method. However, this is too time consuming, and thus, it is almost impossible to use it. In this case, a 3-D beam-propagation method (BPM) is a better choice to simulate the light propagation in the whole region. Unfortunately, the 3-D BPM simulation is still very time consuming, particularly when a repeated calculation is needed for the optimization of the auxiliary waveguides. In this paper, we use a hybrid method based on a combination of a 3-D BPM and the Kirchhoff Huygens diffraction formula [12]. This hybrid method is accurate and efficient. First, we simulate the field propagation in the waveguide array (including the auxiliary waveguides) by using a 3-D BPM and obtain the field distribution E(x, y) at the end of the waveguide array. Then, the far field E far (x,y) at the image plane is given by E far (x,y)=a far 0 (x,l)u FPR 0 (y), where u FPR 0 (y) is the fundamental slab mode of FPR, and a far 0 (x,l) is given by using the Kirchhoff Huygens formula [12] a far 0 (x i L)= λ/n FPR 0 + a 0 (x) exp ( in FPR 0 kr ) r cos θ in + cos θ dr dx (1) 2 where a 0 (x) is the excitation coefficient for the fundamental slab mode u FPR 0 (y) of FPR [i.e., a 0 (x) = + E(x, y)ufpr 0 (y)dy], L is the length of FPR, a FPR 0 (x,l) is the far field distribution at the image plane, θ in is the incident angle, θ dr is the diffraction angle, r = (x x) 2 + L 2, λ is the free-space wavelength, k =2π/λ, and n FPR 0 is the effective index for the fundamental slab mode u FPR 0 (y) of FPR. More details about the calculation based on the Kirchhoff Huygens formula can be found in [12]. Here, we define two parameters (ripple R and 10-dB bandwidth BW) to evaluate the shape of the intensity distribution E far (x,y) 2 of the far field as follows: The ripple R 105

109 SHENG et al.: IMPROVE CHANNEL UNIFORMITY OF Si-NANOWIRE AWG DEMULTIPLEXER BY AUXILIARY WAVEGUIDE 3003 Fig. 3. Contour plot of R (in decibels) as a function of l c and w g with (a) dual-tapered auxiliary waveguides and (c) single-tapered auxiliary waveguides. Contour plot of BW (in micrometers) as a function of l c and w g with (b) dual-tapered auxiliary waveguides and (d) single-tapered auxiliary waveguides. is the intensity variance (in decibels) across the output aperture (which is the span covering all output waveguides). Indeed, ripple R represents the nonuniformity, i.e., a smaller ripple indicates a smaller nonuniformity (i.e., a better performance in channel uniformity). The 10-dB bandwidth BW of intensity distribution E far (x,y) 2 is defined as the lateral separation (in micrometers) between two points where the intensity drops to the level of 10 db below the peak of E far (x,y) 2. A smaller 10-dB bandwidth BW indicates that the intensity distribution has a sharper drop outside the output aperture, i.e., less power is focused at the undesired orders (m ± 1). Therefore, a small BW is desirable to reduce the loss for the desired order m. III. RESULT AND DISCUSSION The Si nanowire that is considered in this paper has a silicon core (n =3.455) with a cross section of nm 2,a SiO 2 buffer layer (n =1.46), and an air cladding (n =1.0). The cross section of the Si nanowire is shown as Fig. 2. The free-space wavelength is 1550 nm, and the length of the FPRs is 50 μm. The end separation d g between two adjacent arrayed waveguides (from center to center) is d g =1.1 μm. In our design, the AWG demultiplexer has 50 arrayed waveguides (N WG = 50) and 12 output waveguides (N ch = 12). The separation d o between two adjacent output waveguides is d o = 1.7 μm, and the width of the output aperture is approximately 20.4 μm(= d o N ch ). Then, we use the simulation method that was described in Section II to optimize the auxiliary waveguides. In the simulation, a 3-D semivectorial BPM with a perfectly matched layer boundary treatment is used, and the grid sizes at the lateral directions and the propagation direction are chosen as Δx = Δy =0.01 μm and Δz =0.05 μm, respectively. A fundamental transverse magnetic (TM) mode of the central waveguide is launched as the initial field. All the obtained results in the following part are for the TM polarization if not specified otherwise. To simplify the optimization with multiple variables, we first choose the following parameters for taper I: Tip width w tp1 =0.1 μm (with the consideration of the finite resolution of lithography), and adiabatic taper length l tp1 =10μm. In the 106

110 3004 JOURNAL OF LIGHTWAVE TECHNOLOGY, VOL. 25, NO. 10, OCTOBER 2007 search for an optimal design for taper II, length l c ranges from 2.0 to 4.5 μm, with a step of 0.1 μm, and gap width w g ranging from 0.08 to 0.18 μm, with a step of 0.01 μm. Using the hybrid simulation, we obtain the intensity distribution of the far field for the present configuration with various sets of parameters (l c and w g ). From the intensity distribution, we can obtain the ripple and the 10-dB bandwidth as the parameter set (l c and w g ) varies. Both the results of the conventional design with singletapered auxiliary waveguides and the present design with dualtapered waveguides are shown in Fig. 3. From Fig. 3(a) and (b), we choose the optimal parameters for the dual-tapered auxiliary waveguides as follows: First, we note that both the ripple and 10-dB bandwidth are much more sensitive to the variation of gap width w g than taper length l c, i.e., several tens of nanometers versus several hundreds of nanometers. Therefore, with the consideration of the fabrication tolerance, we choose w g =0.12 μm, which has a relative large tolerance, i.e., about ±20 30 nm when length l c ranges from 2.4 to 3.8 μm. We also note that, with the present design, far field E far (x,y) has sidelobes [see Fig. 4(a)], and the sidelobes increase as l c increases. A larger sidelobe indicates less power that is focused at the desired diffraction order m (i.e., larger insertion loss). For example, when l c =3.3 μm, the sidelobes are at the level of 9 db below the peak of intensity E far (x,y) 2. To depress the sidelobes, we choose a shorter length for taper II (e.g., l c =2.5 μm), and the sidelobes are reduced to about 13 db. From the preceding analysis, we choose l c =2.5 μm and w g =0.12 μm as the optimal parameters. The corresponding fabrication tolerance of gap width w g is ±20 30 nm (which is acceptable when an E-beam lithography is used). For the single-tapered auxiliary waveguides, one sees that a small ripple R and a small 10-dB bandwidth BW can hardly be obtained at the same time [see Fig. 3(c) and (d)]. In other words, by carefully choosing the structure parameters, one can achieve only one of two desirabilities (i.e., a small R or a small BW), while the other one will be remarkably degraded. Fig. 4(b) shows the farfield distributions for two typical designs with the single-tapered auxiliary waveguides. To make a more detailed comparison, the far fields with the present design (with dual-tapered auxiliary waveguides) and the conventional design (without auxiliary waveguides) are also shown in this figure. For one of the designs with the single-tapered auxiliary waveguides (l c =3.3 μm and w g =0.08 μm), the far field distribution has a small ripple R (about 0.23 db) and a toolarge BW (about 75 μm), which indicates too much power focused at the undesired orders (m ± 1), which increases the loss for the desired order m, as mentioned earlier. The other one (with a design of l c =3.0 μm and w g =0.14 μm) has a small BW (about 38 μm), while ripple R is fairly large (0.7 db), in comparison with the optimal design with dual-tapered auxiliary waveguides (which has a ripple of about 0.3 db). Moreover, for the dual-tapered auxiliary waveguides, the ripple R and the 10-dB bandwidth BW of the far field distributions are less sensitive to the variation of the structure parameters than the singletapered counterpart [see Fig. 3(a) (d)]. This indicates that the present dual-tapered design has better fabrication tolerance. Fig. 4. (a) Far field distribution of the present design (with dual-tapered auxiliary waveguides), with w g fixed at 0.12 μm and different values of l c. (b) Two typical far field distributions of the single-tapered auxiliary waveguides with a small R but a large BW (l c =3.3 μm andw g =0.08 μm) and with a small BW but a large R (l c =3.0 μm andw g =0.14 μm). The far field distribution of the conventional design (without auxiliary waveguides) is also shown as a comparison. x is the lateral coordinate along the image plane. For the optimal design of dual-tapered auxiliary waveguides (l c =2.5 μm and w g =0.12 μm), the BPM-obtained field distributions at the plane y =0 (crossing the center of the waveguide) and z =14μm (at the end of the array waveguides) are shown in Fig. 5(a) and (b), respectively. Here, the initial field for the BPM simulation is the fundamental TM mode of the central arrayed waveguide. From this figure, one sees that there is a considerable coupling from the central waveguide to the neighboring arrayed waveguides and auxiliary waveguides. At the end of the arrayed waveguide, one has a field with many sidelobes, as shown in Fig. 5(b). Since the field component that we used is E y, the field has large discontinuity in the y-direction due to the discontinuity of the refractive index [see Fig. 5(b)]. The corresponding far field is shown in Fig. 4(a). To give a comparison, the far field distribution of a 107

111 SHENG et al.: IMPROVE CHANNEL UNIFORMITY OF Si-NANOWIRE AWG DEMULTIPLEXER BY AUXILIARY WAVEGUIDE 3005 Fig. 6. (a) Simulated spectral responses with optimal parameters for the dualtapered auxiliary waveguides. (b) Comparison of the envelopes. Fig. 5. Intensity distribution obtained by using the 3-D BPM simulation at the plane of (a) y =0(crossing the center of the waveguide) and (b) z =14μm (at the end of the array waveguides). The coordinate system that was used here is shown in Fig. 1(c). conventional design with tapered arrayed waveguides (without auxiliary waveguides) is also shown in the same figure. From this figure, one sees that the present design has a flat-top far field and suffers less loss within the output aperture than the conventional design. The 0.5-dB bandwidths for the present design and the conventional design are about 21.4 and 14.7 μm, respectively. Since the spectral response of all channels has an envelope that is similar to the intensity distribution of the far field, the present design is expected to give good channel uniformity. To obtain the spectral responses of the AWG demultiplexer with auxiliary waveguides and evaluate its overall performance, we use the hybrid simulation method that was given in [12] to simulate the whole AWG region (including the input waveguide, the first FPR, the whole arrayed waveguides, the second FPR, and the output waveguides). We have found that, although the channel uniformity is improved when the auxiliary waveguides are introduced, the insertion loss is a little larger than that of the AWG demultiplexer with conventionally tapered arrayed waveguides (without auxiliary waveguides). In addition, if the auxiliary waveguides are introduced at both the input and output ends of the arrayed waveguides, this loss will double because of symmetry. Therefore, for the present AWG demultiplexer, we use an asymmetrical waveguide array that includes a conventional entrance with tapers (no auxiliary waveguides) and an exit with optimal dual-taper auxiliary waveguides. At the conventional entrance, linear tapers are used to connect the input FPR and the single-mode arrayed waveguides. Fig. 6(a) shows the spectral responses that were calculated by using the simulation method that was given in [12] for the designed AWG demultiplexer. The envelope of the spectral responses of all channels is also shown in this figure. The distortion of the spectral responses for the edge channels is due to the aberration, which can be reduced by using a design based on the three-stigmatic-point method [13]. To see the nonuniformity more clearly, we give an enlarged view of the envelope of the spectral responses, as shown in Fig. 6(b). One sees that this envelope has a similar double-peak shape as the far field that was shown in Fig. 4. The nonuniformity L u of the central 12 channels is 0.44 db (satisfying the requirement of L u < 0.5 db). The envelope of the spectral responses in the conventional design (without auxiliary waveguides) is also shown in the same figure for comparison. One sees that the conventional design has a quasi-gaussian-shape envelope, and no more than eight channels are available with the requirement of L u < 0.5 db. The 0.5-dB bandwidths (W 0.5 db ) for the designs are also shown. The available total number of channels of the presently designed AWG demultiplexer is 50% more than that of the conventional one. For the present design, the maximal channel number with a small nonuniformity (< 0.5 db) is 12. If more channels (e.g., 16) are desired, the nonuniformity will increase to 2.5 db for the present design. Even though one does not consider the requirement of L u < 0.5 db, the inherent maximum 108

112 3006 JOURNAL OF LIGHTWAVE TECHNOLOGY, VOL. 25, NO. 10, OCTOBER 2007 Fig. 7. Relationship between W 0.5 db and FPR length L. number of channels is limited due to the free spatial range [= Lλ/(d g n FPR 0 d o )] [2], e.g., N max =16in the present AWG. Therefore, further optimization of the auxiliary waveguides has little effect in increasing the channel number. In this situation, increasing FPR length L becomes necessary to further increase the channel number. Fortunately, one can have low nonuniformity for an AWG demultiplexer of more channels with the present dual-tapered auxiliary waveguides by simply increasing the FPR length (without modifying the structure parameters of the auxiliary waveguides) since the optimal design for the auxiliary waveguide is not sensitive to FPR length L. Fig.7 shows that the 0.5-dB bandwidth (W 0.5 db ) of the intensity distribution E far (x,y) 2 increases almost linearly as the FPR length increases and the slope is From this figure, one can easily choose the FPR length to achieve a low nonuniformity for the desired total number of channels. For example, the FPR length should be larger than 90 μm for a 20-channel AWG demultiplexer. Since Si nanowires are strongly polarization sensitive [14], both the AWG itself and the auxiliary waveguides introduce polarization dependence. Therefore, the present design is only available for one polarization. If the availability for both polarizations is desirable, one should use some special design to make the device polarization insensitive [15]. IV. CONCLUSION We have designed a Si-nanowire AWG demultiplexer with good channel uniformity by introducing and optimizing some dual-tapered auxiliary waveguides at the output end of the waveguide array. With a hybrid simulation method in which we combine a 3-D BPM and the Kirchhoff Huygens formula, the present optimization is more efficient than the conventional pure BPM. We have designed a 12-channel AWG demultiplexer as an example and achieved low channel nonuniformity (less than 0.5 db). The total number of channels that are allowed in the presently designed AWG demultiplexer is 50% more than that of the conventional one. The optimal auxiliary waveguides have a good fabrication tolerance (about ±20 30 nm). Our simulation results have also shown that the optimal design for the auxiliary waveguide is not sensitive to the FPR length, and thus, one can obtain an AWG demultiplexer with good channel uniformity by simply increasing the FPR length (without any modifications for the auxiliary waveguides). REFERENCES [1] M. K. Smit and C. Van Dam, PHASAR-based WDM-devices: Principles, design and applications, IEEE J. Sel. Topics Quantum Electron., vol. 2, no. 2, pp , Jun [2] A. Kaneko, T. 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Dragone, Waveguide grating routers with greater channel uniformity, Electron. Lett., vol. 33, no. 23, pp , Nov [7] Y. H. Min, M.-H. Lee, J. J. Ju, S. K. Park, and J. Y. Do, Polymeric arrayed-waveguide grating router using fluorinated polyethers operating around 1550 nm, IEEE J. Sel. Topics Quantum Electron., vol. 7, no. 5, pp , Sep./Oct [8] S. Suzuki, Y. Inoue, and Y. Ohmori, Polarization-insensitive arrayedwaveguide grating multiplexer with SiO 2 -on-sio 2 structure, Electron. Lett., vol. 30, no. 8, pp , Apr [9] H. Takahashi, Y. Hibino, Y. Ohmori, and M. Kawachi, Polarizationinsensitive arrayed-waveguide wavelength multiplexer with birefringence compensating film, IEEE Photon. Technol. Lett., vol. 5, no. 6, pp , Jun [10] K. Sasaki, F. Ohno, A. Motegi, and T. Baba, Arrayed waveguide grating of μm 2 size based on Si photonic wire waveguides, Electron. Lett., vol. 41, no. 14, pp , Jul [11] C. Dragone, C. R. Doerr, P. Bernasconi, M. Cappuzzo, E. Chen, A. Wong- Foy, and L. Gomez, Low-loss N N wavelength router, Electron. Lett., vol. 41, no. 13, pp , Jun [12] D. Dai, L. Liu, and S. He, Three-dimensional hybrid modeling based on a beam propagation method and a diffraction formula for an AWG demultiplexer, Opt. Commun., vol. 270, no. 2, pp , Feb [13] D. Wang, G. Jin, Y. Yan, and M. Wu, Aberration theory of arrayed waveguide grating, J. Lightw. Technol., vol. 19, no. 2, pp , Feb [14] D. Dai, Y. Shi, and S. He, Characteristic analysis of nanosilicon rectangular waveguides for planar light-wave circuits of high integration, Appl. Opt., vol. 45, no. 20, pp , Jul [15] W. Bogaerts, D. Taillaert, P. Dumon, D. Van Thourhout, R. Baets, and E. Pluk, A polarization-diversity wavelength duplexer circuit in siliconon-insulator photonic wires, Opt. Express, vol.15,no.4,pp , Feb Zhen Sheng was born in Shandong, China, in He received the B.Eng. degree from Zhejiang University, Hangzhou, China, in He is currently working toward the Ph.D. degree at Zhejiang University. He is currently with the Centre for Optical and Electromagnetic Research, State Key Laboratory of Modern Optical Instrumentation, Zhejiang University, and the Joint Research Center of Photonics of the Royal Institute of Technology and Zhejiang University. His research interests include the design and fabrication of planar lightwave circuits. 109

113 SHENG et al.: IMPROVE CHANNEL UNIFORMITY OF Si-NANOWIRE AWG DEMULTIPLEXER BY AUXILIARY WAVEGUIDE 3007 Daoxin Dai (M 07) was born in Jiangxi, China, in He received the B.Eng. and Ph.D. degrees from Zhejiang University, Hangzhou, China, in 2000 and 2005, respectively. He is currently with the Centre for Optical and Electromagnetic Research, State Key Laboratory of Modern Optical Instrumentation, Zhejiang University, and the Joint Research Center of Photonics of the Royal Institute of Technology and Zhejiang University. He has authored about 30 papers in refereed international journals. His research interests include the modeling and fabrication of integrated photonic devices. Sailing He (M 92 SM 98) received the Licentiate of Technology and Ph.D. degrees in electromagnetic theory from the Royal Institute of Technology, Stockholm, Sweden, in 1991 and 1992, respectively. Since 1992, he has been with the faculty of the Royal Institute of Technology. Since 1999, he has also been with the Centre for Optical and Electromagnetic Research, State Key Laboratory of Modern Optical Instrumentation, Zhejiang University, Hangzhou, China, as a Special Changjiang Professor appointed by the Ministry of Education of China. He is also a Chief Scientist for the Joint Research Center of Photonics of the Royal Institute of Technology and Zhejiang University. He has first-authored one monograph (Oxford University Press, New York) and authored or coauthored about 200 papers in refereed international journals. He is the holder of 12 patents in optical communications. 110

114 Available online at Optics Communications 281 (2008) Novel ultrasmall Si-nanowire-based arrayed-waveguide grating interleaver with spirals Daoxin Dai *, Sailing He Centre for Optical and Electromagnetic Research, State Key Laboratory for Modern Optical Instrumentation, Zhejiang University, Hangzhou, Zhejiang , China Received 31 January 2008; received in revised form 27 February 2008; accepted 27 February 2008 Abstract A novel layout is presented to achieve an ultrasmall arrayed-waveguide grating (AWG) interleaver based on Si-nanowire waveguides. Spiral waveguides are inserted in the middle of arrayed-waveguide to obtain a large lightpath (required for the ultra-high diffraction order) in a small occupied area. A designed ultrasmall AWG interleaver with a free spectral range of 0.8 nm has a total size of only about 73 lm 372 lm (0.027 mm 2 ). Ó 2008 Elsevier B.V. All rights reserved. OCIS: ; Introduction The channel spacing of current DWDM system is typically 100 GHz. However, narrower channel spacing is desirable in the future to satisfy the increasing demand of the transmission capacity. The most popular technology for (de)multiplexing is using arrayed-waveguide gratings (AWG), which, however, is not easy for the case of narrow channel spacing (e.g., 50 GHz) due to the large chip size. One cost-effective solution is to use DWDM interleavers, which can separate the input DWDM wavelengths into two interleaved sequences. In this way, the channel spacing of the interleaved sequence is doubled. One can realize an interleaver by using various structures and methods, among which interleavers based on planar lightwave circuit technologies are most attractive. Huang et al. presented the first design of a DWDM interleaver by using an AWG with an ultra-high diffraction order (i.e., a very large lightpath difference between two adjacent arrayed waveguides) [1]. * Corresponding author. Tel.: x215; fax: address: dxdai@zju.edu.cn (D. Dai). In their design, a conventional layout was used and thus a large footprint was introduced. In Ref. [2], a novel architecture for designing planar-echelle-grating interleavers was presented and a reduced footprint (3 188 mm 2 ) was achieved in comparison with the previous designs. However, it is still relatively large. Recent development of Si-nanowire waveguides with an ultra-high index contrast enables the realization of ultrasmall photonic integrated devices [3 8], and thus the study of Si-nanowire waveguides and devices has become very attractive. Si-nanowire-based AWGs with ultra-small sizes have been developed as (de)multiplexers or wavelength routers [6 9]. For a wavelength router or DWDM interleaver, the free spectral range (FSR) Dk FSR is usually small (Dk FSR = N ch Dk ch, where Dk ch is the channel spacing, N ch is the total number of channels), and consequently the diffraction order m is usually high [m = k c /(Dk FSR N g /n g )]. In this case, a large lightpath difference DL (usually several tens (or hundreds) of lm) between two adjacent arrayed waveguides is required for the demanded high diffraction order m. For example, for a Si-nanowire-based AWG interleaver with Dk ch = 0.4 nm and Dk FSR = 0.8 nm, the diffraction order should be about 840 and the lightpath difference DL /$ - see front matter Ó 2008 Elsevier B.V. All rights reserved. doi: /j.optcom

115 3472 D. Dai, S. He / Optics Communications 281 (2008) is about 600 lm (refer to our design example in Section 3). In this case, the separation between two adjacent arrayed waveguides in a standard AWG layout will be much larger than the decoupling separation (2 lm) for Si-nanowire waveguides due to the required large lightpath difference. Therefore, the footprint of an AWG interleaver with a conventional layout is still very large even by using Si-nanowire waveguides with an ultrasmall bending radius (about several micrometers) due to the ultrahigh index contrast. It is well known that the performance (especially the crosstalk) of Si-nanowire AWGs is very sensitive to the size variation of the arrayed waveguides (e.g., the uniformity of the width and thickness of the Si core). Even though the thickness variation is very small (e.g., <5 nm), a remarkable phase error and consequently a large crosstalk will be introduced. On the other hand, it is still difficult to have a very uniform Si core layer in a large area even for commercial SOI wafers. Therefore, it is really necessary to reduce the size of Si-nanowire-based AWGs further for the improvement of the AWG performances. In our previous work [9], we proposed a novel ultracompact Si-nanowire-based arrayed-waveguide grating with microbends, which is suitable for the AWG (de)multiplexers with a relatively high diffraction order (e.g., 100). However, for an AWG interleaver with an ultra-high diffraction order (close to 1000), the separation between arrayed waveguides is still very large (about 100 lm) and consequently the AWG interleaver with microbends is still too large even with our previous AWG design with microbends [9]. In Ref. [10], the authors demonstrated Mach Zehnder interferometer with a high diffraction order of 300 and a corresponding channel spacing of 2.5 nm within a small device foot space by using a flexible layout of the waveguide. However, there is no report on AWG interleavers based on Si-nanowires to the best of our knowledge. In this paper we present an ultra-compact Si-nanowire-based AWG interleaver with a novel layout, which includes two overlapped FPRs (free propagation regions) and arrayed waveguides with spirals. The spirals enable a large lightpath difference in a small occupied area, and consequently minimize the total size of the interleaver. 2. Layout Fig. 1 shows the schematic configuration of the present layout with spirals in the lth waveguide (l > 0). In this figure, we only plot two arrayed waveguides (more is necessary in an actual design). The shortest arrayed-waveguide (l = 0) has five straight sections and four bending sections as shown in Fig. 1. We choose the same bending radius R for all the bends in the spirals. The FPRs are overlapped to minimize the size of the whole structure. The width of the FPR is large enough to avoid any undesirable effects (e.g., channel crosstalk and return loss). For the spiral used in the lth arrayed-waveguide (l > 0), one has V Y l l 1 Δh v 1 h 0 h i ¼ 2h 0 þ 2R þð2i 1ÞDh; v i ¼ v 0 þð2i 1ÞDv; y O l=0 h 1 H v 0 Δv l L io (R 20,θ 20 ) S 30 ð1aþ ð1bþ where i (>1) is an integer, h i and v i are the lengths of the ith straight sections in the horizontal and vertical directions, respectively, Dh and Dv are the separation between two adjacent parallel sections (see Fig. 1), respectively. According to the geometrical relations, one has the lightpath P spiral of the spiral as follows: P spiral =ð2n S Þ¼Nv 0 þð2n 1Þh 0 þ NðN 1ÞDv þ½ðn 1Þ 2 1=2ŠDh þ½gp þðpg þ 2Þð2N 1ÞŠR=2; ð2þ where N is the total number of cycles in a spiral, g = n B /n S (in which n S,andn B are the effective indices in the straight and bending sections). For the total lightpath P l of the lth arrayed-waveguide, one has the following relations: P l =ð2n S Þ¼S 1l þ g 1 R 1l h 1l þ S 2l þ P spiral =ð2n S Þ; ð3þ P l P l 1 ¼ mk c DP; ð4þ where g 1 = n B1 /n S, S 1l and S 2l are the lengths of straight sections, R 1l is the curvature radii of the bending sections, h 1l = p/2 a l (here a l is the radial angle) (see Fig. 1). From Fig. 1, one also has the following relation: L io =2 ¼ X l H l =2 ¼ðS 1l þ L FPR Þ cos a l þ R 1l ð1 cos h 1l Þ ðh 0 þ 2R þðn 3=2ÞDhÞ: ð5þ where X l =(S 1l + L FPR ) cos a l + R 1l (1 cos h 1l ). The height Y l of the lth arrayed-waveguide is given by (see Fig. 1) Y l ¼ðS 1l þ L FPR Þ sin a l þ R 1l sin h 1l þ S 2l þ R; ð6þ From Eqs. (4) (6), one can get the expressions of S 1l, S 2l, and v 0. Then obtain the other geometrical parameters for the lth arrayed-waveguide. For the shortest (l = 0) ar- h 0 R O v 1 S 1l x S 2l (R 1l, θ1l) Fig. 1. Schematic configuration for the present AWG interleaver with spirals. X l 112

116 D. Dai, S. He / Optics Communications 281 (2008) rayed-waveguide, no spiral is used and one can easily get the relations between the geometrical the parameters (such as S 10, S 20, S 30, R 10, R 20, a 0, L FPR, R 30 ). 3. Design examples Here we give a design example to demonstrate the size minimization of an AWG interleaver with a free spectral range of Dk FSR = 0.8 nm (100 GHz) and a channel spacing of Dk ch = 0.4 nm (50 GHz). Fig. 2 shows the cross section of a Si-nanowire, which has a SiO 2 insulator layer, a Si core and an air cladding. The thickness of the SiO 2 insulator layer is thick enough to prevent the leakage to the substrate. Here we choose h SiO2 = 1.5 lm. The width and height of the core are w co = 500 nm and h co = 300 nm to have a low scattering loss [11]. In this case, the FPR of the AWG interleaver is multimode and we add tapers at the ends of the input/output waveguides to diminish the multimode effects in the FPR [12]. The width and length of the used taper are 1.5 lm and 10 lm, respectively. It is well known that the central wavelength and the channel spacing of such a Si-nanowire-based AWG device are usually seriously polarization-dependent because both the arrayed waveguides and the FPR slab waveguide are polarization dependent [13]. One can obtain a polarization-insensitive Si-nanowire-based AWG device by choosing the cross section (w co, h co) of the Si-nanowire and the diffraction order carefully. However, it is not easy to control the size accurately in the fabrication process. A better solution is using a special polarization-diversity approach given in Ref. [14] recently. Here we consider the TM polarization only (while one can have a similar design for the TE polarization). The refractive indices for the core and insulator layers are and 1.460, respectively. In this case, the group index N g and the effective index n g for the considered TM mode are N g = , and n g = , respectively, which are calculated by a full-vectorial finitedifference method (FV-FDM) [15]. The other parameters are given as follows: the central wavelength k c = nm, the total number of channels N ch = 2. For an AWG interleaver, we obtain the diffraction order m = 840 from w co Dk FSR = k c /(mn g /n g ). The separation (between arrayed waveguides) d g = 2.0 lm, the separation (between output waveguides) d o = 2.48 lm, and the FPR length L FPR = 16 lm. We choose the total number of arrayed waveguides N WG = 5, 7, 9, and calculate the corresponding spectral responses by using the hybrid simulation method given in Ref. [16]. Fig. 3 shows the corresponding spectral responses (Channel #2) of the designed AWG interleaver. From this figure, one sees that the sidelobes decrease greatly when the total number N WG increases. On the other hand, a larger total number N WG will make the chip larger. Thus, below we choose N WG = 7 (corresponding to a low crosstalk of < 40 db). For the design with N WG = 7, the parameters for the shortest arrayed-waveguide are given as follows: S 10 = 10 lm, S 20 =0lm, S 30 =4lm, R 10 = R 20 = R =5lm, and a 0 = For the spirals, we choose Dv = Dh = 2 lm, and the initial values v 0 = h 0 =2lm (v 0 and h 0 will be adjusted for the spirals in different arrayed waveguides). Table 1 gives the parameters for all the arrayed waveguides. One sees that the largest separation (=X l+1 X l ) is about than 11.5 lm and the smallest separation is about 1.4 lm (close to the decoupling separation). Therefore, the total size of the interleaver is minimized with the present layout. The designed AWG with the present layout is shown in Fig. 4a. One sees that with the present novel design the device size is only about mm 2 (73 lm 372 lm). Fig. 4b shows the calculated spectral responses of two channels. The excess loss due to the inserted spirals in the Power (db) N WG =5 N WG =7 N WG = Wavelength (nm) Fig. 3. The calculated spectral response of channel #2 when N WG =5,7, and 9. h co Si h SiO2 SiO 2 Si Fig. 2. The cross section of a Si-nanowire. Table 1 The parameters for all the arrayed waveguides l Q S 1l (lm) S 2l (lm) X l (lm) Y l (lm) h 0l (lm) v 0l (lm)

117 3474 D. Dai, S. He / Optics Communications 281 (2008) a b Power (db) Power (db) Power (db) 0 Ch #1-20 Ch # wavelength (nm) c power (db) L=10dB/mm L=5dB/mm L=1dB/mm L=0.5dB/mm wavelength(nm) Fig. 4. (a) The present AWG layout; (b) the spectral response of channel #1 and #2; (c) the spectral response when the Si-nanowire waveguide with different losses. arrayed waveguides is small when the bending radius is large enough (e.g., 5 lm in our design). From Fig. 4b, one sees that the calculated crosstalk is about 40 db. The reported results in the previous papers show that it is not easy to have a measured crosstalk as low as 20 db for a fabricated Si-nanowire-based AWG because a small size variation will introduce a considerable phase error [6 8]. Therefore, for a fabricated AWG interleaver with the present design, the channel crosstalk will be mainly determined by the phase error introduced by the fabrication inaccuracy. A good performance will be achieved with an improved fabrication process. Since the present layout includes many 90 bends with bending losses, we should consider the influences of the bends on the performances of the AWG interleaver, e.g., the bending loss, and the excitation of the higher order modes at the transition between the straight sections and the bends. Fortunately, the higher order modes could be depressed by introducing an appropriate offset [17,18]. Furthermore, for the used bends with a bending radius of R =5lm, the bending loss (the sum of the pure bending loss and the transition loss) is negligible (For example, a low measured bending loss of db/90 was shown in Ref. [19] for a Si-nanowire with a similar cross section). Such a low transition loss indicates that the fundamental modes of the straight and bending sections match to each other very well. Therefore, the excitation of the higher order at the transition should be very small. We note that Si-nanowire waveguides usually have a relative large scattering loss as compared with conventional micrometric waveguides. When the length of an arrayed waveguide is short (e.g., several tens of micrometers), the excess loss due to the scattering is usually acceptable (no more than 1 db) even the waveguide has a high loss of 10 db/mm. 114

118 D. Dai, S. He / Optics Communications 281 (2008) However, for the present AWG interleaver, the length of the longest arrayed waveguides will be more than 3.6 mm (the length difference DL lm), which may introduce a considerable loss. We assume that the used Si-nanowire waveguide has a loss of 10 db/mm, 5 db/mm, 1 db/mm, 0.5 db/mm, and the corresponding calculated spectral responses are shown in Fig. 4c. From this figure, one sees that the scattering loss introduce a considerable loss as predicted, e.g., the total loss is about 15.8 db when the loss L = 10 db/mm. Furthermore, the spectral responses become asymmetrical, which is because the amplitude distribution at the exit of the arrayed waveguides is not symmetrical (the longer waveguide has the larger loss). With an optimal fabrication process, the scattering loss of a Si-nanowire waveguide can be as low as 0.2 db/mm [3] and the corresponding total loss of our AWG interleaver is about 1.6 db (which is acceptable). Thus, our AWG interleaver has better performances when lower-loss Si-nanowire waveguides are developed. For photonic integrated devices based on Si-nanowires, one should consider the polarization effects, such as the polarization-dependency [7] and the polarization crosstalk at the microbend [20]. One can realize polarization-insensitive Si-nanowire-based AWGs by using a special polarization-diversity approach [14] or optimizing the height and width of the core [13]. According to the analysis given in Ref. [20], the polarization crosstalk should be negligible at the microbend (5 lm) of the spirals when the sidewall of a Si-nanowire is vertical. 4. Conclusion In this paper, we have proposed a novel layout design for an ultra-small Si-nanowire-based AWG interleaver, for which an ultra-high diffraction order (at the order of 1000) is required. Arrayed waveguides with spirals have been introduced to reduce the separation between arrayed waveguides and thus obtain the large lightpath difference in a small occupied area. This minimizes the total size of the AWG interleaver. As an example, an ultrasmall AWG interleaver with a narrow FSR (Dk FSR = 0.8 nm) has been designed and the total size is only about mm 2 (0.073 mm mm). Acknowledgement This project was supported by research grants (Nos and 2006R10011) of the provincial government of Zhejiang Province of China, the National Science Foundation of China (Nos and ). References [1] D.W. Huang, T.H. Chiu, Y. Lai, Arrayed Waveguide Grating DWDM Interleaver, Presented at the Optical Fiber Communications Conf. (OFC), Anaheim, CA, March 17 22, 2001, Paper WDD80-1. [2] Serge Bidnyk, Ashok Balakrishnan, André Delage, Mae Gao, Peter A. Krug, Packirisamy Muthukumaran, Matt Pearson, J. Lightwave Technol. 23 (3) (2005) [3] W. Bogaerts, R. Baets, P. Dumon, V. Wiaux, S. Beckx, D. Taillaert, B. Luyssaert, J. Van Campenhout, P. Bienstman, D. Van Thourhout, J. Lightwave Technol. 23 (2005) 401. [4] T. Tsuchizawa, K. Yamada, H. Fukuda, T. Watanabe, J. Takahashi, M. Takahashi, T. Shoji, E. Tamechika, S. Itabashi, H. Morita, IEEE J. Sel. Top. Quantum Electron. 11 (2005) 232. [5] K.K. Lee, D.R. Lim, D. Pan, C. Hoepfner, W-Y Oh, K. Wada, L.C. Kimerling, K.P. Yap, M.T. Doan, Opt. Lett. 30 (2005) 498. [6] K. Sasaki, F. Ohno, A. Motegi, T. Baba, Electron. Lett. 41 (2005) 801. [7] D. Dai, L. Liu, L. Wosinski, S. He, Electron. Lett. 42 (2006) 400. [8] P. Dumon, W. Bogaerts, D. Van Thourhout, D. Taillaert, R. Baets, J. Wouters, S. Beckx, P. Jaenen, Opt. Express 14 (2006) 664. [9] Daoxin Dai, Sailing He, Opt. Express 14 (12) (2006) [10] Fumiaki Ohno, Tatsuhiko Fukazawa, Toshihiko Baba, Jpn. J. Appl. Phys. 44 (7A) (2005) [11] F. Grillot, L. Vivien, S. Laval, D. Pascal, E. Cassan, IEEE Photon. Technol. Lett. 16 (2004) [12] Daoxin Dai, Sailing He, Opt. Commun. 247 (4-6) (2005) 281. [13] D. Dai, S. He, Opt. Lett. 31 (2006) [14] W. Bogaerts, D. Taillaert, P. Dumon, D. Van Thourhout, R. Baets, Opt. Express 15 (4) (2007) [15] N.-N. Feng, G.-R. Zhou, C. Xu, W.-P. Huang, J. Lightwave Technol. 20 (2002) [16] D. Dai, L. Liu, S. He, Opt. Commun. 270 (2) (2007) 195. [17] V. Subramaniam, G.N. DeBrabander, D.H. Naghski, J.T. Boyd, J. Lightwave Technol. 15 (6) (1997) 990. [18] M. Rajarajan, S.S.A. Obayya, B.M.A. Rahman, et al., IEE Proc. Optoelectron. 147 (6) (2000) 382. [19] Y.A. Vlasov, S.J. McNab, Opt. Express 12 (8) (2004) [20] A. Sakai, T. Fukazawa, T. Baba, J. Lightwave Technol. 22 (2) (2004)

119 654 IEEE JOURNAL OF QUANTUM ELECTRONICS, VOL. 45, NO. 6, JUNE 2009 Theoretical Investigation for Reducing Polarization Sensitivity in Si-Nanowire-Based Arrayed-Waveguide Grating (de)multiplexer With Polarization-Beam-Splitters and Reflectors Daoxin Dai, Member, IEEE, Yaocheng Shi, and Sailing He, Senior Member, IEEE Abstract A novel design for reducing polarization sensitivity in silicon-on-insulator-based arrayed-waveguide grating (AWG) (de)multiplexer is presented. Each arrayed waveguide has two sections separated by a polarization beam splitter (PBS). These two sections have different core widths and length differences. With these PBSs, one polarization is reflected and the other one goes through. The through polarization enters the second section and is then reflected by a reflector at the end of the second section of the arrayed waveguide. The theoretical simulation shows that one can diminish greatly the polarization sensitivity of both the central channel wavelength and the channel spacing by optimizing the core width and length difference of the second section. The design procedure and formulas are given and an appropriate diffraction order is chosen to obtain a good fabrication tolerance. As an example, an ultrasmall ( m 2 ) AWG (de)multiplexer with eight channels and a channel spacing of 4 nm is designed to have minimized polarization sensitivity and Bragg-grating PBSs and photonic crystal reflectors are used. Index Terms Arrayed-waveguide grating (AWG), polarizationinsensitive, reflective, Si nanowire. I. INTRODUCTION Silicon-on-insulator (SOI) waveguides [1], [2] have become popular for planar lightwave circuits (PLC) because of their compatibility with mature CMOS technologies. The recently developed SOI nanowires have ultrahigh refractive index contrasts and enable ultrasharp bending [1], [2], thus attracting much attention. It is well known that an arrayed-waveguide grating (AWG) (de)multiplexer is one of the most important components in various wavelength-division multiplexing (WDM) modules and systems [3]. Therefore, it has become very attractive to develop ultrasmall AWG devices by using Si nanowires [4] [6]. Due to the ultrahigh refractive index Manuscript received May 08, 2008; revised July 19, Current version published May 13, This work was supported in part by the National Nature Science Foundation of China under Grant The authors are with the Centre for Optical and Electromagnetic Research, State Key Laboratory for Modern Optical Instrumentation, Zhejiang University, Hangzhou , China, and also with the Joint Research Center of Photonics of KTH (the Royal Institute of Technology, Sweden) and Zhejiang University, Hangzhou , China ( dxdai@zju.edu.cn). Color versions of one or more of the figures in this paper are available online at Digital Object Identifier /JQE contrast and the small cross section of a Si nanowire, there are several challenges for the development of photonic integrated devices based on Si nanowires, such as the large scattering loss and the low coupling efficiency to a single-mode fiber (SMF). Fortunately, people have obtained low-loss Si nanowires by using improved fabrication processes (e.g., double thermal oxidation steps [7]) and high coupling efficiency to an SMF by using some mode converters (e.g., inverse-tapers [2], bilevel tapers [8], grating couplers [9]). However, it is well known that photonic integrated devices based on an Si nanowire are usually severely polarization sensitive [5], [10] [12]. For AWG (de)multiplexers-based Si nanowires, since the arrayed waveguides and the free propagation region (FPR) slab waveguides have very large birefringence, not only the central channel wavelength but also the channel spacing is seriously polarization-dependent [13]. This is very different from the AWG (de)multiplexers based on conventional micrometric optical waveguides. The polarization compensation methods developed for AWG (de)multiplexers based on micrometric waveguides usually compensate only the polarization dependence of the central channel wavelength [14] [16]. Thus, they are not suitable for Si-nanowire-based AWG (de)multiplexers. In our previous paper [13], we presented a design of polarization-insensitive AWG (de)multiplexers by choosing optimal cross section for the arrayed waveguides. However, this limits the flexibility of choosing AWG parameters (e.g., the diffraction order, the core width, and core height of arrayed waveguides) to some degree, and is not compatible to other circuits with a special core height on the same substrate. Recently, a method of polarization diversity has been demonstrated [17], which is a good solution in some cases, e.g., for an individual AWG chip. However, this becomes difficult to utilize when one wants to integrate a polarization-insensitive AWG device with other photonic circuits on the same substrate. To avoid these problems, we present in this paper a novel reflective polarization-insensitive AWG (de)multiplexer based on Si nanowire by introducing a polarization beam splitter (PBS) in each arrayed waveguide. Therefore, each arrayed waveguide has two sections divided by a PBS. With these PBSs, one polarization is reflected and the other goes through. The through one is then reflected by a reflector placed at the end of the second section. In this way, the two polarizations (TE and TM) will have different lightpaths. Since both the central channel wavelength /$ IEEE Authorized licensed use limited to: Zhejiang University. Downloaded on May 15, at 00:41 from IEEE Xplore. Restrictions apply.

120 DAI et al.: THEORETICAL INVESTIGATION FOR REDUCING POLARIZATION SENSITIVITY IN WG (de)multiplexer 655 1) Central Channel Wavelength : For the present reflective AWG (de)multiplexer, the grating equation is given as (1) Fig. 1. Schematic configurations of (a) the present AWG (de)multiplexer and (b) the Bragg grating PBS and the PhC reflector. and the channel spacing in Si-nanowire-based AWG (de)multiplexers are polarization sensitive, one should have at least two adjustable parameters to realize polarization insensitivity. With the present design, one can diminish the polarization dependence of both the central channel wavelength and the channel spacing by adjusting the lightpaths, i.e., optimizing core width and length of the second sections. Furthermore, such a reflective-type structure is beneficial to achieve a compact AWG (de)multiplexer [18]. where is the diffraction order, is the wavelength, and are the effective indexes in the first and second sections of the arrayed waveguide, is the effective index in the FPR, and are the lengths of the first and second sections in the shortest arrayed waveguide, and are the length differences between adjacent arrayed waveguides in the first and second sections, is the end separation of two adjacent arrayed waveguides, is the FPR length, and (, are the positions of the input and output waveguides, respectively). From (1), one has that is For the central wavelength, one has and thus (2) (3) II. STRUCTURES Fig. 1(a) shows our present polarization-insensitive AWG (de)multiplexer, which includes an input waveguide (at, e.g., the edge), an FPR, several output waveguides (on the same side of the FPR as the input waveguide), and many arrayed waveguides. Each arrayed waveguide has two sections separated by a PBS. With this PBS, one polarization is reflected and the other goes through. The beam of through polarization is reflected by the reflector connected at the end of the second section. The PBSs and reflectors can be realized by using, e.g., 2-D or 1-D (Bragg gratings) photonic-crystal (PhC) structures, as shown in Fig. 1(b). In this way, the two polarizations (TE and TM) will have different lightpaths so that it is possible to diminish the polarization sensitivity by appropriately choosing the parameters (i.e., the core width and the length ) for the second sections of the arrayed waveguides. In order to improve the transmission/reflection efficiencies of the PBS and the reflector, we broaden the core width by using tapers [like that shown in Fig. 1(b)] and here, we choose in our design [see Fig. 1(b)]. In the following part, we will give the formula to determine width and length difference between two adjacent arrayed waveguides in Section II. (4) For a polarization-insensitive AWG, one should have the same central channel wavelength for both polarizations, i.e.,. For the case shown in Fig. 1(b), the TM polarization is reflected by the PBS; and thus, one has and for the TM polarization. Therefore, it follows from (2) that When parameters of arrayed waveguides in the first section and the diffraction orders and are given, one can obtain the corresponding length difference for any given core width. (5) Authorized licensed use limited to: Zhejiang University. Downloaded on May 15, at 00:41 from IEEE Xplore. Restrictions apply.

121 656 IEEE JOURNAL OF QUANTUM ELECTRONICS, VOL. 45, NO. 6, JUNE ) Channel Spacing : In this part, the dispersion characteristics for the present AWG are considered. From (1), one has In order to study dispersion position, i.e., (6), we consider a fixed input Substituting (4) into the previous equation, one has where For the focus position and Usually,, one has and (8) can be rewritten as, therefore (7) (8) (9) (10) For a polarization-insensitive AWG demultiplexer, one has the same central wavelength (i.e., ) and the same dispersion coefficients for TE and TM polarizations, i.e., From (10) and (11), one has (11) (12) For Si nanowires with (which is used for photonicintegrated devices in most published papers [4] [6]), one has From (12), one has. Note that if one chooses Si nanowires with, one will have, which means that TE polarization should be reflected by the PBS and the through TM polarization will be reflected by the reflector at the end. 3) Design Procedure for the Present Polarization-Insensitive AWG (de)multiplexers.: In order to obtain a polarization-insensitive AWG (de)multiplexer, we give the following the procedure. Step Step Step Step 1) Design an AWG (de)multiplexer by considering only TM polarization first. This step is for determining parameters like the cross section of arrayed waveguides, the FPR length, the length difference, the end separation, the diffraction order, etc. 2) According to (12), one can obtain the optimal length for any given core width ; Plot curve #I for relating and. 3) According to (5), one can obtain the optimal length for any given core width ; Plot curve #II for relating and. 4) Get the cross point of these two curves (i.e., curve and curve ), which give the optimal design for the second part. III. DESIGNS According to the procedure described in Section II, the first step is to design an AWG (de)multiplexer for TM polarization. We choose the following AWG parameters: the central wavelength nm, the channel number and the channel spacing nm, the number of arrayed waveguides, the diffraction order, the FPR length m, and the end separation m. Here, we choose a relatively large channel spacing in order to have a small AWG size. When one chooses smaller channel spacing, the device size will increase. For the present design, we use an SOI wafer with a 300 nm Si layer on a 1 m insulator layer and the width of arrayed waveguides is nm. In this case, the effective indexes for the arrayed waveguides and the FPR slab waveguides are,,, and. The group indexes are,,, and. With such a design, the separation between two adjacent output waveguides is about m, and the length difference of the first section is m. For the reflective AWG (de)multiplexer, we choose the edge access waveguide as the input waveguide, i.e., m. Therefore, from (12), one has m, where is determined by core width. This gives the first condition for determining length difference and the core width, as shown by the thick curve in Fig. 2(a). The second one is given by (5). The diffraction order for TE polarization in (5) is related to core width and length difference (which is unknown so far). Therefore, we choose a series of integers as possible Authorized licensed use limited to: Zhejiang University. Downloaded on May 15, at 00:41 from IEEE Xplore. Restrictions apply.

122 DAI et al.: THEORETICAL INVESTIGATION FOR REDUCING POLARIZATION SENSITIVITY IN WG (de)multiplexer 657 Fig. 2. (a) Length difference 1L as core width w varies. (b) The optimal width w and the optimal length 1L for any given diffraction order m. diffraction order for TE polarization in the range of. Then, for any given diffraction order in this range, (5) will give a second equation for relating the length difference and the core width [see the thin curves in Fig. 2(a)]. From this figure, one sees that there are several cross points when the diffraction order for the TE polarization is in the range of. These crosses give the corresponding optimal lengths and the optimal core widths, which are shown in Fig. 2(b). From this figure, one sees there are five sets of values for achieving polarization-insensitive AWG (de)multiplexers. In practical cases, usually there are some fabrication errors. Here, we consider the case with a fabrication error of the core width in the range of [ 20, 20] nm. Fig. 3(a) and (b) shows the residual polarization-dependent channel spacing and the residual polarization-dependent wavelength. When the core width deviates from its optimal value, both and increase almost linearly. From Fig. 3(a), one sees that the residual polarization-dependent channel-spacing is not sensitive to deviation. Even when is as large as 20 nm, one has nm (less than 1.25% of the channel spacing) for any given diffraction order ranging from 26 to 30. Fig. 3(a) also shows that it is possible to reduce further by choosing an appropriate diffraction order. For example, for the design with, one has nm when nm. Fig. 3. For the case with a fabrication error w of the core width, (a) the residual polarization-dependent channel spacing 1 and (b) the residual PD denoted by. Since the residual for the edge channel is given by, which should be smaller than 1/10 of the channel spacing, the residual polarization-dependent channel-spacing will limit the maximal available channel number. Fortunately, for our present design nm, because (e.g., 0.02 nm) is very small, the available channel number is close to 40, which is adequate for most applications. In Fig. 3(b), one sees that the slopes of the lines for the residual differ quite a lot, which indicates that fabrication tolerance may differ quite much when choosing a different diffraction order. For example, for the design with, the residual is more than 5 nm when there is a very slight deviation of 10 nm. In this case, one has to control the fabrication very precisely to guarantee the deviation nm (even smaller). Fortunately, it is possible to relax the fabrication requirement by choosing an appropriate diffraction order. From Fig. 3(b), one sees that the curve for has the minimal slope, which indicates a maximal fabrication tolerance. When there is a fabrication error of nm, the residual (i.e., ) isas small as 0.5 nm (which is about 1/8 of the channel spacing). Therefore, in our design, we choose and one has the optimal length m and the optimal core width m correspondingly. Authorized licensed use limited to: Zhejiang University. Downloaded on May 15, at 00:41 from IEEE Xplore. Restrictions apply.

123 658 IEEE JOURNAL OF QUANTUM ELECTRONICS, VOL. 45, NO. 6, JUNE 2009 Fig. 4. Reflection or transmission spectral responses for (a) the designed Bragg grating PBS and (b) the designed 2-D PhC reflector. When a larger fabrication tolerance is required, one should choose the AWG parameters more carefully. For example, if we slightly modify the diffraction order to, the FPR length will be adjusted to m so that the separation of output waveguides is almost unchanged. With this design, we obtain four sets of optimal values for the parameters with different diffraction orders for the TE polarization (, 26, 27, and 28). Among them, the design with gives a curve of [similar to that shown in Fig. 3(b)] with a very small slope at the range of nm nm. In this case, the residual (i.e., ) is as small as 0.4 nm (which is only about 1/10 of the channel spacing) when nm nm. This indicates a larger fabrication tolerance. In the following part, we give a design for the PBS and the reflector used in the present polarization-insensitive AWG (de)multiplexer. In order to minimize the excess insertion loss and crosstalk due to the inserted PBSs, it is important to have high reflection efficiency for TM polarization as well as large transmission for TE polarization by using optimized PBSs. In order to avoid a time-consumed 3-D FDTD simulation, a 2-D FDTD modeling based on an EIM is used for calculating the reflection and transmission in the designed Bragg grating PBS. In our case, the effective indexes for the TE and TM polarizations are and (at the rate of 1550 nm), respectively. For the PBS, we use a Bragg grating with the period number, the period length nm, and the air gap length nm. The taper width wtp1 is chosen to be the same as core width, i.e., m and the taper length is m. In this way, the third taper in the middle [see Fig. 1(b)] is avoided. The calculated reflection spectrum for TM polarization and the transmission spectrum for TE polarization of the Bragg grating PBS are shown in Fig. 4(a) by the thick curve and the thin curve, respectively. Here, the TE and TM polarization modes have their main electric field components parallel to the horizontal and vertical directions, respectively. From this figure, one sees that TM polarization has high reflection efficiency (about 93.6% at the rate of 1550 nm) while TE polarization has large transmission (about 95% at the rate of 1550 nm) over a broad band of [1500, 1600] nm. PhC structures have been used as ultracompact reflectors (which could be shorter than a Bragg grating reflector) with good performances [19]. Thus, we use a 2-D-PhC structure for the reflector (at the end) for TE polarization in order to obtain a broadband reflection spectrum with high efficiency as shown by the inset of Fig. 4(b) (one can also use a reflector based on Bragg gratings). The parameters of the PhC reflector are chosen as follows: the lattice constant nm and the diameter of air holes nm so that we have a photonic bandgap (PBG) in the window around 1550 nm for the TE polarization. When the operation wavelength is within the bandgap of a PhC structure, the incident light will be reflected almost completely in an ideal case. Therefore, the PhC reflector should have relatively large sizes to include enough period numbers of holes in both and directions so that the PBG characteristic is supported. Here, we choose and [see the inset in Fig. 4(b)]. In order to enhance the reflection efficiency, we use a cosine taper with m and m. The calculated reflection efficiency of the designed 2-D-PhC reflector for TE polarization is shown in Fig. 4(b), from which one sees that there is a high reflection efficiency ( 98%) over the whole window of [1500, 1600] nm. With such a design, the theoretical additional loss due to the inserted reflector is very small. Such a PhC reflector is very compact (the length is only about 2.1 m) and has a good performance. For the fabrication of Bragg grating PBSs and PhC reflectors, one usually needs to use high-resolution E-beam or deep-uv lithography technologies. People have demonstrated good experimental results for Bragg grating filters [2] and PhC corner reflector [19] based on SOI-wafers. One can use similar fabrication techniques for the present Bragg grating PBSs and PhC reflectors. Fig. 5 shows the layout of the designed polarization-insensitive AWG (de)multiplexer with the Bragg grating PBSs and the PhC reflectors designed earlier. In this figure, the enlarged view of the Bragg grating PBS and the PhC reflector used here are also shown. The middle separations between two adjacent arrayed waveguides are m, which are larger than the decoupled separation [20]. The bending radius is m, which is large enough for a low bending loss [21]. The edge access waveguide is chosen as the input waveguide and the other waveguides are used as the output waveguides. The designed AWG has a very small footprint of only Authorized licensed use limited to: Zhejiang University. Downloaded on May 15, at 00:41 from IEEE Xplore. Restrictions apply.

124 DAI et al.: THEORETICAL INVESTIGATION FOR REDUCING POLARIZATION SENSITIVITY IN WG (de)multiplexer 659 Fig. 6. Calculated spectral responses of the designed polarization-insensitive AWG (de)multiplexer for TE and TM polarizations. Fig. 5. Layout of the designed polarization-insensitive AWG (de)multiplexer. about m (0.007 mm ). When one chooses smaller channel spacing, the device size will be larger. In order to estimate the performances of the designed polarization-insensitive AWG (de)multiplexer, we calculate the spectral responses for both polarizations with an analytical formula of [22], where and are the coupling coefficients from the input waveguide and output waveguide to the th arrayed waveguide, respectively, is the phase delay of the th arrayed waveguide, is the attenuation coefficient due to these inserted PBSs and reflectors. One has for TE polarization and for TM polarization, where and are, respectively, the transmission coefficient (for TE polarization) and the reflection coefficient (for TM polarization) of the Bragg PBS, is the reflection coefficient (for TE polarization) of the PhC-reflector [see Fig. 4(a) and (b)]. We also note that these coefficients have wavelength-dependent phase terms. On the other hand, for an AWG demultiplexer, what one needs to consider is the phase difference between adjacent arrayed waveguide (other than the phase delay itself). In the present case, since all the arrayed waveguides have the identical PBSs and reflectors, the phase difference between adjacent arrayed waveguide will be independent of the phase terms of these coefficients. Thus, only the wavelength-dependent amplitude coefficients are included in the calculation of the spectral responses. Fig. 6(a) shows the calculated spectral responses of all channels for TE and TM polarizations. From these figures, one can see that the central wavelengths of both polarizations almost coincide for all the eight channels. This indicates that both the central channel wavelength and the channel spacing are polarization insensitive. In order to see this more clearly, in Fig. 6(b), we show the enlarged view of the top of the spectral responses. From this figure, one sees that the is very small for all the channels. We note that there is a polarization-dependent loss (PDL) of about 0.9 db, which is caused by the polarization dependence of the coupling coefficients (, and ). The PDL could be reduced by further optimizing the used PBSs and reflectors and by improving the coupling efficiency as well as (e.g., by using some mode converters like bilevel tapers [6]). The spectral responses in Fig. 6(b) have relatively large channel nonuniformity, which can be improved easily by increasing the FPR length (e.g., choosing ) if needed. IV. CONCLUSION In this paper, we have proposed a novel design for reducing polarization sensitivity in Si-nanowire-based AWG (de)multiplexer, in which each arrayed waveguide has a PBS and a reflector. With the PBSs, one of the TE and TM polarizations goes through and the other is reflected. The through polarization is then reflected by the reflector connected at the end of each arrayed waveguide. In this way, the TE and TM polarizations have different lightpaths. One should note that it is important to improve performances of the PBSs and reflectors (e.g., high-polarization-splitter ratio and low insertion loss) through optimal designs so that the performances of the designed polarization-insensitive AWG (de)multiplexer do not degrade much. By optimizing the core width and the length difference of the second section (between the PBS and the reflector), the polarization sensitivity of both the central channel wavelength and the channel spacing has been canceled. We have also given the design procedure and formulas to determine the optimal core width and length difference in the second sections. Finally, we have given an example for the design of a polarization-insensitive AWG (de)multiplexer with Bragg-grating PBSs and PhC reflectors. Our calculated spectral responses have shown that both the central wavelength and the channel spacing are polarization-insensitive. Meanwhile, there is a 0.9 db PDL caused by the polarization dependence of the coupling coefficients (,, and ) and this PDL could be reduced by further optimization. Even though we only give a design for an AWG demultiplexer with a relatively large channel spacing, theoretically speaking, the present design is suitable for reducing polarization sensitivity in Si-nanowire-based AWG (de)multiplexers with any channel spacing. However, one should note that the fabrication tolerance will become smaller for the case of smaller channel spacing. For example, for an optimized AWG (de)multiplexer with a channel spacing of 100 GHz, one has to control the fabrication error in the range of nm so Authorized licensed use limited to: Zhejiang University. Downloaded on May 15, at 00:41 from IEEE Xplore. Restrictions apply.

125 660 IEEE JOURNAL OF QUANTUM ELECTRONICS, VOL. 45, NO. 6, JUNE 2009 that the residual (i.e., ) is less than 0.1 nm (which is only about 1/8 of the channel spacing). REFERENCES [1] W. Bogaerts, P. Dumon, D. V. Thourhout, D. Taillaert, P. Jaenen, J. Wouters, S. Beckx, V. Wiaux, and R. G. Baets, Compact wavelengthselective functions in silicon-on-insulator photonic wires, IEEE J. Sel. Top. Quantum Electron., vol. 12, no. 6, pp , Nov. Dec [2] T. Tsuchizawa, K. Yamada, H. Fukuda, T. Watanabe, J. Takahashi, M. Takahashi, T. Shoji, E. Tamechika, S. Itabashi, and H. Morita, Microphotonics devices based on silicon microfabrication technology, IEEE J. Sel. Top. Quantum Electron., vol. 11, no. 1, pp , Jan. Feb [3] M. K. Smit and C. van Dam, Phasar-based WDM-devices: Principles, design and applications, IEEE J. Sel. Top. Quantum Electron., vol. 2, no. 2, pp , Jun [4] K. Sasaki, F. Ohno, A. Motegi, and T. Baba, Arrayed waveguide grating of m size based on Si photonic wire waveguides, Electron. 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In 2004, he was selected to be an exchange Ph.D. student at KTH. Then, he joined Zhejiang University as an Assistant Professor and become Associate Professor in He has authored about 40 refereed international journals papers. His current research interests include silicon micro-/nanophotonics for optical communications, optical interconnections, and optical sensing. Yaocheng Shi received the B.Eng. degree from the Department of Optical Engineering, Zhejiang University, Hangzhou, China, and the PhD degree from the Royal Institute of Technology (KTH), Stockholm, Sweden, in 2003 and 2008, respectively. Currently, he is a Postdoctoral Fellow with the Centre for Optical and Electromagnetic Research, Zhejiang University. His current research interests include the design and fabrication of photonic integrated devices. Sailing He (M 92 SM 98) received the Licentiate of Technology and the Ph.D. degree in electromagnetic theory from the Royal Institute of Technology (KTH), Stockholm, Sweden, in 1991 and 1992, respectively. Since 1992, he has been a member of the faculty of KTH. He has also been with the Centre for Optical and Electromagnetic Research, Zhejiang University, Zhejiang, China, since 1999 as a Special Changjiang Professor appointed by the Ministry of Education of China. He is also a Chief Scientist for the Joint Research Center of Photonics of KTH and Zhejiang University. He has first-authored one monograph, authored/coauthored over 200 papers in refereed international journals, and has been granted a dozen of patents in optical communications. Authorized licensed use limited to: Zhejiang University. Downloaded on May 15, at 00:41 from IEEE Xplore. Restrictions apply.

126 Design and fabrication of a 200 GHz Si-nanowire-based reflective arrayed-waveguide grating (de)multiplexer with optimized photonic crystal reflectors Yaocheng Shi, Xin Fu, and Daoxin Dai* Centre for Optical and Electromagnetic Research, State Key Laboratory of Modern Optical Instrumentation, Zhejiang University, Hangzhou, China *Corresponding author: dxdai@zju.edu.cn Received 26 April 2010; revised 26 July 2010; accepted 2 August 2010; posted 11 August 2010 (Doc. ID ); published 2 September 2010 A compact Si-nanowire-based reflective arrayed-waveguide grating (AWG) for dense wavelength-division multiplexing is proposed. At the end of each waveguide in the array, there is an individual photonic crystal (PhC) reflector, which makes the AWG layout design very flexible. All the PhC reflectors are with the same design. With such a design, the total size of the AWG (de)multiplexer is reduced by more than a half. The reflection efficiency of the used PhC reflectors is enhanced by optimizing the taper between the arrayed waveguides and the PhC reflector. A 200 GHz AWG (de)multiplexer is designed and fabricated as an example. The total size is only about 193 μm 168 μm Optical Society of America OCIS codes: , /10/ $15.00/ Optical Society of America 1. Introduction In the past decade, the most popular material system used for arrayed-waveguide gratings (AWGs) is the SiO 2 -on-si buried optical waveguide because of its low loss and high coupling efficiency to single-mode fibers. However, the bending radius of such a buried waveguide is very large (e.g., about 5000 μm) due to the low index contrast [1]. Consequently, the AWG chip usually has a large size of about 10 cm 2.Itis desirable to reduce the AWG size so that more AWG chips can be included in a single wafer to lower the cost. Furthermore, in the future it will become increasingly desirable to integrate more components with AWGs in a single chip to realize more complex functions for a wavelength-division multiplexed (WDM) system. How to reduce the AWG size has attracted much attention in the past years. Recently, Si-nanowire waveguides and devices on silicon-on-insulator (SOI) wafers have been developed dramatically [2 5]. Because of the ultrahigh index contrast between the core (Si) and the cladding (SiO 2 or air), Si nanowires have the capability for sharp bending with a radius of about 2 μm. With Si nanowires, several groups have developed ultracompact photonic-integrated devices including AWG (de)multiplexers/routers [2 4]. Such Si-nanowire AWGs (about 10 4 μm 2 ) are usually 1=10 5 smaller than the conventional AWG chip (about 10 cm 2 ). However, for AWG-based Si nanowires, the performance (especially the crosstalk) is very sensitive to the size variation of the arrayed waveguides (e.g., the uniformity of the width and thickness of the Si core layer). A very small size variation (<5 nm) will cause remarkable phase errors and consequently a large crosstalk. The size variation comes not only from the lithography and the etching, but also from the SOI wafer itself. Currently, it is still difficult to have a very uniform Si layer in a large area even for commercial SOI wafers. Therefore, for Si-nanowirebased AWGs, it is desirable to reduce the device size further to improve the AWG performances. In our previous papers, we proposed ways to reduce the AWG size by introducing novel layouts [6,7]. Another typical and effective method to reduce 10 September 2010 / Vol. 49, No. 26 / APPLIED OPTICS

127 the AWG size is by using the reflective type [8 10]. However, for those demonstrated reflective-type AWGs based on micrometric optical waveguides [8], the freedom for the layout design of the AWG chip is restricted in some degree. First, in some cases, one usually has to arrange all arrayed waveguides parallel at the end connecting to the same reflection mirror and make the mirror perpendicular to all the arrayed waveguides [8 10]. Second, one usually has to place fiduciary marks at the end of the waveguide grating to define the reflecting surface and then carefully cleave or dice the arrayed waveguides. The cleaved or diced facet should be diamond polished further to assure easy coupling and flatness [8]. In this way, when one wants to integrate a reflective AWG with other components, the AWG usually has to be placed at the edge of the chip. In addition, one usually has to enhance the reflection efficiency by introducing dielectric or metal films (e.g., Cr Au film [8]) at the facet [8 10]. This makes the fabrication relatively complex. It is also not easy to achieve a high-quality reflection mirror [10], and thus the performances of a reflective AWG are usually not good [11]. For the case of Si-nanowire-based AWGs, the situation will be more difficult if one uses the conventional reflective mirror since the intrinsic small size makes the fabrication of a mirror much more difficult (almost impossible). In this paper, we propose a reflective Si-nanowire AWG with microreflectors based on a photonic crystal (PhC) structure. By using the bandgap effect of PhC structures [12], one could realize highly reflective reflectors [13,14]. To enhance the reflectivity of the PhC reflector, we introduce and optimize a taper inserted between the arrayed waveguide and the PhC reflector. The PhC reflectors could also be replaced by a Bragg-grating (i.e., a onedimensional PhC structure) reflector proposed by [15,16]. A Bragg-grating reflector is a good option because the design is simple. However, usually the trench width for a broadband Bragg-grating reflectors is about 100 nm [15]. In contrast, the diameter of air holes in an Si-based PhC reflector is usually over 250 nm, which should be better for the fabrication when using the deep-uv lithography process (instead of the E-beam lithography). With PhC reflectors, the fabrication of such an ultrasmall reflective AWG is easy and compatible to the standard complementary metal-oxide-semiconductor (CMOS) process, and no additional fabrication process is needed in comparison with the fabrication of regular AWGs based on Si nanowires. Furthermore, for the present reflective AWG, each waveguide in the array has its own PhC reflector and, consequently, the layout design of arrayed waveguides becomes very flexible. Fig. 1. (Color online) Schematic configurations: (a) present reflective AWG; (b) PhC reflector; (c) cross section of a Si nanowire. 2. Layout and Design Figure 1(a) shows the schematic configuration of the present reflective AWG with PhC reflectors. For such a reflective AWG, there are an input waveguide, several output waveguides, a free propagation region (FPR), and a plurality of arrayed waveguides. The input and the output waveguides are put on the same side of the FPR. Each waveguide in the array perpendicularly connects to an individual PhC reflector with the same design. With such a layout design, the arrayed waveguides could be arranged freely according to the requirements of the AWG performances (e.g., the channel number and channel spacing) so that the occupied area of the arrayed waveguides is minimized. When a large diffraction order is desired, the arrayed waveguides can include several bends to minimize the area occupied by the arrayed waveguides [as shown in Fig. 1(a)]. Because the decoupled separation of two parallel Si nanowires is usually about 2 3 μm[17], in our design 4860 APPLIED OPTICS / Vol. 49, No. 26 / 10 September

128 Fig. 2. (Color online) For the PhC reflectors with P x ¼ 11 and P z ¼ 9: (a) the average reflection efficiency R av as the width and length of the taper vary; (b) the reflection efficiency in the window of ½1500; 1600Š nm for the design with ðw tp ; L tp Þ¼ð1:25; 4Þ μm, and ð1:6; 6Þ μm. we choose Δx ¼ 2:2 μm and Δy ¼ 2:5 μm. By using a reflective AWG, it is also possible to avoid any bending for the arrayed waveguides when it is needed (e.g., the case with a low diffraction order). The design procedure of the arrayed waveguides is similar to those of conventional reflective AWG (de) multiplexers. For example, there is a length difference between adjacent arrayed waveguides, i.e., 2n eff ðl lþ1 L l Þ¼mλ c, where n eff is the effective refractive index of the arrayed waveguide, L l is the length of the lth arrayed waveguide, λ c is the central wavelength, and m is the diffraction order. One of the most important things for the present reflective AWG is to have a small-sized PhC reflector with a high efficiency. Therefore, here, we give more details about the optimal design of the PhC reflector. Figure 1(b) shows the schematic configuration of the hexagonal PhC reflector. In our case, we use a SOI wafer with a 220 nm Si layer on a 1 μm SiO 2 insulator layer [see Fig. 1(c)]. The parameters of the PhC sections are chosen as follows: the lattice constant a ¼ 430 nm and the diameter of air holes D ¼ 267 nm so that we have a photonic bandgap (PBG) in the window around 1550 nm for the quasi-te polarization (with the main electric-field component parallel to the horizontal direction). When the operation wavelength is within the bandgap of a PhC structure, the incident light will be reflected almost completely in an ideal case. Therefore, the PhC reflector should have relatively large size ðl x ; L y Þ to include enough period numbers ðp x ; P z Þ of holes in both directions (x and z) so that the PBG characteristic is supported. Here, we choose P x ¼ 11 and P z ¼ 9 initially. To enhance the reflection of the PhC reflector, we broaden the arrayed waveguide with a cosine taper before its connection to the corresponding PhC reflector [see Fig. 1(b)]. In our design, the width w co of arrayed waveguides w co ¼ 500 nm. The taper width w tp and the taper length L tp are optimized for the maximal reflection efficiency. Because the reflection efficiency is dependent on the wavelength, here we consider the average R av of the reflection efficiency over the most important window ½1500; 1600Š nm for optical communications. To avoid a time-consumed 3D finite-difference time-domain (FDTD) simulation, a two-dimensional 2D-FDTD modeling based on an effective index method (EIM) is used for calculating the reflection in the PhC reflector. Figure 2(a) shows the average reflection efficiency R av of the PhC reflector with different taper lengths as the taper width w tp ranges from 1:0 μm to2:0 μm. From this figure, one sees that both the taper width and taper length have great influences on the reflection efficiency. It is well known that a taper should be long enough to have an adiabatic mode transformation in the taper. For example, for the design with a long taper length L tp ¼ 8 μm [see the circled curve in Fig. 2(a)], as the taper width w tp increases from 1:0 μm, the reflection efficiency increases remarkably to a maximal value at w tp ¼ 1:25 μm, and then a small dip appears at w tp ¼ 1:4 μm (due to the discrete holes in the PhC structure). As the taper width increases further, the reflection efficiency increases slightly again and then almost keeps at the same level when the taper width ranges from 1.6 to 2:0 μm. From this analysis, there are two optimal designs, i.e., w tp ¼ 1:25 μm and w tp ¼ 1:6 μm. On the other hand, since a compact PhC reflector is expected for the present reflective AWG, we also consider the designs with shorter taper length (L tp ¼ 6, 4, 3, and 2 μm). When the taper length is shortened to 6 μm, the reflection efficiency is almost the same as that for the case of L tp ¼ 8 μm, except when w tp > 1:6 μm. When w tp > 1:6 μm, the taper becomes increasingly nonadiabatic and, consequently, the reflection efficiency drops remarkably. This is much more serious for the cases with a shorter taper length (e.g., L tp ¼ 4, 3,2 μm). We also note the maximal reflection efficiency at w tp ¼ 1:25 μm does not change much even when the taper length is shortened to be L tp ¼ 3 μm. From the above analysis, we consider two different designs, i.e., (ðw tp ; L tp Þ¼ð1:25; 4Þ μm and ð1:6; 6Þ μm. Their corresponding average reflection efficiencies are about 98.6%, and 97.9%. Figure 2(b) shows that the reflection efficiencies for these two designs are very high in the whole window of ½1500; 1600Š nm. In the following part, we consider the designs with a smaller PhC reflector by reducing the period numbers P x and P z. 10 September 2010 / Vol. 49, No. 26 / APPLIED OPTICS

129 Fig. 3. (Color online) Average reflection efficiency R av : (a) as the period number P x decreases; (b) as the period number P z decreases. First, we fix P z ¼ 9 and calculate the reflection efficiency as the period number P x decreases. Figure 3(a) shows the average reflection efficiency R av for the two designs mentioned above. For the first design with ðw tp ; L tp Þ¼ð1:25; 4Þ μm, one sees that the reflection efficiency R av decreases slightly until P x ¼ 6, and there is a small dip around P x ¼ 4. As P x decreases further, the reflection efficiency R av increases slightly and then drops sharply. For example, when one reduces the period number from 3 to 2.5, the reflection efficiency R av decreases from 96.5% to 64.6%. From this result, we choose P x ¼ 6 for the first design to have a large reflection efficiency and a small size. The situation for the second design [with ðw tp ; L tp Þ¼ð1:6; 6Þ μm] is also shown in Fig. 3(a) (see the circled curve). From this figure, one sees that the reflection efficiency R av does not change much when the period number P x decreases from 10 to 6, which is similar to the first design with (ðw tp ; L tp Þ¼ð1:25; 4Þ μm. However, when the period number decreases further, the reflection efficiency increases to a maximum (about 99.2%) at P x ¼ 4 and then drops rapidly. This is very different from the first design [with ðw tp ; L tp Þ¼ð1:25; 4Þ μm]. Therefore, we choose P x ¼ 4:5 for the second design to obtain a high reflection efficiency as well as a good tolerance. Figure 3(b) shows the average reflection efficiencies R av for these two designed PhC reflectors as the period number P z decreases from 9 to 3. The curves for these two designs have the similar trends, and there is a notable reduction of the reflection efficiency when P z < 6. Thus, we choose P z ¼ 6. In addition, Fig. 3(b) also shows the second design with ðw tp ; L tp Þ¼ð1:6; 6Þ μm has a higher reflection efficiency. Therefore, we choose w tp ¼ 1:6 μm, L tp ¼ 6 μm, P x ¼ 4:5, and P z ¼ 6 for the PhC reflectors used in the present reflective AWG demultiplexer. The calculated reflection efficiency in the window of ½1450; 1650Š nm is shown in Fig. 4, from which one sees that the spectral response is flat, especially in the band ½1500; 1600Š nm. The inset in Fig. 4 shows the designed PhC reflector, the size of which is given by L x ¼ P x a ¼ 1:935 μm and L z ¼ P z b ¼ 2:23 μm (where b ¼ 0:866a). Even though the PhC reflector will introduce some phase shift and wavelength dependence of the phase, there is almost no influence on the performances of the reflective AWG (de)multiplexer because all the PhC reflectors are with the same design and, furthermore, the characteristics of the AWG (de)multiplexer are mainly determined by the phase difference between adjacent arrayed waveguides (instead of the phase itself). One should note that some polarization rotation and higherorder mode excitation may take place for a fabricated PhC reflector due to the nonvertical sidewalls, which will introduce some phase error and, consequently, will increase the crosstalk. Therefore, it is very important to improve the fabrication process to have a vertical sidewall. With the layout shown in Fig. 1(a) and the designed PhC reflectors, we give a design for an AWG (de)multiplexer with a similar performance of that shown in [18]: the channel number N ch ¼ 16 and the channel spacing Δλ ch ¼ 1:6 nm. Here, we use the SOI nanowire with a cross section of 500 nm 220 nm. The other parameters for our AWG are chosen as follows: the number of arrayed waveguides N WG ¼ 34, the diffraction order m ¼ 32, the FPR length L FPR ¼ 52:0 μm. The end separation d g and the middle separations ðδx; ΔyÞ between adjacent arrayed waveguides are d g ¼ 1:0 μm, Δx ¼ 2:2 μm, and Δy ¼ 2:5 μm. The bending radius R ¼ 5 μm, which is large enough for a low bending loss [17]. Figure 5(a) shows the designed layout. One can choose one of the access waveguides in the left side of the FPR as Fig. 4. (Color online) Reflection efficiency in the window of ½1450; 1650Š nm when w tp ¼ 1:6 μm, L tp ¼ 6 μm, P x ¼ 4:5, and P z ¼ APPLIED OPTICS / Vol. 49, No. 26 / 10 September

130 Fig. 5. (Color online) (a) Layout of the designed reflective AWG (de)multiplexer. (b) Calculated spectral response of all the output channels. the input waveguide and the other waveguides are used as the output waveguides. The designed AWG has a very small footprint of only about 193 μm 168 μm, which is only 1=3 of the 200 μm 500 μm AWG (de)multiplexer with a conventional layout given in [18]. We use a hybrid method (which combines the beam propagation method and the Kirchhoff Huygens diffraction formula) [19] to calculate the spectral response. Figure 5(b) shows the spectral response when one inputs the light signal from the edge waveguide, as shown in Fig. 5(a). From this figure, one sees that the theoretical results are quite good. The crosstalk for the edge channels is about 25 db [as shown in Fig. 5(b)]. The coupling loss between the input/output waveguides and the single-mode fibers is not included here; however, there are several effective approaches to reduce the coupling loss by using some modal converters [20 22]. The small distortion of the spectral responses shown in Fig. 5(b) for the edge channels is due to the aberration, which can be reduced by using a design based on the three-stigmatic-point method [23]. 3. Fabrication and Measurement Our samples were fabricated using the deep-uv lithography at the Interuniversity MicroElectronics Center (IMEC, Belgium). In our measurement, the input/output single-mode fibers are aligned vertically, and grating couplers are used to have an efficient coupling between the fibers and the chip [24]. The grating period is about 0:63 μm and the trench width is about 0:314 μm for TE polarization. A single-longitudinal-mode tunable laser and polarization controller (Agilent Navigator N7788B) were used. The TE-polarized light was coupled from the single-mode fiber into the input waveguide through the grating coupler with a tilt angle of about 10. Figure 6 shows the measurement result for the coupling loss between a single-mode fiber and the grating coupler. The inset in Fig. 6 shows the picture for the fabricated grating coupler. Figure 7(a) shows the picture of the fabricated reflective AWG (de)multiplexer. Because the input and output waveguides locate at the same side of the FPR, we choose the waveguide at the edge as the input waveguide and the others are used as the output waveguides. To be measured conveniently, the output waveguides are arranged to be parallel at the end to connect with the grating coupler and the separation between adjacent output waveguides is as large as 20 μm. Figure 7(b) shows the measured spectral responses of the central channels for the TE-polarized light when the light signal is launched from the input waveguide at the edge. The coupling loss between the grating coupler and a single-mode fiber has been excluded. One sees that the free spectral response (FSR) is about 22 nm (which is close to the theoretical value). The excess loss of the reflective AWG is relatively high, which mainly comes from the coupling between the FPR and the arrayed waveguides and the PhC reflector loss. Figure 7(c) shows the spectral responses for the adjacent channels. From this figure, it can be seen that the channel spacing is about 1:6 nm, which agrees with the design value. From the measured spectral responses, one sees that the crosstalk is much higher than expected. The possible contribution to the crosstalk is the polarization rotation and higher-order mode excitation due to the nonvertical sidewalls in the fabricated PhC reflector. Therefore, it is quite important to improve the Fig. 6. (Color online) Measured coupling loss of a grating coupler. The insert is a picture of the fabricated grating coupler. 10 September 2010 / Vol. 49, No. 26 / APPLIED OPTICS

131 Fig. 7. (Color online) (a) Picture of the fabricated 200 GHz Sinanowire-based reflective AWG (de)multiplexer with photonic crystal reflectors. (b) Measured spectral response of the central channel. (c) Measured spectral responses of two adjacent channels. fabrication processes to achieve a vertical sidewall. Another possible origin of the crosstalk is the phase error (due to the variations of the waveguide size or index), which could be reduced by using some special designs, e.g., with broadened [24] or shallowly-etched [25] arrayed waveguides. 4. Conclusion In this paper, we have proposed a design for an ultrasmall Si-nanowire-based reflective AWG (de)multiplexer with PhC reflectors. By introducing an individual PhC reflector at the end of each waveguide in the array, the AWG layout design becomes very flexible. With the present design, the total size of the AWG (de)multiplexer can be reduced by more than a half. Furthermore, the fabrication of such a reflective AWG (de)multiplexer is compatible to the standard CMOS process. To enhance the reflection efficiency of the PhC reflectors, we have introduced a taper between the arrayed waveguide and the PhC reflector. The theoretical reflection efficiency of the optimized PhC reflector is up to 98% over the range from 1500 to 1600 nm. The PhC reflectors could also be replaced by Bragg-grating (i.e., a onedimensional PhC structure) reflectors proposed by [16]. Finally, we have designed and fabricated a reflective AWG (de)multiplexer with a narrow channel spacing of 200 GHz. The designed AWG (de)multiplexer has a total size of about 193 μm 168 μm, which is only 1=3 of the 200 μm 500 μm AWG (de)multiplexer with a conventional layout given in [18]. Our samples were fabricated using the deep- UV lithography at the IMEC. In our measurement, the input/output single-mode fibers are aligned vertically, and grating couplers are used to have an efficient coupling between the fibers and the chip. The measured channel spacing and the FSR are close to the design values. Even though the excess loss and the crosstalk between channels are not as good as expected, the improvement of the fabrication processes in the future will be helpful to have better performances. For example, a vertical sidewall could be achieved by improving the dry etching process so that one can minimize the higher-order mode excitation due to the nonvertical sidewalls in the PhC reflector. Another possible origin of the crosstalk is the phase error due to the variations of the waveguide size or index. To reduce the crosstalk, we will introduce some special designs (e.g., with broadened [24] or shallowly-etched [25] arrayed waveguides) in the future work. This project was partially supported by the Zhejiang Provincial Natural Science Foundation of China (R ) and the National Science Foundation of China (NSFC) ( ). References 1. M. K. Smit and C. Van Dam, Phasar-based WDM-devices: principles, design and applications, IEEE J. Sel. Top. Quantum Electron. 2, (1996). 2. K. Sasaki, F. Ohno, A. Motegi, and T. Baba, Arrayed waveguide grating of μm 2 size based on Si photonic wire waveguides, Electron. Lett. 41, (2005). 3. D. Dai, L. Liu, L. Wosinski, and S. He, Design and fabrication of ultra-small overlapped AWG demultiplexer based on alpha- Si nanowire waveguides, Electron. Lett. 42, (2006). 4. P. Dumon, W. Bogaerts, D. Van Thourhout, D. Taillaert, R. Baets, J. Wouters, S. Beckx, and P. Jaenen, Compact wavelength router based on a Silicon-on-insulator arrayed waveguide grating pigtailed to a fiber array, Opt. Express 14, (2006). 5. D. Dai and S. He, Optimization of ultracompact polarizationinsensitive multimode interference couplers based on Si nanowire waveguides, IEEE Photonics Technol. Lett. 18, (2006). 6. D. Dai and S. He, Ultra-small overlapped arrayedwaveguide grating based on Si nanowire waveguides for dense 4864 APPLIED OPTICS / Vol. 49, No. 26 / 10 September

132 wavelength division demultiplexing, IEEE J. Sel. Top. Quantum Electron. 12, (2006). 7. D. Dai and S. He, Novel ultracompact Si-nanowire-based arrayed-waveguide grating with microbends, Opt. Express 14, (2006). 8. L. Grave de Peralta, A. A. Bernussi, S. Frisbie, R. Gale, and H. Temkin, Reflective arrayed waveguide grating multiplexer, IEEE Photonics Technol. Lett. 15, (2003). 9. J. B. D. Soole, M. R. Amersfoort, H. P. LeBlanc, A. Rajhel, C. Caneau, C. Youtsey, and I. Adesida, Compact polarisation independent InP reflective arrayed waveguide grating filter, Electron. Lett. 32, (1996). 10. A. A. Bernussi, L. Grave de Peralta, V. Gorbounov, J. A. Linn, S. Frisbie, R. Gale, and H. Temkin, Mirror quality and the performance of reflective arrayed-waveguide grating multiplexers, J. Lightwave Technol. 22, (2004). 11. Y. Inoue, A. Himeno, K. Moriwaki, and M. Kawachi, Silicabased arrayed-wave-guide grating circuit as optical splitter router, Electron. Lett. 31, (1995). 12. C. Bayer and M. Straub, Small-hole waveguides in silicon photonic crystal slabs: efficient use of the complete photonic bandgap, Appl. Opt. 48, (2009). 13. H. J. Yu, J. Z. Yu, Y. Yu, Z. C. Fan, and S. W. Chen, Design, fabrication, and characterization of an ultracompact low-loss photonic crystal corner mirror, IEEE J. Quantum Electron. 43, (2007). 14. Y. Shi, D. Dai, and S. He, Proposal for an ultracompact polarization-beam splitter based on a photonic-crystal-assisted multimode interference coupler, IEEE Photonics Technol. Lett. 19, (2007). 15. T. Brouckaert, W. Bogaerts, S. Selvaraja, P. Dumon, R. Baets, D. Van Thourhout, Planar concave grating demultiplexer with high reflective Bragg reflector facets, IEEE Photonics Technol. Lett. 20, (2008). 16. C. Dragone, Efficient reflective multiplexer arrangement, U.S. patent 5,450,511 (12 September 1995). 17. D. Dai, Y. Shi, and S. He, Comparative study of the integration density for passive linear planar lightwave circuits based on three different kinds of nanophotonic waveguides, Appl. Opt. 46, (2007). 18. W. Bogaerts, P. Dumon, D. Van Thourhout, D. Taillaert, P. Jaenen, J. Wouters, S. Beckx, V. Wiaux, and R. G. Baets, Compact wavelength-selective functions in silicon-on-insulator photonic wires, IEEE J. Sel. Top. Quantum Electron. 12, (2006). 19. D. Dai, L. Liu, and S. He, Three-dimensional hybrid method for efficient and accurate simulation of AWG demultiplexers, Opt. Commun. 270, (2007). 20. D. Taillaert, W. Bogaerts, P. Bienstman, T. F. Krauss, P. V. Daele, I. Moerman, S. Verstuyft, K. D. Mesel, and R. Baets, An out-of-plane grating coupler for efficient butt-coupling between compact planar waveguides and single-mode fibers, IEEE J. Quantum Electron. 38, (2002). 21. D. Dai, S. He, and H. K. Tsang, Bilevel mode converter between a silicon nanowire waveguide and a larger waveguide, J. Lightwave Technol. 24, (2006). 22. V. R. Almeida, R. R. Panepucci, and M. Lipson, Nanotaper for compact mode conversion, Opt. Lett. 28, (2003). 23. D. Wang, G. Jin, Y. Yan, and M. Wu, Aberration theory of arrayed waveguide grating, J. Lightwave Technol. 19, (2001). 24. W. Bogaerts, S. K. Selvaraja, and P. Dumon, Silicon-on-insulator spectral filters fabricated with CMOS technology, IEEE J. Sel. Top. Quantum Electron. 16, (2010). 25. D.-J. Kim, J.-M. Lee, J. H. Song, J. Pyo, and G. Kim, Crosstalk reduction in a shallow-etched silicon nanowire AWG, IEEE Photonics Technol. Lett. 20, (2008). 10 September 2010 / Vol. 49, No. 26 / APPLIED OPTICS

133 2594 OPTICS LETTERS / Vol. 35, No. 15 / August 1, 2010 Experimental demonstration of an ultracompact Si-nanowire-based reflective arrayed-waveguide grating (de)multiplexer with photonic crystal reflectors Daoxin Dai,* Xin Fu, Yaocheng Shi, and Sailing He Centre for Optical and Electromagnetic Research, State Key Laboratory for Modern Optical Instrumentation, East Building No.5, Zijingang Campus, Zhejiang University, Hangzhou , China *Corresponding author: dxdai@zju.edu.cn Received May 19, 2010; revised July 1, 2010; accepted July 2, 2010; posted July 13, 2010 (Doc. ID ); published July 27, 2010 An ultracompact reflective arrayed-waveguide grating (AWG) (de)multiplexer based on Si nanowires is demonstrated for the first time (to our knowledge). Each waveguide in the array has an individual photonic crystal (PhC) reflector at its end, making the AWG layout design very flexible. An eight-channel AWG (de)multiplexer with a channel spacing of 400 GHz is demonstrated experimentally. The total size of the fabricated AWG is as small as 134 μm 115 μm. The excess loss of the fabricated reflective AWG (de)multiplexer is about 3 4 db, and the crosstalk is about 12 db Optical Society of America OCIS codes: , Arrayed-waveguide gratings (AWGs) have been used very successfully in various wavelength-divisionmultiplexing (WDM) systems. To integrate more components with AWGs in a single chip, a smaller AWG is desired. An effective way to reduce the AWG size is using the recently developed Si nanowire [1 4], which enables the bending radius as small as 2 μm because of the ultrahigh Δ. With Si nanowires, several groups have developed ultracompact AWG (de)multiplexers/ routers [2 4], which are usually 1=10 5 smaller than the conventional AWG chip ( 10 cm 2 ). Because of the ultrahigh Δ and ultrasmall cross section of Si nanowires, the AWG performance (especially the crosstalk) is very sensitive to the size variation of the arrayed waveguides (e.g., the nonuniformity of the Si-core dimension). A very small thickness variation (<5 nm) will cause remarkable phase errors and consequently a large crosstalk. On the other hand, it is still difficult to have a very uniform Si layer in a large area, even for commercial SOI wafers. Therefore it is helpful to minimize the phase error if the AWG occupies a very small area. Consequently, in order to improve the AWG performance, it is desirable to reduce the Si-nanowire AWG size further. Since the Si nanowire is capable of ultrasharp bending and small decoupled separation ( 2 μm) [5], the design of the AWG layout becomes very important for the size reduction [3,6]. It is well known the AWG size could be also reduced by a half or more when using the reflective-type layout [7,8] (which is a little similar to etched diffraction grating [4]). However, for reflective-type AWG based on micrometric optical waveguides [7], the freedom for the layout design of the AWG chip is restricted, because one usually has to arrange all arrayed waveguides in parallel at the end (connecting to the same reflection mirror) and make the mirror perpendicular to all the arrayed waveguides [7,8]. Furthermore, the arrayed waveguides need to be cleaved (or diced) carefully, and a diamond polish process is necessary to make the cleaved (or diced) facet smooth and flat [7]. This will make the layout design inconvenient, especially when integrating a reflective AWG with other components. To enhance the reflection efficiency, one usually has to introduce dielectric or metal films (e.g., Cr Au film [7]) at the facet [7,8], which increases the complexity of the fabrication. However, it is still not easy to achieve a high-quality reflection mirror [8], which degrades the performances of a reflective AWG [9]. For Si-nanowire-based AWGs, the intrinsic small size makes the fabrication of a conventional mirror much more difficult (almost impossible). Here we demonstrate an ultracompact reflective Si-nanowire AWG with photonic crystal (PhC) reflectors. According to the bandgap characteristic of PhCs, it is easy to design a reflector covering the intended wavelength band [10]. No additional fabrication process is needed, and it is also compatible to the standard complementary metal-oxide semiconductor (CMOS) process. Furthermore, for our present reflective AWG, each waveguide in the array has its own PhC reflector so that the position for the end of the arrayed waveguide can be adjusted easily. This makes the layout design of arrayed waveguides very flexible. Figure 1 shows the schematic configuration of the present reflective AWG, which includes an input waveguide, several output waveguides, a free propagation region (FPR), a plurality of arrayed waveguides, and PhC reflectors at the end. With such a design, the arrayed waveguides could be arranged freely according to the Fig. 1. (Color online) Schematic configuration of the present reflective AWG (de)multiplexer /10/ $15.00/ Optical Society of America 130

134 August 1, 2010 / Vol. 35, No. 15 / OPTICS LETTERS 2595 requirements (e.g., the diffraction order). This helps to minimize the occupied area of the arrayed waveguides. When a high diffraction order is desired, the arrayed waveguides can include several bends to minimize the occupied area (as shown in Fig. 1). For a low diffraction order, it is possible to avoid any bending for the arrayed waveguides, and consequently the length of the arrayed waveguide could be very short, which helps to reduce the crosstalk owing to the phase error in the waveguide array [11]. An important thing for the present reflective AWG is to have small-sized PhC reflectors with high efficiency. A commercial silicon-on-insulator wafer with a 220 nm Si layer on a 1 μm SiO 2 insulator layer is used in our design and fabrication. The parameters of the PhC sections are chosen as the lattice constant a ¼ 430 nm and the diameter of air holes D ¼ 267 nm, so that we have a photonic bandgap (PBG) in the window around 1550 nm for the quasi-te polarization. The PhC reflector should include enough period numbers ðp x ;P z Þ of holes in both directions (x and z) to support the PBG characteristic. According to our 3D finite-difference time-domain (3D FDTD) simulation, we choose P x ¼ 5 and P z ¼ 8. The arrayed waveguide is broadened with a cosine taper before its connection to the corresponding PhC reflector to have a mode transition (see Fig. 1). In our design, the width w co of arrayed waveguides is w co ¼ 500 nm, and the taper parameters are w tp ¼ 1:6 μm and L tp ¼ 10 μm. By using a 3D FDTD method with grid sizes of Δx ¼ Δy ¼ Δz ¼ 10 nm, we obtain the reflection efficiency in the window of ½1:45; 1:65Š μm, as shown in Fig. 2. It can be seen that the reflectivity is over 90% in the band ½1500; 1600Š nm. One should note that some higher-order modes may be excited in a fabricated PhC reflector owing to the nonvertical sidewalls, which will introduce some crosstalk. Therefore it is important to have a vertical sidewall by improving the fabrication process. Our samples were fabricated using the deep-uv lithography at IMEC (Interuniversity MicroElectronics Center, Belgium). The well-developed fabrication processes at IMEC help to fabricate Si nanowires and PhC structure with good profiles especially when the Si layer is thin (e.g., 220 nm here) [4,12]. Here we demonstrate an eight-channel AWG (de)multiplexer with a channel spacing Δf ch ¼ 400 GHz as an example. The bending radius is R ¼ 5 μm, which is large enough for a low bending loss [5]. The other parameters Fig. 2. (Color online) Calculated reflection efficiency in the window of ½1:45; 1:65Š μm. Fig. 3. (Color online) (a) Picture of the fabricated reflective AWG (de)multiplexer with GHz channels, (b) microscope picture for the measurement setup. for our AWG are chosen as follows: the number of arrayed waveguides N WG ¼ 27, the diffraction order m ¼ 25, and the FPR length L FPR ¼ 40 μm. The end separation d g between adjacent arrayed waveguides is d g ¼ 1:2 μm. The separation between the adjacent output waveguides is d out ¼ 1:88 μm. The designed AWG has a very small footprint of only about μm 2. Figure 3(a) shows the picture for the fabricated device. In our measurement [as shown in Fig. 3(b)], the input/ output single-mode fibers are aligned vertically, and grating couplers are used to have an efficient coupling between the fibers and the chip [4]. Figure 4(a) shows the measured spectral responses of all the channels for TE polarization when light is launched from the edge waveguide. These results are normalized by the transmission of a straight waveguide so that the coupling loss to fibers is excluded. The excess loss of the reflective AWG is about 3 4 db, which mainly comes from the coupling between the FPR and the arrayed waveguides and the PhC reflector loss. The channel spacing and the FSR are about 3:2 nm (400 GHz) and 28 nm, respectively, which agree well with the design values. The crosstalk between adjacent channels is about 12 db. One possible contribution to the crosstalk is the higher-ordermode excitation due to the nonvertical sidewalls in the fabricated PhC reflector. Another possible origin of 131

135 2596 OPTICS LETTERS / Vol. 35, No. 15 / August 1, :2 nm experimentally. The fabrication is compatible to the standard CMOS process, and no additional process is needed. The total size is only about 134 μm 115 μm with the help of PhC reflectors, which has very high reflectivity (>90%) in the range from 1500 nm to 1600 nm. The PhC reflectors could also be replaced by Bragg grating reflectors [4]. The measured excess loss of the reflective AWG is about 3 4 db, and the crosstalk between adjacent channels is about 12 db. Better performances could be achieved by improving the fabrication processes further as well as using some special designs (e.g., with broadened [4] or shallowly etched [13] arrayed waveguides). This project was partially supported by Zhejiang Provincial Natural Science Foundation (No. R ) and the National Nature Science Foundation of China (NSFC) (Nos and ). Fig. 4. (Color online) (a) Measured spectral responses of all the channels, (b) spectral response of the third channel. crosstalk is the phase error (due to the variations of the waveguide size or index), which could be reduced by using, e.g., broadened [4] or shallowly etched [13] arrayed waveguides. In summary, we have demonstrated a eight-channel reflective AWG (de)multiplexer with a channel spacing of References 1. P. J. Bock, P. Cheben, A. Delâge, J. H. Schmid, D.-X. Xu, S. Janz, and T. J. Hall, Opt. Express 16, (2008). 2. K. Sasaki, F. Ohno, A. Motegi, and T. Baba, Electron. Lett. 41, 801 (2005). 3. D. Dai, L. Liu, L. Wosinski, and S. He, Electron. Lett. 42, 400 (2006). 4. W. Bogaerts, S. K. Selvaraja, P. Dumon, J. Brouckaert, K. De Vos, D. Van Thourhout, and R. Baets, IEEE J. Sel. Top. Quant. Electron. 16, 33 (2010). 5. D. Dai, Y. Shi, and S. He, Appl. Opt. 46, 1126 (2007). 6. D. Dai and S. He, Opt. Express 14, 5260 (2006). 7. L. G. de Peralta, A. A. Bernussi, S. Frisbie, R. Gale, and H. Temkin, IEEE Photon. Technol. Lett. 15, 1398 (2003). 8. A. A. Bernussi, L. Grave de Peralta, V. Gorbounov, J. A. Linn, S. Frisbie, R. Gale, and H. Temkin, J. Lightwave Technol. 22, 1828 (2004). 9. Y. Inoue, A. Himeno, K. Moriwaki, and M. Kawachi, Electron. Lett. 31, 726 (1995). 10. Y. Shi, D. Dai, and S. He, IEEE Photon. Technol. Lett. 19, 825 (2007). 11. T. Goh, S. Suzuki, and A. Sugita, J. Lightwave Technol. 15, 2107 (1997). 12. S. K. Selvaraja, P. Jaenen, W. Bogaerts, D. Van Thourhout, P. Dumon, and R. Baets, J. Lightwave Technol. 27, 4076 (2009). 13. D.-J. Kim, J.-M. Lee, J. H. Song, J. Pyo, and G. Kim, IEEE Photon. Technol. Lett. 20, 1615 (2008). 132

136 Ultra-small Si-nanowire-based 400 GHz-spacing arrayed-waveguide grating router with microbends X. Fu and D. Dai An ultra-small arrayed-waveguide grating (AWG) router with microbends based on silicon-on-insulator nanowires is demonstrated experimentally. The presented AWG router has 15 input/output channels and the channel spacing is 400 GHz. The device size is only mm. The thermal-tunability of the presented ultra-small AWG router is also characterised. Introduction: The arrayed-waveguide grating (AWG) (de)multiplexer/ router is one of the most important components in various wavelength-division multiplexing (WDM) modules and systems [1]. In past decades, a SiO 2 -on-si buried optical waveguide was usually used as the platform for AWGs because of its low loss and high coupling efficiency to singlemode fibres. When using such low index-contrast (D) optical waveguides, the AWG device usually has a large size (at the order of 10 cm 2 ). To reduce the AWG size as well as lower the average cost, an effective way is using the recently developed siliconon-insulator (SOI) nanowires [2 4]. Owing to the ultra-high D, SOI nanowire enables an ultra-small bending radius ( 2 mm [5]) and a small decoupled separation between two parallel waveguides ( 2 mm [5]), which allows one to place two waveguides very close. minimise the size of an SOI-nanowire AWG. To overcome this issue, we presented novel designs of layout for ultra-compact AWG (de)multiplexers/routers in our previous work [7 9]. In this Letter, we experimentally demonstrate ultra-compact AWG routers with microbends for the first time. Structure: Fig. 1a shows a picture of the fabricated AWG routers with microbends. In the present design, the two free propagation regions (FPR) are overlapped and there are microbends inserted in the arrayed waveguides (see inset of Fig. 1a), which help to minimise the area occupied by the arrayed waveguides [8]. There are 34 arrayed waveguides and the total size is only mm. The designed AWG (de)multiplexer has 15 channels with 400 GHz channel spacing. Fig. 2 Measured spectral responses of fabricated AWG router with microbends (15 channels) Fig. 1 Picture of fabricated AWG router with microbends, and microscope picture for measurement setup a Fabricated AWG router with microbends b Measurement setup However, for the case when a high diffraction order m is desired (e.g. a dense AWG (de)multiplexer or router), a large path difference (about several tens of microns) between two adjacent arrayed waveguides is required. To achieve the large path difference as required, the separation between two adjacent arrayed waveguides will have to be much larger than the decoupling separation ( 2 mm) for SOI nanowires if using a standard layout, which can be seen clearly from the design shown in [6]. In this case, the size of an AWG is determined mainly by the separation of arrayed waveguides instead of the bending radius. Consequently, a conventional layout design might not be suitable to Fig. 3 Measured spectral responses for central output channel as temperature varies, and central wavelength shifts as temperature increases a Measured spectral responses b Central wavelength shifts Fabrication and measurement: This AWG was fabricated using the deep-uv lithography at IMEC on a silicon-on-insulator (SOI) wafer with a 220 nm top Si layer and 2 mm buried oxide. To couple from/to optical fibres, we use the vertical coupling system with grating couplers [10], which is very good for test in wafer (no need for dicing and polishing). Fig. 1b shows the microscope picture for the measurement setup. A 200 mm-long taper is used to connect the 500 nm-wide nanowires ELECTRONICS LETTERS 17th February 2011 Vol. 47 No

137 and the 10 mm-wide section of the grating coupler to have adiabatic mode conversion. Since the grating coupler is polarisation-dependent, here we consider the TE polarisation only. The coupling loss from a singlemode fibre to the SOI nanowires is about 7 8 db per junction with the grating coupler. The propagation loss of a straight nm SOI nanowire is about 1.6 db/cm. Fig. 2 shows the measured spectral responses of 15 channels when the TE polarisation light is input from the central input waveguide. These results are normalised by the transmission of a straight waveguide with a two grating coupler so that the coupling loss to fibres is excluded. The channel spacing is around 3.1 nm (close to the design value 3.2 nm). The crosstalk between adjacent channels is around 25to 28 db, which is mainly due to the phase errors in the arrayed waveguides with microbends. We also characterised the temperature dependence for the AWG router with microbends. Fig. 3a shows the spectral response of the central output channel as the temperature varies from 23 to 1108C. Fig. 3b shows the temperature dependence of the central wavelength. From these measurement results, one sees that the central wavelength shifts about nm/108c. It indicates that one could tune the channel wavelength to the desired value effectively in the thermal way. Conclusion: We have demonstrated the experimental results of ultrasmall SOI-nanowire AWG routers with microbends. The channel spacing of the fabricated AWG router is 400 GHz and the device size is only mm. To have an efficient coupling between the chip and the fibre, we have used the vertical coupling system with grating couplers and the coupling loss is about 6 7 db per facet. The thermal tunability of the presented ultra-small SOI-nanowire AWG router has been also characterised. The temperature dependence of the central wavelength is about nm/8c, which indicates that it is an effective way to tune the wavelength thermally. Acknowledgments: This project was partially supported by the Zhejiang Provincial Natural Science Foundation (no. R ) and the National Nature Science Foundation of China (no ). One or more of the Figures in this Letter are available in colour online. X. Fu and D. Dai (Centre for Optical and Electromagnetic Research, Zhejiang University, Zijingang, Hangzhou , People s Republic of China) dxdai@zju.edu.cn References 1 Smit, M.K., and van Dam, C.: PHASAR-based WDM-devices: principles, design and applications, IEEE J. Sel. Top. Quantum Electron., 1996, 2, pp Bogaerts, W., et al.: Silicon-on-insulator spectral filters fabricated with CMOS technology, IEEE J. Sel. Top. Quantum. Electron., 2010, 16, pp Dai, D.X., et al.: Design and fabrication of ultra-small overlapped AWG demultiplexer based on a-si nanowire waveguides, Electron. Lett., 2006, 42, pp Sasaki, K., et al.: Arrayed waveguide grating of mm 2 size based on Si photonic wire waveguides, Electron. Lett., 2005, 41, pp Dai, D., et al.: Comparative study of the integration density for passive linear planar lightwave circuits based on three different kinds of nanophotonic waveguides, Appl. Opt., 2007, 46, pp Dumon, P., et al.: Compact wavelength router based on a silicon-oninsulator arrayed waveguide grating pigtailed to a fiber array, Opt. Express, 2006, 14, pp Dai, D.X., and He, S.L.: Ultrasmall overlapped arrayed-waveguide grating based on Si nanowire waveguides for dense wavelength division demultiplexing, IEEE J. Sel. Top. Quantum Electron., 2006, 12, pp Dai, D., and He, S.: Novel ultrasmall Si-nanowire-based arrayedwaveguide grating with microbends, Opt. Express, 2006, 14, pp Dai, D.X., et al.: Novel ultrasmall Si-nanowire-based arrayedwaveguide grating interleaver with spirals, Opt. Commun., 2008, 281, pp Taillaert, D., et al.: An out-of-plane grating coupler for efficient buttcoupling between compact planar waveguides and single-mode fibers, IEEE J. Quantum. Electron., 2002, 38, pp # The Institution of Engineering and Technology October 2010 doi: /el ELECTRONICS LETTERS 17th February 2011 Vol. 47 No

138 JOURNAL OF LIGHTWAVE TECHNOLOGY, VOL. 33, NO. 11, JUNE 1, Compact Dense Wavelength-Division (De)multiplexer Utilizing a Bidirectional Arrayed-Waveguide Grating Integrated With a Mach Zehnder Interferometer Sitao Chen, Xin Fu, Jian Wang, Yaocheng Shi, Sailing He, Fellow, IEEE, Fellow, OSA, and Daoxin Dai, Member, IEEE Abstract A compact wavelength-division (de)multiplexer is proposed and demonstrated experimentally to achieve doubled channel number and halved channel spacing by utilizing a bidirectional arrayed-waveguide grating integrated with an Mach Zehnder interferometer optical interleaver. As an example, an 18-channel wavelength-division (de)multiplexer with a channel spacing of 200 GHz is designed and fabricated. The measured excess loss is about 8 db and the channel crosstalk is db. The footprint of this fabricated (de)multiplexer is about 520 μm 190 μm. Index Terms Arrayed-waveguide grating (AWG), bidirectional, interleaver, silicon nanowire. I. INTRODUCTION DENSE wavelength-division-multiplexing (DWDM) has been used very successfully as one of the most important techniques to improve the capacity of an optical communication link. It is well known that a wavelength division (de)multiplexer is a key component [1], which can be realized with microring resonators (MRRs) [2] [6], etched-diffraction gratings (EDGs) [7], [8], as well as arrayed-waveguide gratings (AWGs) [9] [22]. MRR is a simple element to achieve passive and active devices for many applications [23] [25]. Particularly, an array of MRRs cascaded in series can be used to realize a multi-channel (de)multiplexer with an ultra-small footprint while it is not easy to have uniform channel spacing due to the fabrication deviation. Both AWGs and EDGs are planar waveguide (de)multiplexers, which enable multiple channels in parallel with very uniform channel spacing and thus have been widely used in practical WDM systems. A general issue for an EDG is that high quality grating-facets are needed critically to minimize the excess loss, and an EDG usually has lower dispersion ability than an AWG Manuscript received January 8, 2015; revised February 8, 2015 and February 17, 2015; accepted February 17, Date of publication March 15, 2015; date of current version March 20, This work was supported in part by a 863 project under Grant 2011AA010301, the Nature Science Foundation of China under Grants , , and , the Doctoral Fund of Ministry of Education of China under Grant , and the Fundamental Research Funds for the Central Universities. The authors are with the Centre for Optical and Electromagnetic Research, State Key Laboratory for Modern Optical Instrumentation, Zhejiang Provincial Key Laboratory for Sensing Technologies, Zhejiang University, Hangzhou , China ( dxdai@zju.edu.cn). Color versions of one or more of the figures in this paper are available online at Digital Object Identifier /JLT due to the small interference order. Therefore, an AWG is usually preferred for DWDM applications. Furthermore, it is easy to realize N N AWG, which is useful for some applications. Therefore, in the past decades AWGs have attracted intensive attention and been realized on various material platforms, like silica-on-silicon [9], InP [10], polymer [11], Si 3 N 4 [12], [13], and silicon-on-insulator (SOI) [14] [22]. Among them, the submicron optical waveguides based on SOI enable ultra-sharp bending due to the very high index contrast and provide one of the most promising platforms to realize ultra-small AWGs [14] [22]. In the past decade, SOI-nanowire AWGs have been developed by several groups. For the AWGs with relatively large channel spacing (e.g., 400 GHz), the footprint is small and the performances are pretty good [16] [19]. However, for those SOI-nanowire AWGs with smaller channel spacing (e.g., GHz), which are desired for DWDM applications, the device footprint increases greatly and the performance (e.g., the channel crosstalk) degrades significantly [16], [20], [21]. For example, the channel crosstalk of the SOI-nanowire AWG (de)multiplexers demonstrated in [16] are db, db, and 9 15 db, respectively, when with the channel spacing is 400, 250, and 100. It is a challenge to realize an ultra-small wavelength division multiplexer with a dense channel spacing as well as excellent performances. Note that an optical interleaver can be used to divide the input 2N channels (λ 1, λ 2,...,λ N,...,λ 2N ) into an odd group (λ 1, λ 3,..., λ 2N 1 ) and an even group (λ 2, λ 4,..., λ 2N ) so that these two groups with doubled channel spacing can be separately (de)multiplexed by using e.g., N-channel AWG (de)multiplexers with doubled channel-spacing. Usually two AWG (de)multiplexers are needed to work with an optical interleaver (as shown in Fig. 1). In [26], a Mach Zehnder interferometer (MZI) and two AWGs have been monolithically integrated on silica-based PLC platform to realize a (de)multiplexer with 64 channels and a channel spacing of 25 GHz. One should note that such a configuration including an optical interleaver and two AWG (de)multiplexers is pretty complicated and the footprint is very large. Furthermore, it is not easy to realize two AWG (de)multiplexers with critically aligned central wavelengths for all the channels because there are some fabrication deviations, especially for devices on SOI platform. This might be the reason IEEE. Personal use is permitted, but republication/redistribution requires IEEE permission. See standards/publications/rights/index.html for more information. 135

139 2280 JOURNAL OF LIGHTWAVE TECHNOLOGY, VOL. 33, NO. 11, JUNE 1, 2015 Fig. 1. Schematic configuration of a traditional dense wavelength division multiplexer consisting of two AWGs and an MZI-based optical interleaver. that there is no much work reported for the realization of such a monolithically integrated device on SOI nanowires. In this paper, we demonstrate a dense wavelength division (de)multiplexer by integrating an MZI-based optical interleaver with only one (N +1) (N +1)AWG (de)multiplexer, which has doubled channel spacing of that for the multiplexed input signal. And this (N +1) (N +1) AWG works bidirectionally so that it plays the role of two 1 N AWGs whose central wavelengths for all the channels are aligned perfectly. In [27] and [28], a bi-directional AWG structure was utilized to eliminate the polarization dependent wavelength shift when working with a polarization diversity circuit. One should also realize that there are some drawbacks for a bi-directional AWG, like the degradation of the return loss and the directivity due to the light loopback. Furthermore, the insertion loss also increases a little because the input waveguide is positioned at the edge. Fortunately, the performance degradation is acceptable and excellent bi-directional AWGs have been demonstrated [27], [28]. In this paper, the demonstrated dense wavelength division (de)multiplexer consisting of a bi-directional AWG and an MZI-based optical interleaver also shows excellent performances while the channel spacing is halved and the channel number is doubled. II. STRUCTURE AND DESIGN Fig. 2 shows the schematic configuration of the present wavelength division de-multiplexer consisting of a bi-directional AWG and an optical interleaver based on an asymmetrical MZI. As shown in Fig. 2, the bi-directional AWG has N +1 access optical waveguides at both sides. Among the access optical waveguides at each side, there is an input waveguide and N output waveguides. In the present case, the access waveguide at the inner-edge works as the input waveguide in order to have a convenient layout design (avoiding any crossings). There are two input waveguides for the bi-directional AWG to be connected respectively with the two output ports of the MZI interleaver in the front. This MZI is designed to have a free spectral range (FSR) equal to the channel spacing of the bi-directional (N +1) (N +1)AWG. As a consequence, the wavelengthdivision-multiplexed signals (λ 1, λ 2,...,λ 2N ) with a channel spacing of Δλ ch launched from one of the input ports of the Fig. 2. (a) Schematic configuration of the present dense wavelength division multiplexer consisting of a bi-directional AWG and an MZI-based optical interleaver. (b) The enlarged view for the MZI-based optical interleaver connecting with the two input waveguides of the bi-directional AWG. MZI are then interleaved into two groups, i.e., the odd group (λ 1, λ 3,...,λ 2N 1 ) and the even group (λ 2, λ 4,...,λ 2N ). The channel spacing for these two groups of channels becomes doubled, i.e., Δλ ch =2Δλ ch. Since these two groups of channels share the same waveguide grating and the free propagation regions (FPRs), it is expected that the separation d o between the adjacent output waveguides at both sides are the same. As shown in Fig. 2(b), the output waveguides are arranged uniformly with a separation d o, which is given by d o = DΔλ ch = R a ΔLλ c n g Δλ ch (1) d a c n FPR in which λ c is the central wavelength, ΔL is the length difference between the adjacent arrayed waveguides, n g is group index of the arrayed-waveguide mode, n FPR is the slab mode index in FPRs, Δλ ch is the desired channel spacing, R a is the length of the FPR region, d a is the separation between the adjacent arrayed waveguides at the end connecting with the FPRs. In the present design, the output waveguides at both sides are arranged symmetrically to make the layout design convenient. The two groups of signals are then injected to the two input waveguides of the bi-directional AWG respectively. Since the central wavelengths for the two groups of channels are interleaved, the two input waveguides of the bi-directional AWG should be positioned asymmetrically. For the odd group of channels (λ 1, λ 3,...,λ 2N 1 ), the position of the input waveguide is given by x odd = d o INT(N/2), where INT(x) is the function to achieve 136

140 CHEN et al.: COMPACT DENSE WAVELENGTH-DIVISION (DE)MULTIPLEXER UTILIZING A BIDIRECTIONAL ARRAYED-WAVEGUIDE GRATING 2281 the maximal integer less than x. Correspondingly the position of the input waveguide for the even group of channels (λ 2, λ 4,..., λ 2N ) is given by x even = x odd + d o /2. As example, a 220 nm-thick SOI wafer is considered and the designed SOI nanowire is 460 nm wide and 220 nm high to be singlemode for the arrayed waveguides. In this case, the values of the following parameters for the central wavelength λ c = nm are given as: n FPR = , and n g =4.1. The channel spacing of the bi-directional AWG is chosen to be Δλ ch =3.2nm (Δf ch = 400 GHz), and the channel number is N =9so that a 18-channel dense de-multiplexer with a channel spacing of Δλ ch =1.6nm (Δf ch = 200 GHz) will be enabled. The other parameters of the bi-directional AWG are given as follows. The diffraction order is chosen as m =30to make the FSR be larger than the product N ch Δλ ch (=28.8nm) so that 18 channels are available. The path difference between the adjacent arrayed waveguides is ΔL = μm, calculated with the formula ΔL = mλ c /n eff, where λ c is the central wavelength (λ c = nm), and n eff is the effective index of the transversal electric (TE) fundamental mode in the arrayed waveguide (n eff = ). When choosing the gap between the adjacent arrayed waveguides at the end connecting with the FPRs, one should make a tradeoff carefully. In order to reduce the excess loss and the facet reflection, a small gap is desired. However, a small gap will introduce the lag effect in the dry etching process [29], [30]. This usually makes the part with small gaps in the arrayed waveguides non-uniform, which introduces some notable phase errors and thus some channel crosstalk. In order to make the etching uniformly regarding the lag effect, in our design we choose the gap width as w gap = 300 nm [31]. The separation between the adjacent arrayed waveguides at the end connecting with the FPRs is chosen as d a =1.6μm. The length of the FPRs is R a = 100 μm, and correspondingly the end separation between the output waveguides is about d o =3.69 μm and. With this design, the footprint for the part including the arrayed waveguides and the two FPRs is about 440 μm 190 μm. For the design of the MZI-based optical interleaver, the length difference ΔL MZI of the MZI s arms should be chosen to achieve an FSR Δλ FSR MZI matched to the channel spacing of the bi-directional AWG, i.e., Δλ FSR MZI =Δλ ch =3.2nm. In addition, the central wavelengths of the MZI and the AWG should be also aligned well. As a result, the length difference is chosen as ΔL MZI = μm optimally. For the 3 db power splitter/combiner in the MZI optical interleaver, we use 2 2 multimode-interference (MMI) couplers to be fabrication tolerant. The pair-interference mechanism in a MMI section is utilized and the input/output waveguides are positioned at x = ±w MMI /6. Regarding that the separation of the input/output waveguides should be large enough to avoid any undesired coupling, we choose the width of the MMI section as W MMI =2.4 μm. The length of the MMI coupler is optimized by maximizing the transmission at the crossing port of a symmetric MZI structure consisting of a pair of 2 2 MMI couplers, as shown by the insets in Fig. 3(a). According to the MZI s principle, the transmission at the crossing port is given by κt 2 because the constructive interference happens (where κ and t Fig. 3. (a) Simulated transmission of an MZI consisting of the MMI couplers with W MMI =2.4μmandL MMI =6.3μm. The inset shows the propagation for the optimized structure. (b) The simulated wavelength dependence for the power splitting ratio of the MMI coupler. are the cross and through coupling ratio). A three-dimensional finite-difference time-domain method is used for the simulation of light propagation in the symmetric MZI and the simulation result for the optimal design with L MMI =6.3 μm is shown by the blue curve in Fig. 3(a). It can be seen that the theoretical transmission at the crossing port of the MZI is about 85% ( 0.7 db) over a broad band ranging from 1.5 to 1.6 μm, which indicates that the designed MMI coupler enables a low-loss MZI-based optical interleaver in theory. Here very weak oscillation is observed and this is from the F-P cavity effect due to the reflection at the facets of these two MMIs. For an MZI, the extinction of the cross port is high intrinsically in theory while the extinction of the through port is dependent of the power splitting ratio of the MMI-based 3 db couplers. Here the wavelength dependence of the power splitting ratio of the present 3 db MMI coupler is also calculated, as shown in Fig. 3(b). It can be seen that the power splitting ratio of the MMI-based 3 db couplers is wavelength dependent in some degree. This is the reason why the extinction of the transmission at the through port of the MZI is wavelength dependent (as shown in Fig. 7 below). III. FABRICATION AND CHARACTERIZATION For the fabrication of the present (de)multiplexer, the process was started from a 220 nm-thick SOI wafer. An E-beam lithography process with MA-N2403 photoresist was carried out to 137

141 2282 JOURNAL OF LIGHTWAVE TECHNOLOGY, VOL. 33, NO. 11, JUNE 1, 2015 Fig. 4. Measured transmissions for the same straight waveguide when the fiber alignment is optimized for different wavelengths λ = 1540, and 1580 nm. make the waveguide pattern, which is then transferred to the silicon layer with an inductively coupled plasma (ICP) etching process. Grating couplers are then made with another shallowetching process to achieve efficient coupling between the fibers and the chip. Finally PMMA photoresist is spin-coated on top of the devices to form a thin file for protection. For the characterization of photonic integrated devices, a popular method is using the setup with a tunable laser and a powermeter. In this case, the positions of the input/output fibers are aligned carefully to have a maximal transmission for a given wavelength λ 0. On the other hand, it is well known that the coupling efficiency of a grating coupler is wavelength-sensitive and the central wavelength with the maximal coupling efficiency is dependent on the longitudinal position of the fiber. When one chooses different laser wavelength λ 0 for the fiber alignment, the fiber will be aligned to the different longitudinal position of the grating coupler and thus one obtains different spectral responses for the same straight waveguide with grating couplers (see Fig. 4). Therefore, one should choose the same laser wavelength for the fiber alignment when characterizing the devices, which is feasible for measuring straight waveguides with grating couplers because of the broadband spectral response. However, when measuring the spectral responses of an AWG, one can not choose the same laser wavelength for the fiber alignment to measure all the N channels because of the wavelength selectivity of the AWG. Instead, the fiber is usually aligned optimally for the corresponding central wavelength of any AWG channel to be measured. Accordingly, in order to make the normalization for the transmission responses of the N channels of AWG, the reference straight waveguide should also be measured N times by choosing different laser wavelengths for the fiber alignment, which makes the measurement very inconvenient. In order to overcome this problem, here the devices were measured by using another setup with a broad-band ASE (amplified spontaneous emission) light source and an optical spectrum analyzer. In this measurement, the fiber alignment is optimized by maximizing the total power in a given wavelength band, e.g., ranging from 1535 to 1565 nm, which corresponds to the wavelength band of our AWG. This rule is complied when Fig. 5. SOI nanowire-waveguide spirals. (a) Microscopic images. (b) The measured total loss of these spirals (consisting of the fiber-chip coupling loss). measuring the devices (e.g., AWGs, and MZIs) as well as the straight waveguides so that the measurement results can be normalized conveniently. Fig. 5(a) shows the fabricated spiral structures with different lengths, which are designed to estimate the propagation loss of our fabricated SOI nanowire waveguides. Here the cross section of the SOI nanowires is chosen to be 460 nm 220 nm to meet the single mode condition. For the spirals, the minimal bending radius for the S-bend in the middle is 15 μm, which is large enough to guarantee a negligibly low bending loss [32]. Therefore, the total propagation loss is assumed reasonably to be proportional to the length of the spiral. For the present case, the length for the longest spiral waveguide is up to 6.1 cm so that the total propagation loss is measurable regarding the propagation loss per unit length is small, which helps to extract the propagation loss per unit length. The measured total losses of all these spirals for the fundamental TE mode are shown in Fig. 5(b). From this figure, the propagation loss of the fabricated SOI nanowires is estimated to be db/cm, which is reasonable and acceptable in comparison with the reported values in the literatures [33], [34]. Fig. 6 shows the optical micrographs for the fabricated device. The footprint of the present wavelength division (de)multiplexer is 520 μm 190 μm (not including the expanded output waveguides), which is 50% smaller than the design with two AWGs shown in Fig. 1. Fig. 7 shows the measured transmission responses of an MZI-based optical interleaver on the same chip. 138

142 CHEN et al.: COMPACT DENSE WAVELENGTH-DIVISION (DE)MULTIPLEXER UTILIZING A BIDIRECTIONAL ARRAYED-WAVEGUIDE GRATING 2283 Fig. 6. Microscopic images of the fabricated bi-directional AWG and MZI based interleaver. Fig. 8. Measured results of the fabricated 18-channel de-multiplexer with a channel spacing of 200 GHz. (a) The measured spectral responses for all the channels. Dashed lines are for the odd channels, while the solid lines are for the even channels. (b) The wavelength difference between the MZI-based interleaver and the bi-directional AWG for all the wavelength channels. Fig. 7. Measured transmission of the fabricated MZI-based optical interleaver with 2 2 MMI couplers. From this measurement result, it can be seen that the FSR of the MZI is about 3.2 nm, which is consistent with the design value. The excess loss is estimated to be 1.0 db around the central wavelength 1550 nm. It is also observed that the extinction ratio at the cross port is over 30 db in a wide wavelength range. This is because that the extinction of the cross port is high intrinsically in theory [35]. In contrast, the extinction ratio for the through port is dependent on the wavelength dependence of the power splitting ratio of the MMI coupler. The un-balance of the MMI-based 3 db coupler degrades the extinction at the through port. Fig. 8(a) shows the measured spectral responses for all the 18 channels of the present dense wavelength division (de)multiplexer comprising an MZI interleaver and a bi-directional AWG. The solid curves are for the odd channels from the ports at the right side, while the dashed curves are for the even channels from the ports at the left side. It can be seen that these two groups of channels are interleaved very well with a wavelength offset of 1.6 nm. This is guaranteed intrinsically by such a bi-directional AWG working as two AWGs sharing the identical dispersion AWG. The excess loss for the central channel is about 8 db, which mainly from the MZI as well as the AWG. According to our measurement results for them separately, the MZI interleaver and the bi-directional AWG contribute an excess loss of 2 and 6 db, respectively. Particularly, for the bi-directional AWG, there is an extra loss due to the input waveguide positioned at the edge and this extra loss is estimated to be 1.5 db according to the formula given in [36]. From Fig. 8(a), it can be seen that the channel nonuniformity is about 2 db, which is partially from the intrinsic channel non-uniformity of an AWG according to [36]. The MZIbased optical interleaver also introduces some non-uniformity due to the wavelength misalignment between the MZI and the AWG. The channel crosstalk is about db, which is similar to a compact nine-channel AWG with a channel spacing of 3.2 nm fabricated on the same chip. 139

143 2284 JOURNAL OF LIGHTWAVE TECHNOLOGY, VOL. 33, NO. 11, JUNE 1, 2015 Fig. 9. Measured spectral responses for the fabricated simple regular AWG with a channel spacing of 200 GHz. TABLE I COMPARISON BETWEEN A SIMPLE REGULAR 200 GHZ AWG AND THE PRESENT (DE)MULTIPLEXER Simple regular AWG The present device Channel spacing (GHz) Device footprint (μm μm) Channel Number Crosstalk (db) Excess loss (db) 6 8 Besides, we make a comparison for all the wavelength channels of the fabricated de-multiplexer (including a MZI and a bi-directional AWG), with that of a single MZI fabricated on the same chip, as shown in Fig. 8(b). The deviation is less than 0.5 nm, which is due to the mismatch between the MZI s FSR and the AWG s channel spacing, resulting from the fabrication errors. This acceptable value for the wavelength misalignment is attributed to the excellent E-beam lithography and ICP etching processes. It is possible to further improve the wavelength alignment when the responses of the AWG and the MZI are flattened by introducing special designs [19], [37]. In order to give a comparison, we also fabricated a simple regular 14-channel AWG with a channel spacing of 200 GHz (see the inset in Fig. 9) and the measured spectral responses are shown in Fig. 9. Table I gives a comprehensive comparison between the simple regular AWG and the present (de)multiplexer. It can be seen that the device footprint is shrunk by 27% with the present design in comparison with the simple regular AWG. Furthermore, the present (de)multiplexer has much lower channel crosstalk ( 18 db) than the regular 200 GHz AWG (whose crosstalk is about 10 db). On the other hand, the excess loss for the present (de)multiplexer becomes higher in some degree due to the introduction of the MZI and the edge input, as predicted. IV. CONCLUSION In summary, we have proposed and demonstrated a compact dense wavelength division (de)multiplexer consisting of an asymmetrical MZI-based optical interleaver and a single bidirectional AWG. In this way, the channel number becomes doubled, and the channel spacing becomes halved in comparison with the single AWG. More importantly, the device s footprint only has a slight increase and the performance does not degrade notably. As an example, a 18-channel wavelength division (de)multiplexer with a channel spacing of 200 GHz (i.e., Δλ ch =1.6 nm) has been realized by using a bidirectional AWG with a channel spacing of 400 GHz (i.e., Δλ ch =3.2 nm). The device has a footprint of 520 μm 190 μm, which is 50% smaller than the design with two AWGs. According to the measurement results for the fabricated 18-channel 200 GHz (de)multiplexer, it can be seen that the channel crosstalk is db (similar to a single nine-channel 400 GHz AWG on the same chip). 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Bowers, Considerations for the design of asymmetrical Mach-Zehnder interferometers used as polarization beam splitters on a sub-micron silicon-on-insulator platform, J. Lightw. Technol., vol. 29, no. 12, pp , Jun [36] M. K. Smit and C. V. Dam, PHASAR-based WDM-devices: Principles, design and applications, IEEE J. Sel. Topics Quantum Electron., vol. 2, no. 2, pp , Jun [37] J. Song, Q. Fang, S. H. Tao, M. B. Yu, G. Q. Lo, and D. L. Kwong, Passive ring-assisted Mach-Zehnder interleaver on silicon-on-insulator, Opt. Exp., vol. 16, pp , Sitao Chen received the B.Eng. degree from the Department of Optical Engineering, Zhejiang University, Hangzhou, China, in 2011, where he is currently working toward the Ph.D. degree in the same department. His research interests include silicon wavelength-division (de)multiplexers. Xin Fu received the B.Eng. degree from the Department of Optical Engineering, Zhejiang University, Hangzhou, China, in 2010, where she is currently working toward the Ph.D. degree in the same department. Her research interests include silicon hybrid photonic integrated devices. Jian Wang received the B.Eng. degree from the Nanjing University of Technology, Nanjing, China, in He is currently working toward the Ph.D. degree in the Department of Optical Engineering, Zhejiang University, Hangzhou, China. His research interests include on-chip mode (de)multiplexers. Yaocheng Shi received the B.Eng. degree from Department of Optical Engineering, Zhejiang University, Hangzhou, China, and the Ph.D. degree from the Royal Institute of Technology, Stockholm, Sweden, in 2003 and 2008, respectively. He joined Zhejiang University as an Assistant Professor in 2008 and became an Associate Professor in His research interests include silicon photonic integrated devices. He has published >40 refereed international journals papers. Sailing He (M 92 SM 98 F 13) received the Ph.D. degree from the Royal Institute of Technology (KTH), Stockholm, Sweden, in Since then, he has been at KTH as an Assistant Professor, an Associate Professor, and a Full Professor. Currently, he is also a National Distinguished Professor appointed by China s central government (through Qian-Ren program) and a Chief Scientist for the Joint Research Center of Photonics of KTH, Stockholm, and Zhejiang University, Hangzhou, China. He has authored one monograph (Oxford University Press) and about 500 papers in refereed international journals. His current research interests include metamaterials, biophotonics, photonic integration technologies, fiber optical communication technologies, and optical sensing technologies. He is a Fellow of the OSA, SPIE, and The EM Academy. Daoxin Dai (M 07) received the B.Eng. degree from the Department of Optical Engineering, Zhejiang University, Hangzhou, China, and the Ph.D. degree from the Royal Institute of Technology (KTH), Stockholm, Sweden, in 2000 and 2005, respectively. Then he joined Zhejiang University as an Assistant Professor and became an Associate Professor in 2007, and a Full Professor in He worked at the University of California at Santa Barbara as a Visiting Scholar from 2008 until His research interests include silicon photonic integrated devices and the applications. He has published >120 refereed international journals papers (including seven invited review papers). He is serving as the Associate Editor of the journals of IEEE PHOTONICS TECHNOLOGY LETTERS, Optical and Quantum Electronics, andphotonics Research. 141

145 JOURNAL OF LIGHTWAVE TECHNOLOGY, VOL. 29, NO. 13, JULY 1, Compact Arrayed Waveguide Grating Devices Based on Small SU-8 Strip Waveguides Bo Yang, Yunpeng Zhu, Yuqing Jiao, Liu Yang, Zhen Sheng, Sailing He, and Daoxin Dai Abstract Compact and arrayed waveguide grating (AWG) devices are realized by using SU-8 strip waveguides fabricated with the process of direct ultraviolet (UV) photolithography. The demonstrated 48-channel and 23-channel AWG devices operating around 1550 nm have a channel spacing of 0.8 nm (100 GHz) and 3.2 nm (400 GHz), respectively. Due to the high index-contrast of the SU-8 strip waveguide, the fabricated AWG has a very compact size of only about cm.forthe fabricated 100 GHz-spaced AWG, the crosstalk between adjacent channels is less than db, and the polarization-dependent wavelength is about 0.72 nm (@ nm). The fabricated 400 GHz-spaced AWG device exhibits a crosstalk of less than db, a polarization-dependent wavelength of 0.02 nm (@ nm). Finally the temperature tenability of the present AWG device is also characterized. A 12 nm tuning range is observed as the temperature changes from 25 Cto115 C. Index Terms Arrayed waveguide grating (AWG)polymer, strip waveguide, SU-8. I. INTRODUCTION T HE explosive demand for optical interconnect services and data communication promotes the rapid development of the dense wavelength division multiplexing (DWDM) systems. In DWDM modules and systems, wavelength (de)multiplexer is the key component for increasing the capacity of the system. Because of the excellent performances (e.g., compact sizes and the capacity to incorporate a large number of channels) and the mass productibility [1], [2], the AWG (de)multiplexer has become one of the most successful commercial photonic integrated devices, especially for a DWDM system with a large channel number (e.g., tens of channels). AWGs have also been used for optical sensing [3] and optical spectrometers [4]. Among various material systems for planar lightwave circuits (PLCs), polymer is a popular system because of its simple fabrication process, high exibility and high yields [5]. People have developed many types of polymer materials with excellent optical performances (e.g., large transparent window [5], easily-adjustable refractive indexes [6], etc.). By using buried polymer waveguides, AWG devices have been demonstrated in the past years [7], [8]. However, for the buried Manuscript received October 27, 2010; revised February 11, 2011, April 19, 2011; accepted May 13, Date of publication May 23, 2011; date of current version June 17, This project was supported in part by Zhejiang Provincial Natural Science Foundation under No. R , and in part by the National Science Foundation of China under No The authors are with Centre for Optical and Electromagnetic Research, State Key Laboratory of Modern Optical Instrumentation, Zhejiang University, Zijingang, Hangzhou, China ( dxdai@zju.edu.cn). Digital Object Identi er /JLT polymer waveguide, which has a low index contrast, a large bending radius is inevitable. This prevents manufacturing PLCs with high integration densities. A simple way to achieve higher integration density is to use high index contrast optical waveguides, which can have the ability for a small bending radius. For example, InP-based deeply etched waveguides and silicon-on-insulator (SOI) nanowire waveguides have been used to realize ultrasmall AWGs whose size is at the order of m [9] [12]. However, for InP-based deeply etched waveguides and SOI nanowire waveguides, there are usually several challenges, e.g., relatively expensive fabrication, and high scattering loss due to the sidewall roughness. Because of the large absorption coef cient in the visible light range, the semiconductor (InP, and Si) optical waveguides are not available for visible light, which is desired for some sensing applications. Here we use small strip SU-8 polymer waveguides with air claddings. SU-8 polymer is a type of epoxy-based photosensitive polymer and consequently only a UV photolithography is needed [13], [14]. In addition, SU-8 polymer has high transmission for wavelength range above 400 nm [13]. SU-8 polymer has also been used for photonic integrated circuits (PLCs) in telecommunication [15] and sensing [16]. In our previous work [17], it has shown that a 75 m bending radius is possible for SU-8 optical strip waveguides due to the high index contrast between the air-cladding and the SU-8 polymer core. We have also demonstrated compact photonic integrated devices in our previous work, e.g., multimode interference coupler [18], microring resonator [19], etc. In this work, we design and fabricate compact 100 GHzspaced and 400 GHz-spaced AWG devices by using the small SU-8 strip waveguides. The polarization- and temperature dependence of the fabricated AWG devices are also characterized. II. DESIGN AND FABRICATION The SU-8 strip waveguide used here includes a SiO buffer layer, a SU-8 core and an air cladding as shown in Fig. 1. The cross section of the fabricated SU-8 strip waveguide is shown in the inset. The SiO buffer is 6 m thick to prevent the light leakage towards the Si substrate. The refractive nm of SU-8 and SiO are and 1.455, respectively. By using the prism coupling method, the measured material birefringence of SU-8 is as low as [14]. In comparison with the material birefringence, the birefringence caused by the geometrical asymmetry may be dominant and introduces a considerable polarization dependency for AWG devices. In our design, the core size is chosen to m to satisfy the single mode condition [20]. Due to fabrication errors, the waveguide /$ IEEE 142

146 2010 JOURNAL OF LIGHTWAVE TECHNOLOGY, VOL. 29, NO. 13, JULY 1, 2011 Fig. 1. Cross-sectional view of the present small SU-8 ridge waveguide (the inset shows the cross section of the fabricated SU-8 strip waveguide). Fig. 2. Schematic con guration of an AWG device. size of the fabricated AWGs will be slightly different and consequently different polarization dependencies are observed for our fabricated AWG devices shown below. Fig. 2 shows the schematic con guration of the present AWG device, which consists of input/output channel waveguides, two free propagation regions (FPRs) and arrayed waveguides. Here we use a regular AWG layout for which each arrayed waveguide has ve sections, i.e., three straight sections and two bending sections (as shown in Fig. 2). Since the small SU-8 strip waveguide used here has a strong con nement due to the air cladding, the bending radius is allowed to be as small as 100 m[17], which is helpful to achieve a compact AWG device. In our present design, we set radii m and 150 m for the bending sections in the arrayed waveguides for a compact 48-channel AWG devices with a channel spacing of 100 GHz. To minimize the coupling loss between the FPR and the arrayed waveguide, narrow gaps between the adjacent arrayed waveguides are usually preferred for an AWG. However, considering the resolution limitation of the regular UV lithography process, we set the gap width m in our design. The other design parameters involved are as follows: the FPR length m, the number of arrayed waveguides, the diffraction order. With these parameters, the total size of the designed 100 GHz-spaced AWG with mis cm, which is several tens times smaller than the conventional AWG based on low-index contrast SiO buried optical waveguides. We have also designed an AWG with a larger channel spacing ( GHz). Here we choose a relatively large bending radius min order to minimize the mode distortion at the straight-bending junctions in the bending section so that the crosstalk could be reduced. The corresponding total size of the 400 GHz-spaced AWG is still quite small ( 0.55 cm ) because the separation between the adjacent output waveguide is small ( 4.5 m). This is still much smaller than the conventional AWG based on low-index contrast SiO buried optical waveguides. The other design parameters for the 400 GHz AWG are: m, m, and. The fabrication process was going as follows. A 6 m-thick SiO buffer layer was deposited on a Si substrate by the plasma enhanced chemical vapor deposition (PECVD) system. ThereaftertheSU-8thin lmwasformedonthesio buffer layer by spin-coating. After the pre-baking process, a regular UV lithography process, the post-baking and the development followed. The propagation loss measured by using the cut-back method is about 0.17 db/mm when the core width is 2.0 m[17]. Fig. 3(a) shows the SEM view of the fabricated AWG device. Fig. 3(b) and (c) show the enlarged views of the arrayed waveguides and output waveguides, respectively. From the cross section of the fabricated SU-8 strip waveguide shown in Fig. 1, one sees that the optical waveguide has a vertical sidewall. III. CHARACTERIZATION AND DISCUSSION For the characterization of the fabricated AWG devices, a semiconductor laser diode (SLD) with a central wavelength of 1550 nm is used as the light source in our measurement system. An in-line ber polarizer and a polarization controller are used at the input ber to obtain TE- or TM- polarized light. In order to improve the coupling ef ciency, tapered lens bers (TLFs) are used to couple the input light into the optical waveguide and collect the output light from the output end of the optical waveguides. The output TLF is connected to an optical spectrum analyzer (OSA) to measure the spectral responses. Light is launched from the central input waveguide for each AWG device. Fig. 4(a) and (b) shows the measured spectral responses for the two 100 GHz-spaced AWGs with bending radii of mand m, respectively. The results for both polarizations (i.e., TE and TM) are measured to characterize the polarization dependence. Here the spectral responses are normalized by the transmission of a straight waveguide which has the same length as the device (about 0.22 cm). The insertion loss of the straight waveguide used to for the normalization is about 14 db, which is mainly due to the large coupling loss (i.e., 6 db per facet). From Fig. 4(a) and (b), one sees that the excess loss of the fabricated SU-8 AWGs is about 5 10 db. The origin for the excess loss of an AWG mainly comes from the bending loss and the mode mismatching between the FPRs and the arrayed waveguides. From the comparison between Fig. 4(a) and (b), one sees that the AWG with one with m has higher excess loss than the m. When the bending radius increases 143

147 YANG et al.: COMPACT ARRAYED WAVEGUIDE GRATING DEVICES 2011 Fig. 4. Normalized transmission spectra of the 100 GHz-spaced channel AWG with different structural parameters for TE and TM polarizations nm): (a) m, m, m, (b) m, m, m. Fig. 3. (a) SEM view of the fabricated AWG device ( m). (b) Enlarged view for the arrayed waveguides. (c) Enlarged view for the output waveguides. from 100 m to 150 m, the excess loss reduces from 9dB to 5 db. No notable reduction of excess loss is observed when the bending radius increases further to 1000 m (as shown in Fig. 6). Therefore, when the bending radius is as large as 150 m, the mode mismatching between the FPRs and the arrayed waveguides becomes the dominant origin of the excess loss. In order to reduce the mode mismatching loss, one has to reduce the gap between the arrayed waveguide. In our present design the gap width between adjacent arrayed waveguides is about 1.5 m with the consideration to the resolution limitation of the regular UV lithography process. It could however be improved further by optimizing the fabrication processes. From Fig. 4(a) and (b), it can be also seen that the crosstalk becomes much larger when the bending radius is reduced from 150 mto100 m. This is probably due to the excitation of higher-order modes at the junction between the straight and bending sections in the arrayed waveguides. For a smaller bending radius (100 m), the mode mismatching is more serious and more power is coupled into the higher-order modes. In Fig. 4(a) and (b), the measured spectral responses for both polarizations (i.e., TE and TM) are shown. As mentioned above, the polarization dependence of the SU-8 strip waveguide is mainly due to the geometrical asymmetry. For the two fabricated AWGs corresponding to Fig. 4(a) and (b), the waveguide core sizes are slightly different due to the process errors, i.e., m and m. Their theoretical birefringences are about and (@ nm), respectively. The theoretically introduced polarization-dependent wavelengths are about 0.20 nm and 0.77 nm, which are close to the measured values (

148 2012 JOURNAL OF LIGHTWAVE TECHNOLOGY, VOL. 29, NO. 13, JULY 1, 2011 Fig. 5. Normalized transmission spectra of the fabricated 100 GHz-spaced AWG device with bending radius of m for TE polarization. Fig. 6. Measured spectral responses of the fabricated 400 GHz-spaced AWG device for TE and TM polarizations. nm and 0.72 nm) shown in Fig. 4(a) and (b). The difference between the theoretical and experimental results is due to the non-uniformity of the SU-8 lm thickness. Nevertheless, it has been shown that the polarization dependence could be reduced by choosing appropriate structural parameters. Fig. 5 shows the measured spectral responses for TE polarization of all the 48 output channels of the fabricated 100 GHz-spaced AWG with a bending radius of m, when TE polarized light is injected into the central input channel. In this gure, the free spectral range (FSR) is about 38.9 nm. For the 48 channels from 1530 nm to 1569 nm, the minimal excess loss is about 3.7 db (@ nm). The channel crosstalk of the fabricated AWG device is lower than db as shown in Fig. 5. From Fig. 5 one also sees that the spectral responses of all channels have a Gaussian-like envelope and that the output power non-uniformity over the 48 channels is about 4.5 db. In order to improve the channel uniformity, one can use the way of increasing the FPR length or using some special designs (e.g., introducing auxiliary waveguides [21]). For the 400 GHz-spaced AWG devices with bending radius of m, both the pure bending loss and the transition loss (due to the mode-mismatching) at the straight-bending junctions is negligible. Consequently low loss and low crosstalk are expected. The waveguide core size of the fabricated 400 GHz-spaced AWG is m, which is expected to have the small polarization dependence according the theoretical calculation for the birefringence. The theoretical birefringence is about (@ nm), which results in the polarization-dependent shift of about 0.08 nm. Fig. 6 shows the measured normalized spectral responses for TE and TM polarizations of channel #19 of the AWG when light is launched into the central input channel. The polarization-dependent wavelength is about 0.02 nm (@ nm), which is of the same order of value as the theoretical results and only 0.5% of the channel spacing. From Fig. 6, one also sees that there is a polarization-dependent loss of about 1 db, which might be due to the polarization dependences of the waveguide- ber coupling loss and the mode mismatching loss between the FPRs and the arrayed waveguides. Fig. 7 shows the measured transmission spectrum Fig. 7. Normalized transmission spectra response of the 400 GHz-spaced AWG device. for TE polarization of all channels of the fabricated 400 GHzspaced AWG. The minimal excess loss is about 4.3 db and the channel non-uniformity is about 2.2 db. The excess loss of the present SU-8 AWG is comparable to that of the 400 GHz-spaced AWGs based on InP [9] and SOI [11]. We should note that it is possible to reduce the insertion loss further by reducing the gap width if the fabrication process is improved. The present SU-8 AWG has a crosstalk of less than db, which is better than that of InP-based [9] and SOI-based [11] compact AWGs. Limited by the bandwidth of the SLD source, the transmission spectra of channel 13 to channel 23 come from order,and channel 1 to channel 12 come from order. It is well known that polymer usually has a large negative thermooptical coef cient. Therefore, the transmission passband of polymeric AWG multiplexers can be controlled over a wide range by heating. In our experiments, the chip is heated by a thermoresistor. The temperature is controlled by tuning the applied voltage. Fig. 8(a) shows the transmission spectrum of the central output channel as the temperature varies from 25 C to 115 C. Raising the temperature caused a peak shift to the 145

149 YANG et al.: COMPACT ARRAYED WAVEGUIDE GRATING DEVICES 2013 range of 12 nm when changing the temperature within the range of 25 C 115 C. Since the SU-8 strip waveguide has an air cladding, the demonstrated AWG device could be used for optical sensing. To further improve the performance of the AWG device, the fabrication process as well as the structural design should be optimized in the future. With improved performances, the compact AWG devices could be used in many applications such as optical sensing, optical spectrometers, and (de)multiplexing, etc. Fig. 8. (a) Spectral response of the central output channel of the fabricated 400 GHz-spaced AWG as the temperature increases (light is input from the central input channel #12). (b) Peak wavelength as the temperature increases. shorter wavelength region due to the negative thermooptical coef cient. Fig. 8(b) shows the peak wavelength as the temperature increases. The tuning range is about 12 nm when the temperature increases from 25 Cto115 C. The slope is about nm C. The corresponding thermooptical coef- cient Tis about. This makes it possible to realize a thermally tunable AWG lter with a large tuning range. IV. CONCLUSION We have designed and fabricated 100 GHz-spaced and 400 GHz-spaced AWG devices based on the SU-8 strip waveguides which is fabricated by using a simple direct UV-lithography process. The footprint of the present AWG devices is cm, which is only 1/40 of its counterpart based on the low index-contrast buried polymer waveguide. The fabricated 100 GHz-spaced and 400 GHz-spaced AWG devices have a crosstalk of less than db and db, respectively. The polarization dependencies of the fabricated AWG devices with different waveguide core sizes have been characterized. Finally, the thermal tenability of the fabricated AWG device has also been characterized. 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Tahani, J. Zyss, L. Camberlein, and E. Gaviot, SU-8 waveguiding interferometric micro-sensor for gage pressure measurement, Sens. Actuators: A. Phys., vol. 135, no. 1, pp , Mar [17] B. Yang, L. Yang, R. Hu, Z. Sheng, D. Dai, Q. Liu, and S. He, Fabrication and characterization of small optical ridge waveguides based on SU-8 polymer, J. Lightw. Technol., vol. 27, no. 18, pp , Sep [18] L. Yang, B. Yang, Z. Sheng, J. Wang, D. Dai, and S. He, Compact 2 2 tapered multimode interference couplers based on SU-8 polymer rectangular waveguides, Appl. Phys. Lett., vol. 93, no. 20, pp ,

150 2014 JOURNAL OF LIGHTWAVE TECHNOLOGY, VOL. 29, NO. 13, JULY 1, 2011 [19] D. Dai, L. Yang, Z. Sheng, B. Yang, and S. He, Compact microring resonator with 2 2 tapered multimode interference couplers, J. Lightw. Technol., vol. 27, no. 21, pp , Nov [20] R. Hu, D. Dai, and S. He, A small polymer ridge waveguide with a high index contrast, J. Lightw. Technol., vol. 26, no. 13, pp , Jul [21] Z. Sheng, D. Dai, and S. He, Improve channel uniformity of an Si-Nanowire AWG demultiplexer by using dual-tapered auxiliary waveguides, J. Lightw. Technol., vol. 25, no. 10, pp , Oct Bo Yang was born in Hunan, China, in She received the B.Eng. degree from Zhejiang University, Zhejiang, China, in 2007, where she is currently pursuing the Ph.D. degree in the Department of Optical Engineering. Her research activities are in the design and fabrication of planar lightwave circuits. Yunpeng Zhu was born in Jiangsu, China, in He received the B.Sci. degree in optical information science and technology from Nanjing University of Posts and Telecommunication, Nanjing, China, in 2007, where he is now pursuing the Ph.D. degree at the Centre for Optical and Electromagnetic Research. Yuqing Jiao was born in Zhejiang, China, in He received the B.Eng. degree from the Department of Optical Engineering, Zhejiang University, China, in 2008, where he is currently pursuing the Ph.D. degree. His research activities are in the design and fabrication of planar lightwave circuits. Liu Yang received the B.Eng. degree from Kunming University of Science and Technology, China, in 2004, and the Ph.D. degree in the Department of Optical Engineering, Zhejiang University, China, in Currently she is working in Zhejiang University as a post-doctoral fellow. Her research activities are in the design and fabrication of planar lightwave circuits. Zhen Sheng received the B.Eng. and Ph.D. degrees from the Department of Optical Engineering, Zhejiang University, China, in 2005 and 2010, respectively. In July 2010, he joined the Shanghai Institute of Microsystem and Information Technology (SIMIT), Chinese Academy of Sciences (CAS), Beijing, China. His current research interests include silicon photonics for optical communications and interconnections. Sailing He (M 92-SM 98) received the Licentiate of Technology and Ph.D. degree in electromagnetic theory from the Royal Institute of Technology, Stockholm, Sweden, in 1991 and 1992, respectively. She has been a member of Faculty of the Royal Institute of Technology since He is also with the Centre for Optical and Electromagnetic Research, Zhejiang University, China as a distinguished Professor appointed by the central government of China. He also serves as a Chief Scientist at the Joint Research Center of Photonics of the Royal Institute of Technology (Sweden) and Zhejiang University (China). He has rst-authored one monograph (Oxford University Press) and authored/co-authored over 400 papers in refereed international journals, as well as been granted a dozen of patents in optical communications. Daoxin Dai (M 07) received the B.Eng. degree from the Department of Optical Engineering, Zhejiang University, Zhejiang, China, in 2000, where he is pursuing the Ph.D. degree. In 2004, he became an exchange Ph.D. student at the Royal Institute of Technology (KTH), Sweden, where he obtained a Ph.D. degree in Thereafter he joined Zhejiang University and became an associate professor in His current research interests include silicon micro-/nano-photonics for optical communications, optical interconnections, and optical sensing. He has authored about 80 refereed international journal papers. 147

151 Low-loss Si 3 N 4 arrayed-waveguide grating (de)multiplexer using nano-core optical waveguides Daoxin Dai, * Zhi Wang, Jared F. Bauters, M.-C. Tien, Martijn J. R. Heck, Daniel J. Blumenthal, and John E Bowers Department of Electrical and Computer Engineering, University of California, Santa Barbara, CA 93106, USA *dxdai@ece.ucsb.edu Abstract: A 16-channel 200GHz arrayed-waveguide grating (AWG) (de)- multiplexer is demonstrated experimentally by utilizing Si 3 N 4 buried optical waveguides, which have 50nm-thick Si 3 N 4 cores and a 15μm-thick SiO 2 cladding. The structure with an ultra-thin core layer helps to reduce the scattering due to the sidewall roughness and consequently shows very low loss of about 0.4~0.8dB/m. When using this type of optical waveguide for an AWG (de)multiplexer, there is no problem associated with gap refill using the upper-cladding material even when choosing a small (e.g., 1.0 μm) gap between adjacent arrayed waveguides, which helps to reduce the transition loss between the FPR (free-propagation region) and the arrayed waveguides. Therefore, the demonstrated AWG (de)multiplexer based on the present Si 3 N 4 buried optical waveguides has a low on-chip loss. The fabricated AWG (de)multiplexer is characterized in two wavelength ranges around 1310nm and 1550nm, respectively. It shows that the crosstalk from adjacent and non-adjacent channels are about 30dB, and 40dB, respectively, at the wavelength range of 1310nm. The Si 3 N 4 AWG (de)multiplexer has a temperature dependence of about 0.011nm/ C, which is close to that of a pure SiO 2 AWG device Optical Society of America OCIS codes: ( ) Integrated Optics; ( ) Waveguides, planar. References and links 1. C. R. Doerr and K. Okamoto, Advances in silica planar lightwave circuits, J. Lightwave Technol. 24(12), (2006). 2. Y. Hibino, Recent advances in high-density and large-scale AWG multi/demultiplexers with higher indexcontrast silica-based PLCs, IEEE J. Sel. Top. Quantum Electron. 8(6), (2002). 3. K. Kodate and Y. Komai, Compact spectroscopic sensor using an arrayed waveguide grating, J. Opt. A. 10(4), (2008). 4. P. Cheben, J. H. Schmid, A. Delâge, A. Densmore, S. Janz, B. Lamontagne, J. Lapointe, E. Post, P. Waldron, and D.-X. Xu, A high-resolution silicon-on-insulator arrayed waveguide grating microspectrometer with submicrometer aperture waveguides, Opt. Express 15(5), (2007). 5. R. Adar, M. R. Serbin, and V. Mizrahi, Lss-than-1 db per meter propagation loss of silica wave-guides measured using a ring-resonator, J. Lightwave Technol. 12(8), (1994). 6. A. Sugita, A. Kaneko, K. Okamoto, M. Itoh, A. Himeno, and Y. Ohmori, Very low insertion loss arrayedwaveguide grating with vertically tapered waveguides, IEEE Photon. Technol. Lett. 12(9), (2000). 7. M. B. J. Diemeer, L. H. Spiekman, R. Ramsamoedj, and M. K. Smit, Polymeric phased array wavelength multiplexer operating around 1550 nm, Electron. Lett. 32(12), (1996). 8. B. Yang, Y. Zhu, Y. Jiao, L. Yang, Z. Sheng, S. He, and D. Dai, Compact Arrayed Waveguide Grating Devices Based on Small SU-8 Strip Waveguides, J. Lightwave Technol. (to appear). 9. Y. Barbarin, X. J. M. Leijtens, E. A. J. M. Bente, C. M. Louzao, J. R. Kooiman, and M. K. Smit, Extremely small AWG demultiplexer fabricated on InP by using a double-etch process, IEEE Photon. Technol. Lett. 16(11), (2004). 10. P. D. Trinh, S. Yegnanarayanan, F. Coppinger, and B. Jalali, Silicon-on-insulator (SOI) phased-array wavelength multi/demultiplexer with extremely low-polarization sensitivity, IEEE Photon. Technol. Lett. 9(7), (1997). # $15.00 USD Received 18 May 2011; revised 7 Jun 2011; accepted 7 Jun 2011; published 8 Jul 2011 (C) 2011 OSA 18 July 2011 / Vol. 19, No. 15 / OPTICS EXPRESS

152 11. W. Bogaerts, S. K. Selvaraja, P. Dumon, J. Brouckaert, K. De Vos, D. Van Thourhout, and R. Baets, Siliconon-insulator spectral filters fabricated with CMOS technology, IEEE J. Sel. Top. Quantum Electron. 16(1), (2010). 12. D. Dai, X. Fu, Y. Shi, and S. He, Experimental demonstration of an ultracompact Si-nanowire-based reflective arrayed-waveguide grating (de)multiplexer with photonic crystal reflectors, Opt. Lett. 35(15), (2010). 13. C. R. Doerr, L. Chen, L. L. Buhl, and Y.-K. Chen, 8-Channel SiO2/Si3N4/Si/Ge CWDM Receiver, IEEE Photon. Technol. Lett. (to appear). 14. C. R. Doerr, L. Chen, Y.-K. Chen, and L. L. Buhl, Wide Bandwidth Silicon Nitride Grating Coupler, IEEE Photon. Technol. Lett. 22(19), (2010). 15. M. M. Spühler, B. J. Offrein, G. Bona, R. Germann, I. Massarek, and D. Erni, A very short planar silica spotsize converter using a nonperiodic segmented waveguide, J. Lightwave Technol. 16(9), (1998). 16. J. F. Bauters, M. J. R. Heck, D. John, D. Dai, M.-C. Tien, J. S. Barton, A. Leinse, R. G. Heideman, D. J. Blumenthal, and J. E. Bowers, Ultra-low-loss high-aspect-ratio Si 3N 4 waveguides, Opt. Express 19(4), (2011). 17. M. C. Tien, J. F. Bauters, M. J. Heck, D. J. Blumenthal, and J. E. Bowers, Ultra-low loss Si3N4 waveguides with low nonlinearity and high power handling capability, Opt. Express 18(23), (2010). 18. Y. C. Zhu, F. H. Groen, D. H. P. Maat, Y. S. Oei, J. Romijin, and I. Moerman, A compact PHASAR with low central channel loss, in Proc. Euro. Conf. Integrated Optics 99, Turin, Italy, Apr , (1999). 19. D. Dai, Z. Wang, N. Julian, and J. E. Bowers, Compact broadband polarizer based on shallowly-etched siliconon-insulator ridge optical waveguides, Opt. Express 18(26), (2010). 20. Y. Sakamaki, S. Kamei, T. Hashimoto, T. Kitoh, and H. Takahashi, Loss uniformity improvement of arrayedwaveguide grating with mode-field converters designed by wavefront matching method, J. Lightwave Technol. 27(24), (2009). 1. Introduction As a promising technology for expanding the capacity of an optical communication system, wavelength division multiplexing (WDM) has been used widely in many applications, including optical communications. As a typical integrated (de)multiplexer used in a WDM system, the arrayed-waveguide grating (AWG) is important for many DWDM systems and modules [1,2]. In addition, AWGs have also been used for optical sensing [3] and optical spectrometers [4]. Therefore, significant effort has been made to develop high-performance AWGs based on various materials and waveguide structures, e.g., silica-on-si buried waveguides [5,6], polymer waveguides [7,8], InP ridge waveguides [9], large silicon-oninsulator (SOI) ridge waveguides [10] as well as SOI (silicon-on-insulator) nanowires [11,12]. Silica AWG has been commercialized because of its high performance. However, the bending radius is usually very large because of the low index-contrast, which is not good for a high integration density. In contrast, SOI-nanowire has an ultra-high index contrast, which enables a micro-scale bending, and consequently ultrasmall SOI-nanowire AWGs have been intensively studied in the past years [11-12]. The drawback is that the SOI-nanowire AWG needs very high resolution fabrication technology and usually has a high insertion loss and high crosstalk. As an alternative platform with a moderate index contrast, Si 3 N 4 waveguide is of interest [13-14]. In this paper, we demonstrate an AWG based on Si 3 N 4 waveguides with a nano-core layer. For AWGs, low loss is highly desirable, especially for applications in which low power consumption is required. When an AWG is connected with fibers, the fiber-to-chip coupling loss is one of the major loss origins, especially if the waveguide mode is not well-matched to the fiber mode. Nevertheless, this coupling loss could be minimized by using various mode converters [15]. On the other hand, for an AWG integrated with other components on the same chip, the on-chip loss is usually more important. Therefore, in this paper we focus on the AWG s on-chip loss, which includes the material loss, bending loss, waveguide scattering loss, and the transition loss between the FPR (free propagation region) and the arrayed waveguides. Usually the material loss can be minimized in the desired wavelength range by choosing the material appropriately. The bending loss can be reduced simply by choosing a large bending radius (even though small bending radius is desired to obtain a small footprint). Thus, in order to achieve a low-loss AWG, a reduction of the waveguide scattering and transition losses is essential. The scattering loss can be reduced significantly by minimizing the roughness with an improved fabrication technology (especially the etching process). On the other hand, the # $15.00 USD Received 18 May 2011; revised 7 Jun 2011; accepted 7 Jun 2011; published 8 Jul 2011 (C) 2011 OSA 18 July 2011 / Vol. 19, No. 15 / OPTICS EXPRESS

153 scattering loss also depends on the optical field distribution, which can be modified by designing the waveguide structure. Since the top and bottom surfaces for a planar optical waveguide are much smoother than the sidewalls, the scattering loss is usually dominated by the sidewall roughness. It is expected to have a reduced scattering loss if a nano-scale core layer is used. In Ref [16], we reported a low loss of 0.03dB/cm at 1550nm for 2-mm bend radius by using a buried optical waveguide which has a wide but ultra-thin Si3N4 core (2μm 80nm). This provides a promising way to realize low-loss large-scale photonic integration circuits. In this paper, we demonstrate a low-loss AWG (de)multiplexer by using a thinner, lower loss optical waveguide with a 50nm-thick SiN core layer, and a loss of about 0.4~0.8dB/m [17]. As mentioned earlier, the transition loss between the FPR and the arrayed waveguides is another important origin for the on-chip loss of an AWG [6,18]. The transition loss is due to a field mismatch between the FPR and the arrayed waveguides because there are gaps between arrayed waveguides and the gap size is limited by the fabrication process. First, one usually cannot obtain a zero-gap because of the resolution limit of UV lithography. A potential solution is using e-beam lithography [18], which could make nano-scale gaps; however, the fabrication becomes very expensive and inefficient. For SiO 2 -on-si AWGs in particular, the gaps are usually not allowed to be narrower than 2μm (which is not limited by UV lithography) so that one could refill the upper-cladding material into the gaps without voids. In order to reduce the transition loss, there are several approaches, e.g., using a double-etch technology, which has been used for AWGs based on InP waveguides [9], and SOI nanowires [11]. Another similar approach of using vertical tapers is introduced at the junctions and the transition loss could be reduced by 1dB [6]. However, the fabrication is not easy. The waveguide reported in this paper has an ultra-thin core layer, and so it becomes very easy to refill the upper-cladding material into the gaps even when the gap width is reduced to less than 2μm. Considering the resolution limitation of the UV-lithography process, in our design we choose 1-μm-wide gaps, and a low-loss AWG is achieved as the experimental results show below. In addition, the ultra-thin core layer allows a singlemode optical waveguide to be as wide as several microns even though the Si 3 N 4 core has much higher refractive index than the SiO 2 cladding. Since a wider optical waveguide is more tolerant to the width variation, the present wide Si 3 N 4 optical waveguide also helps to obtain a lowcrosstalk AWG (de)multiplexer. Table 1 shows a comparison for AWGs on various platforms, including SiO 2, SOI, InP, polymer as well as Si 3 N 4 in the present paper. From this comparison, one sees that the present Si 3 N 4 platform is a good option for realizing AWGs with good performances. Table 1. Comparison for AWGs on various platforms. (non)adjacent on-chip Channel number crosstalk loss channel spacing Waveguide size Footprint SiO 2WG [6] ~ 40dB 0.75dB GHz 6μm 6μm Polymer buried WG ~ 25dB ~8dB 8 400GHz 6μm 6μm 6.4cm 1.4cm [7] Polymer strip WG [8] ~ 20dB ~5dB GHz 2μm 1.5μm 0.22cm 0.47cm InP [9] ~ 12dB <5dB 4 400GHz 2μm 0.72μm 230μm 330μm SOI rib WG [10] ~ 22 ~6dB 4 240GHz 5μm 2.7cm 2.7cm SOI nanowire [12] ~ 12dB ~3dB 9 400GHz 500nm 220nm 134μm 115μm SiN WG < 30dB (this work) (~ 40dB) ~<0.5dB GHz 5.5μm 50nm 2cm 1.5cm 2. Design, fabrication and characterization Figure 1(a) shows the cross section of the present buried Si 3 N 4 optical waveguides, which have a wide and ultrathin Si 3 N 4 core (about 50nm thick). The SiO 2 lower-cladding has a # $15.00 USD Received 18 May 2011; revised 7 Jun 2011; accepted 7 Jun 2011; published 8 Jul 2011 (C) 2011 OSA 18 July 2011 / Vol. 19, No. 15 / OPTICS EXPRESS

154 thickness of 15μm to avoid any leakage loss to the substrate. The SiO 2 upper-cladding is also 15μm-thick to make the waveguide symmetrical. The waveguides and devices were fabricated with LioniX BV s TriPleXTM technology [16]. The process begins with the thermal oxidation of a standard silicon wafer form the lower cladding. This is followed by LPCVD deposition of stoichiometric Si3N4. A single photolithography step is then performed followed by reactive ion etching to form the ridge waveguide. Finally, a thick SiO2 layer is deposited using plasma-enhanced CVD (PECVD) to complete the upper cladding layer. The refractive indices for the Si 3 N 4 core and SiO 2 cladding are about 1.99 and 1.45, respectively. In this structure, the sidewall area is very small and consequently the overlap of the optical field with the sidewall is minimized, which is helpful to reduce the scattering loss from the roughness of the sidewall. Figure 1 (b) and 1(c) show the profiles for TE- and TM- polarized fundamental mode fields, which are from the full-vectorial FEM (finite-element method) mode solver. For the present Si 3 N 4 waveguide, the TM polarized mode has a much weaker confinement than the TE polarized mode. Consequently the bending loss of TM polarization is much higher than TE polarization. Therefore, in this paper we only consider operation with TE polarization. SiO 2 caldding SiN nano-core layer: 50nm-thick h bf=15μm Si substrate (a) TE SiO 2 cladding (a) TE TE SiO 2 cladding (b)tm 50nm-thick SiN 50nm-thick SiN y (μm) y (μm) n eff = x (μm) (b) n eff = x (μm) (c) Fig. 1. (a). The cross section of the present low-loss buried optical waveguide with a 50nmthick Si 3N 4 core; (b) the mode profile of the TE-polarized fundamental mode; (c) the mode profile of the TM-polarized fundamental mode. For the AWG design, we choose the following parameters: the central wavelength λ 0 = 1550nm, the channel number N ch = 16 and the channel spacing Δλ ch = 1.6nm (200GHz), the number of arrayed waveguides N WG = 150, the diffraction order m = 60, the FPR length L FPR = 3000μm, and the end separation of the output waveguides d g = 20μm. Figure 2 shows the layout of the designed AWG (de)multiplexer. Two reference waveguides are put at the bottom of the AWG for normalizing the AWG s response. The total size is about 2cm 1.5cm, which is comparable to a conventional SiO 2 AWG. It is possible to reduce the footprint by choosing # $15.00 USD Received 18 May 2011; revised 7 Jun 2011; accepted 7 Jun 2011; published 8 Jul 2011 (C) 2011 OSA 18 July 2011 / Vol. 19, No. 15 / OPTICS EXPRESS

155 a relatively thick Si 3 N 4 core layer (e.g., 100nm~200nm) so that the minimal bending radius could be reduced to sub-millimeter. Here we choose the Si 3 N 4 thickness as 50nm in order to be compatible to the design for ultra-low loss waveguiding in the same wafer. Arrayed WG 1.5 cm Reference waveguides 2 cm Fig. 2. The layout of the designed AWG (de)multiplexer. In order to characterize the fabricated AWG, we use a measurement setup consisting of a free-space optical system with a bulk polarizer to have a TE-polarized input light at the input side [19]. A lens fiber was used for the coupling and the coupling loss is less than 2dB/facet for a 5.5μm-wide input/output waveguide. Figure 3(a) shows the measured spectral responses in the wavelength range from 1510nm to 1610nm by using a tunable laser and a photodetector. The tunable laser was tuned with a step of 0.1nm. The responses are normalized by the transmission of the reference waveguide. It can be seen that the spectral response is repeated over a wavelength span, which is called free spectral range (FSR). The FSR is about 25.3nm for the AWG device. The channel spacing is about 1.58nm, which is very close to the designed value (1.6nm). Therefore, there are 16 channels available in a FSR. From the normalized responses shown in Fig. 3(a), it can be seen that the excess loss of the fabricated AWG is low (almost zero for the central channel), which is mainly due to the small gap between the arrayed waveguides and good refilling of the upper-cladding layer because of the core layer is very thin. Figure 3(b) shows the responses of the central channel (#8). From this figure, one can see that the crosstalk from the adjacent channels is about 25dB while the non-adjacent crosstalk is as low as 30dB. We also note that there are two significant sidelobes at both sides of the major peak. These two sidelobes are due to the coupling between the adjacent output waveguides. # $15.00 USD Received 18 May 2011; revised 7 Jun 2011; accepted 7 Jun 2011; published 8 Jul 2011 (C) 2011 OSA 18 July 2011 / Vol. 19, No. 15 / OPTICS EXPRESS

156 10 FSR=25.3nm 10 #7 #8 #9 # Power (dbm) Power (dbm) dB 30dB Wavelength (nm) (a) -30 Side lobes Wavelength (nm) (b) Fig. 3. (a). The measured spectral responses of all the channels in the wavelength range around 1550nm; (b) the response for channel FSR=18.4nm #7 #8 #9 #10 Power (dbm) Power (dbm) ~30dB ~32dB 40dB Wavelength (nm) (a) Wavelength (nm) (b) Fig. 4. (a). The measured spectral responses of all the channels in the wavelength range around 1310nm; (b) the response for channel #9. The OSA resolution is 0.1nm in the measurement. When the wavelength becomes shorter, the optical confinement of the Si 3 N 4 optical waveguide becomes stronger and consequently the coupling between adjacent output waveguides is reduced. Therefore the sidelobes are expected to be smaller. Here we also measure the AWG s responses in a short wavelength range from 1280nm to 1360nm by using an ASE light source along with an optical spectral analyzer (OSA) whose resolution is 0.1nm. Figure 4(a) shows the measured spectral responses of all the channels in the wavelength range from 1310nm to 1335nm. These spectral responses are normalized by the transmission of the reference waveguide. In this case, the FSR of the AWG becomes 18.4nm because of the shorter operation wavelength and the channel spacing is about 1.34nm, which is smaller than that in the wavelength range around 1550nm. Consequently, only 13 channels are available in a FSR. The central channels have very low excess loss. For the outer channels, the loss is higher due to the envelope of the far field [20]. Figure 4(b) shows the response of the central channel. From this figure, one sees that the crosstalk from the adjacent channel is less than 30dB, and the non-adjacent channel crosstalk is about 40dB. We also characterize the temperature dependence of the presented AWG. Figure 5(a) shows the measured spectral response of the central channel (#9) when the substrate temperature is set as 10, 40, 70, and 100 C, respectively. It can be seen that the central wavelength increases as the temperature increases. Since the present Si 3 N 4 waveguide has a 50nm-thick core surrounded by a thick SiO 2 cladding, most power of the fundamental # $15.00 USD Received 18 May 2011; revised 7 Jun 2011; accepted 7 Jun 2011; published 8 Jul 2011 (C) 2011 OSA 18 July 2011 / Vol. 19, No. 15 / OPTICS EXPRESS

157 mode is confined in the SiO 2 cladding and consequently the thermal performance is expected to be very similar to a pure SiO 2 buried waveguide. Figure 5(b) shows the central wavelength as the temperature varies. And the slope is about λ/ T = nm/ C, which is very close to that of an AWG based on pure SiO 2 buried waveguides as expected Power (db) T=10, 40, 70, 100 C Central wavelength (nm) λ/ T= nm/ C Wavelength (nm) (a) T ( C) (b) Fig. 5. (a). The spectral response of channel #9 as the temperature varies; (b) the central wavelength of channel #9 as the temperature increases from 10 to 100 C. 3. Conclusions In this paper, we have demonstrated a low-loss, low-crosstalk AWG (de)multiplexer by using Si 3 N 4 buried optical waveguides. The presented AWG (de)multiplexer has 16 channels and the channel spacing is 200GHz (i.e., 1.6nm). The singlemode Si 3 N 4 optical waveguide used here has a 5.5μm 50nm Si 3 N 4 core and a 15μm-thick SiO 2 cladding. With such a structure, the Si 3 N 4 optical waveguide has a very low scattering loss due to small mode overlap with the sidewall roughness. For the design of an AWG (de)multiplexer, we have chosen a small gap (about 1μm-wide) between adjacent arrayed waveguides to reduce the transition loss between the FPR and the arrayed waveguides. The fabricated AWG (de)multiplexer has been characterized in two wavelength ranges around 1310nm, and 1550nm, respectively. At the shorter wavelength range, the optical confinement becomes stronger and consequently the crosstalk is lower than that at longer wavelengths. It has shown that the crosstalk of adjacent and non-adjacent channels are about 30dB, and 40dB, respectively, at the wavelength range of 1310nm. The design could be optimized further to improve the AWG performance at longer wavelength by choosing a thicker core (e.g., 100~200nm). Finally we have also characterized the temperature dependence of the fabricated Si 3 N 4 AWG (de)multiplexer and the temperature dependence is about 0.011nm/ C, which is close to that of a pure SiO 2 AWG device because most power of the fundamental mode is confined in the SiO 2 cladding. Acknowledgements This work was supported by DARPA MTO under the iphod contract No: HR C The authors thank Scott Rodgers, Demis John and John Barton for useful discussions. The optical waveguides were fabricated by LioniX BV, Netherlands. # $15.00 USD Received 18 May 2011; revised 7 Jun 2011; accepted 7 Jun 2011; published 8 Jul 2011 (C) 2011 OSA 18 July 2011 / Vol. 19, No. 15 / OPTICS EXPRESS

158 Author's personal copy Optics Communications 279 (2007) Highly-sensitive sensor with large measurement range realized with two cascaded-microring resonators Daoxin Dai *, Sailing He Centre for Optical and Electromagnetic Research, State Key Laboratory for Modern Optical Instrumentation, Zhejiang University, Hangzhou , China Joint Research Center of Photonics of KTH (The Royal Institute of Technology, Sweden) and Zhejiang University, East Building No. 5, Zijingang Campus, Zhejiang University, Hangzhou , China Received 6 April 2007; received in revised form 1 July 2007; accepted 7 July 2007 Abstract A highly-sensitive sensor consisting of two cascaded-microring resonators (MRR) is suggested and investigated theoretically. The two MRRs are based on nanoslot waveguides and Si nanowires. By appropriately choosing the parameters, the MRR-based on nanoslot waveguides has a high sensitivity. The other MRR-based on Si nanowires is designed to have a large free spectral range (about 38 nm) and consequently a large measurement range (though its sensitivity is low). In this way, a highly-sensitive sensor with a large measurement range is achieved theoretically from the output spectral response from the bus waveguide of the two cascaded-mrrs. In order to make the design flexible and compact and reduce the crosstalk, the two drop waveguides for the cascaded-mrrs are perpendicular to the horizontal input bus waveguide. Ó 2007 Elsevier B.V. All rights reserved. OCIS: ; Keywords: Sensor; Microring resonator; Nanowire; Nanoslot; Cascaded 1. Introduction * Corresponding author. Address: Centre for Optical and Electromagnetic Research, State Key Laboratory for Modern Optical Instrumentation, Zhejiang University, Hangzhou , China. Tel.: x215; fax: addresses: dxdai@zju.edu.cn, ddxopt@yahoo.com.cn (D. Dai). In the recent years, there are rapid demands for lowcost, high sensitive and ultra-compact sensors used in various areas such as biological, environmental and chemical detections [1 7]. To satisfy such demands, integrated optical sensors based on planar lightwave circuits (PLCs) technologies emerge as one of the most promising candidates. There have been many types of integrated optical sensors based on different structures, such as Mach-Zehnder interferometers [1,2], surface plasmon sensors [3], microring/ disk resonators [4 7], etc. Among them, versatile microring/disk resonators (which have been successfully used as a key element in various functional components for optical communications, e.g., add-drop filters [8], optical switches [9]) are becoming one of the most attractive candidates for optical sensing because of its ultra-compact size, and easy to realize an array of sensors with a large-scale integration [8]. When detecting target chemicals by using micro-resonator sensors, one can use a certain chemical binding on the surface. In this way, the effective index of the waveguide varies with the concentration of the target chemical since the evanescent field penetrates into the target chemical. Consequently the spectral responses of the through and drop channels will vary. There are two typical ways for the measurement of the target chemicals. One is to measure the shift of the resonated wavelength and the other is to measure the intensity variation for a fixed wavelength. The latter is more suitable for a highly-sensitive sensor with a very small measuring range. Moreover, one can also /$ - see front matter Ó 2007 Elsevier B.V. All rights reserved. doi: /j.optcom

159 Author's personal copy 90 D. Dai, S. He / Optics Communications 279 (2007) measure the enhanced fluorescence emitted by biological materials if needed [10]. In this paper, we focus on achieving a high sensitivity to the change of ambient refractive index by measuring the shift of the drop wavelength. Some highly-sensitive resonator sensors based on polymer microrings/disks have been developed [4,5]. However, not much work on microring/disk resonator sensors based on silicon nanowires, which have ultrasmall bending radii due to the ultrahigh refractive index contrast [11]. This has attracted much attention for realizing ultra-compact optical components [12,13]. In fact, a silicon nanowire usually has a high sensitivity to the change of ambient refractive index due to the large evanescent field resulting from its submicron cross section [14,15]. Recently a so-called nanoslot waveguide which can enhance the field in the air slot greatly has been introduced [16]. Therefore, a microring resonator based on nanoslot waveguides is expected to have higher sensitivity than that based on conventional silicon nanowires. However, in this case, the measurement range (limited by the free spectral range, FSR) will become relative small. In this paper, we cascade two microring resonators (MRRs), which are based on nanoslot waveguides and Si nanowire waveguides, respectively, to achieve a highly-sensitive sensor with a large measurement range. The microring based on Si nanowires has a low sensitivity and a relatively large FSR, which gives a large measurement range. To cascade the two microrings, one can puts the two microrings between two straight waveguides [17]. However, in such a configuration there is some crosstalk between these two rings. Furthermore, the cascaded rings then need to have almost the same radii to avoid additional bends, and this reduces the flexibility of the design greatly. In ref. [8], the authors demonstrated an array of microrings in which the input bus waveguide and an add-drop waveguide are crossed at right angles for each basic filter element. With this configuration, one can flexibly design the ring for each filter element. Orthogonal input and drop waveguides was also used in a microdisk sensor to avoid undesired coupling of the input beam into the collecting fiber in the measurement [4]. In this paper, we use a similar structure which has a horizontal input bus waveguide and two vertical drop waveguides. In our case, the add-port is not needed (different from the adddrop filter shown in ref. [8]) and thus the crosses are removed to reduce the loss and crosstalk We demonstrate the design of the present cascaded-microring resonator sensors to achieve a high sensitivity and a large measurement range. 2. Theory For an MRR, the resonator wavelength is given by the following equation: n r 2pR ¼ mk; ð1þ where n r is the effective index of the ring, R is the bending radius, and m is the interference order. When the effective index changes by dn r (which can be introduced by the change dn am of the ambient refractive index), there is a wavelength shift dk. From Eq. (1), one has dk ¼ dn r n r k: In our case, the calculation shows that the change dn r of the effective index is almost proportional to the changes dn am of the ambient refractive index (see Fig. 2 below), i.e., dn r Kdn am ; ð3þ where K is a constant depending on the waveguide structure. In this paper, we use a finite-difference method (FDM) mode solver to obtain the relationship between the effective index n r and the ambient index n am. From this relationship, one can easily obtain the constant K with a linearity fitting. Therefore, one has dn am ¼ 1 dk K k n r: ð4þ From this equation one sees that the sensitivity of a single ring is limited by the wavelength resolution and the constant K. In order to have a higher sensitivity, one should choose a waveguide with large K. On the other hand, people usually determine the measurement range for a single MRR according to the condition that its wavelength shift dk should be smaller than its free spectral range (FSR) Dk FSR, i.e., dk < Dk FSR ; ð5þ Input R 1 Ring #1 Ring #2 h co hco Si w s SiO 2 w co Si SiO 2 w co Si R 2 Output spectrum Fig. 1. (a) The schematic configuration of the present sensor, (b) the cross section of a nanoslot waveguide and (c) the cross section of a Si nanowire waveguide. ð2þ 156

160 Author's personal copy D. Dai, S. He / Optics Communications 279 (2007) where n r δ n r δ Dk FSR ¼ k=m 0 ¼ k=ðmn r =n r Þ¼ k2 ; ð6þ 2pRN r and where N r is the group index, and N r = n r k on r /ok. From Eqs. (2), (3) and (5), one has Dk FSR wco=320nm wco=300nm wco=280nm wco=260nm wco=240nm wco=220nm wco=220nm wco=800nm wco=700nm wco=600nm wco=550nm wco=500nm wco=450nm wco=400nm dn am < 1 n r : ð7þ K k One can rewrite it as follows: k dn am < dn amðmaxþ ¼ 2pRKðN r =n r Þ : When the effective index n r is sensitive to the change of the ambient refractive index, i.e., the ratio K is large, and consequently the measurement range dn am(max) become small. This indicates that a high sensitivity and a large measurement range can not be achieved in the same time for a single MRR. In this paper, we suggest and investigate theoretically a cascaded-mrr-based sensor, which includes two microrings (#1 and #2) with different radii (R 1,R 2 ) (see Fig. 1a). The two rings (#1 and #2) are based on nanoslot waveguides and Si nanowire waveguides, respectively. Fig. 1b and c show the cross sections of these two kinds of nanophotonic waveguides, respectively. Ring #1 has a high sensitivity on the changes of the ambient refractive index since most power is confined in the slot. When using Si nanowire waveguides, the bending radius R 2 can be smaller than R 1 and thus ring #2 has a larger FSR from Eq. (6). Ring #2 based on Si nanowires has a low sensitivity and a relatively large FSR, which gives a large measurement range. In this way, the present MRR-based sensor n am Fig. 2. The change of the effective index as the ambient refractive index increases for (a) nanoslot waveguides and (b) Si nanowire waveguides. n am has a high sensitivity (provided by ring #1) as well as a large measurement range (provided by ring #2). Here we make the drop waveguide perpendicular to the horizontal input bus waveguide, which is similar to the design of add-drop filter in [8]. In this way, two microrings are cascaded easily. Since no add-port is needed in our case, the crosses are avoided to eliminate the loss and crosstalk due to the cross (as shown in Fig. 1). In our case, one can immerse the two microrings in the target solution when measuring, e.g., a large volume of liquid. For a microanalysis (usually with a small measurement volume), one can inject the target chemical to the slot of the airslot waveguide and then measure the highly-sensitive wavelength shift of the corresponding drop channel. 3. Results and discussion For the Si nanowires and nanoslot waveguides used in this paper, we choose the thickness of the Si core layer h co = 300 nm and only consider the TE polarization. The refractive indices for the Si core and SiO 2 insulator layers are and 1.460, respectively. We use an FV-FDM [11] to calculate the effective index of Si nanowire waveguides and nanoslot waveguides with different core widths as the ambient refractive index dn am increases from 1.33 (the refractive index of water). Fig. 2a and b show the effective index change dn r due to the ambient change for nanoslot waveguides and Si nanowire waveguides, respectively. In Fig. 2a, we choose the nanoslot waveguide with a slot width w s = 100 nm as an example since the sensitivity dn r /dn am is not sensitive to the slot width. From Fig. 2a and b, one sees that the effective index n r increases almost linearly for both types of waveguides, i.e., the slope dn r / dn am is almost a constant. When the core width decreases, the field in the surrounding ambient medium becomes large and thus the sensitivity (i.e., the slope dn r /dn am ) increases. Fig. 3 shows the sensitivity dn r /dn am for two types of waveguides as the core width increases. From this figure, one sees that a nanoslot waveguide has a much higher sensitivity than a Si nanowire. For a nanoslot waveguide, the sensitivity can be as large as (close to 1) when the core width decreases to 200 nm. One can achieve a higher δn r/ δn am nanoslot waveguide Si nanowire The core width w co (nm) Fig. 3. The sensitivity dn r /dn am for two types of waveguides as the core width increases. 157

161 Author's personal copy 92 D. Dai, S. He / Optics Communications 279 (2007) sensitivity by choosing a smaller core width (e.g., 100 nm). However, the scattering loss and the bending loss (for a given bending radius) will then become larger. In this paper, we choose the following parameters for nanoslot waveguides: w s = 100 nm, w co = 200 nm, and the bending radius R 1 =5lm. From Fig. 3 one also sees that a Si nanowire waveguide is less sensitive than a nanoslot waveguide and the sensitivity (dn r /dn am ) degrades when the core width increases. For example, dn r /dn am = when w co = 500 nm. In the following design, we choose a Si nanowire waveguide with a core width of w co = 500 nm to make it singlemode and the bending radius R 2 =3lm. In order to achieve an effective coupling, we choose a small gap (w g = 100 nm) between the input-bus/drop waveguide and the ring and also choose a small core width (w co = 300 nm) for the input-bus/drop waveguide. In order to avoid a time-consuming three-dimensional (3D) FDTD simulation, we let a 3D optical waveguide structure be equivalent to a two-dimensional (2D) one by using an effective index method (EIM) [18] (an accurate calibration should be done in a real situation). The corresponding equivalent effective index for the TE polarization is about (which is slightly dependent of the ambient refractive index) at the central wavelength k = 1.55 lm. Fig. 4a and b show the spectral responses (obtained with 2D FDTD simulation) for a single microring based on nanoslot waveguides and Si nanowires, respectively, as the ambient refractive index increases. We choose the wavelength window ranging from 1540 nm to 1575 nm (which is a bit larger than the free spectral range of the Si-nanowire-based microring (#1)). From this simulation, one sees that the drop wavelength becomes longer when the ambient refractive index increases. Fig. 4c shows the wavelength shift as the ambient refractive index increases. For the microring based on nanoslot waveguides, the wavelength shift is more than 17 nm when the ambient refractive index varies from 1.33 to The ratio (sensitivity) dk/ dn am of the wavelength shift to the change of ambient refractive index is about nm. The minimal measurable change of the ambient refractive index depends on the resolution of the optical spectrum analyzer (OSA). For example, one can measure a refractive index change as small as when an OSA has a resolution of 0.01 nm. When the ambient refractive index increases from 1.33 to 1.39, the wavelength shift dk of the nanoslot-waveguide-based MRR is about 26.8 nm and the m-th drop wavelength is out of the range of nm. Therefore, in Fig. 4a one can only see the drop wavelength corresponding to the (m 1)-th order in the range from 1540 nm to 1575 nm. From this figure one sees clearly that the measurement range is limited by the FSR when only one MRR is used. The maximal measurement range of the single microring sensor based on nanoslot waveguides Power Power wavelength (nm) Wavelength (nm) 1 n am=1.33 n= n am=1.35 n= n am=1.37 n=1.37 n 0.4 am=1.39 n= Wavelength (nm) Ring #1: Δλ/ δn=444.5nm Ring #2: Δλ/ δn=59.2nm The ambient refractive index Fig. 4. (a) The spectral response of a single microring based on nanoslot waveguides for different ambient refractive indices, (b) the spectral response of a single microring based on Si nanowires for different ambient refractive indices and (c) the resonating wavelength as the ambient refractive index increases. a Power (a.u.) Power (a.u.) Power (a.u.) Power (a.u.) b c d #2: n-th #1: m-th Wavelength (nm) 1 #2: n-th #1: (m 1)-th Wavelength (nm) 1565 #1: 1570 m-th #2: n-th #1: m-th n=1.33 n am =1.35 n am =1.37 #1: (m 1)-th 1545 #2: n-th Wavelength (nm) n am = Wavelength (nm) Fig. 5. The spectral response of the designed cascaded-microrings for different ambient refractive indices (a) n am = 1.33, (b) n am = 1.35, (c) n am = 1.37 and (d) n am =

162 Author's personal copy D. Dai, S. He / Optics Communications 279 (2007) is about dn am = Fig. 4b shows that the sensitivity of the Si-nanowire-based microring (ring #2) is much lower (dk/dn am 59.2 nm). When the ambient refractive index increases from 1.33 to 1.39, the wavelength shift is only 3.55 nm. As mentioned before, the measurement range can be extended greatly by combining these two optimally designed rings (i.e., ring #1 and ring #2). For the present design, the measurable range can be as large as 0<dn am < Fig. 5a d shows the through spectral response of the designed cascaded-microring sensor (see Fig. 1a) for different ambient refractive indices. There are two or three drop wavelengths (k 1,k 2,k 3 ) corresponding to the cascaded two rings. Then one can determine the ambient refractive index n am from these drop wavelengths according to the calibration curves (which are similar to those shown in Fig. 4c). With the present designed cascaded-mrr sensor, we can obtain a large measurement range of 0 < dn am < 0.64 and a high sensitivity (the measurable index change can be as small as dn am = with an OSA of resolution 0.01 nm). 4. Conclusion In this paper, we have suggested and investigated theoretically a design of a highly-sensitive sensor with a large measurement range by cascading two microring resonators (MRR) based on nanoslot waveguides and Si nanowires. By using a nanoslot waveguide with a core width of 200 nm, we have obtained a highly-sensitive MRR which can measure a very small index change of with an OSA of resolution 0.01 nm. Meanwhile, for the Si-nanowires-based MRR, we have chosen a large core width (w co = 500 nm) to extend the measurement range to 0<dn am < 0.64 (though its sensitivity is very low, dk/ dn am =59.2 nm). For the cascaded-mrrs, we have used two drop waveguides (perpendicular to the horizontal input bus waveguide) to remove the crosses (and avoid the associated access losses and crosstalks). With a similar idea, one can also use an array of MRRs and measure the wavelength shifts in the corresponding drop channels for the application of multi-channel bio/chemical sensors. Acknowledgements This project was supported by research Grants (Nos , R104154) of the provincial government of Zhejiang Province of China, the National Science Foundation of China (Nos and ). References [1] J.G. Hong, J.S. Choi, G.Y. Han, J.K. Kang, C.M. Kim, T.S. Kim, D.S. Yoon, Analytica Chimica Acta 573 (2006) 97. [2] A. Densmore, D.-X. Xu, P. Waldron, S. Janz, P. Cheben, J. Lapointe, A. Delâge, B. Lamontagne, J.H. Schmid, E. Post, IEEE Photonics Technology Letters 18 (23) (2006) [3] J. Homola, S.S. Yee, G. Gauglitz, Sensors and Actuators B Chemical 54 (1-2) (1999) 3. [4] Sang-Yeon Cho, Nan Marie Jokerst, IEEE Photonics Technology Letters 18 (20) (2006) [5] Chung-Yen Chao, L. Jay Guoa, Applied Physics Letters 83 (8) (2003) 159. [6] Steve Blair, Yan Chen, Applied Optics 40 (4) (2001) 570. [7] Robert W. Boyd, John E. Heebner, Applied Optics 40 (31) (2001) [8] Y. Kokubun, Y. Hatakeyama, M. Ogata, S. Suzuki, N. Zaizen, IEEE Journal of Selected Topics in Quantum Electronics 11 (1) (2005) 4. [9] Kostadin Djordjev, Seung-June Choi, Sang-Jun Choi, P.D. Dapkus, IEEE Photonics Technology Letters 14 (6) (2002) 828. [10] Steve Blair, Yan Chen, Applied Optics 40 (4) (2001) 570. [11] Daoxin Dai, Yaocheng Shi, Sailing He, Applied Optics 45 (20) (2006) [12] Wim Bogaerts, Pieter Dumon, Patrick Jaenen, Johan Wouters, Stephan Beckx, Vincent, Wiaux, Dries Van Thourhout, Dirk Taillaert, Bert Luyssaert, Roel Baets, Proceedings of SPIE, 5956 (2005) 59560R. [13] Daoxin Dai, Liu Liu, Lech Wosinski, Sailing He, Electronics Letters 42 (7) (2006) 400. [14] A. Densmore, D.-X. Xu, P. Waldron, S. Janz, P. Cheben, J. Lapointe, A. Delâge, B. Lamontagne, J.H. Schmid, E. Post, IEEE Photonics Technology Letters 18 (23) (2006) [15] F. Prieto1, B. Sepulveda1, A. Calle1, A. Llobera, C. Domınguez, A. Abad, A. Montoya, L.M. Lechuga1, Nanotechnology 14 (2003) 907. [16] Q.F. Xu, V.R. Almeida, R.R. Panepucci, M. Lipson, Optics Letters 29 (14) (2004) [17] Q.F. Xu, S. Sandhu, M.L. Povinelli, J. Shakya, S.H. Fan, M. Lipson, Physical Review Letters 96 (12) (2006). Art. No [18] Yaocheng Shi, Daoxin Dai, Sailing He, IEEE Photonics Technology Letters 18 (21) (2006)

163 D. Dai and S. He Vol. 26, No. 3/March 2009/J. Opt. Soc. Am. B 511 Highly sensitive sensor based on an ultra-high-q Mach Zehnder interferometer-coupled microring Daoxin Dai* and Sailing He Centre for Optical and Electromagnetic Research, State Key Laboratory for Modern Optical Instrumentation, Zhejiang University, Hangzhou, China *Corresponding author: dxdai@zju.edu.cn Received October 2, 2008; revised December 18, 2008; accepted January 4, 2009; posted January 13, 2009 (Doc. ID ); published February 23, 2009 A high-q Mach Zehnder interferometer (MZI)-coupled microring is presented for optical sensing with high sensitivity and a large measurement range. By optimizing the length difference between the two arms of the MZI coupler, the MZI-coupled microring with a high-q factor and high extinction ratio is obtained. In the present example, the Q factor of the designed silicon-nanowire-based microring is as high as when the silicon nanowire has a propagation loss L=2 db/ cm. Due to this high-q factor, the sensitivity for the change n of the effective refractive index is about by measuring the shift of the resonant wavelength. Because of the wavelength dependence of the coupling ratio of the MZI coupler, it is possible to have only one resonant wavelength with a high extinction ratio in a very large wavelength span [i.e., the quasi-free spectral range of the MZI-coupler microring], which offers a very large measurement range covering the refractive index change of gas/liquid samples (e.g., 0 n 0.48 in the present example) Optical Society of America OCIS codes: , INTRODUCTION Recently the demands of low-cost, high sensitive, and ultracompact sensors have increased rapidly in various areas, such as biological, environmental, and chemical detections [1 7]. People have developed various integrated optical sensors based on different structures and mechanisms, e.g., Mach Zehnder interferometers (MZIs) [1], surface plasmon sensors [2], microcavities [3 7], etc. Among them, a high-q optical microcavity (including microring/microdisk [3 7]) is becoming one of the most attractive candidates because of its ultracompact size, high sensitivity, and easy fabrication and realization of a sensor array. For a microring sensor, when the concentration of the target material covering on the surface changes, the effective refractive index of the microring waveguide will change and consequently the resonant wavelength of the microring will shift. By measuring the shift of the resonated wavelength or the intensity variation for a fixed wavelength [5], one obtains the change of the refractive index (or the concentration). To have high sensitivity, it is desirable to achieve a microring with a high-q factor by minimizing the intrinsic loss and choosing a small coupling coefficient [8]. The intrinsic loss of a microring includes the propagation loss of the optical waveguides and the bending loss. The propagation loss mainly results from the scattering loss due to the surface roughness of the optical waveguide. Fortunately, various low-loss optical waveguides have been developed. For example, even for silicon-oninsulator (SOI) nanowires, which are popular for realizing ultrasmall photonic integrated devices [8 11], a low propagation loss (e.g., 2 db/cm [9]) has been obtained by reducing the roughness through the postfabrication processes (e.g., thermal-oxidation). To achieve a low bending loss, one of the simplest ways is to choose a large bending radius. Increasing the cavity length is also helpful to have a high-q value [10]. However, a long cavity length will reduce the free spectral range (FSR) of the microring and limits the measurement range for a conventional microring sensor [11]. Besides, in order to achieve a high-q factor, one also needs to design the coupler to have a small coupling coefficient between the microring and the access optical waveguides. One usually uses a multimode interference (MMI) coupler or directional coupler. When using MMI couplers, the coupling ratio is fixed to several specific values (e.g., 50%:50% or 15%:85%), which is suitable for a low-/moderate-q factor [12]. When using directional couplers, one could obtain a flexible coupling ratio by controlling the gap width between the microring and the access optical waveguides. However, the coupling ratio is very sensitive to the gap width and thus one has to precisely control the fabrication process. Another alternative way is using an MZI coupler for the microring, which has been used previously for thermo-optic switching [13], reconfigurable silicon microring resonator-based filter [14]. In this paper, we use an MZI-coupled microring for optical sensing to achieve high sensitivity as well as a large measurement range. To our knowledge, it is the first time to present the use of MZIcoupled microrings for optical sensing. For an MZIcoupled microring, the coupling ratio could be controlled by adjusting the length difference between the two arms of the MZI coupler. By choosing the interference order of the MZI coupler, it is also possible to have only one reso /09/ /$ Optical Society of America 160

164 512 J. Opt. Soc. Am. B/Vol. 26, No. 3/March 2009 D. Dai and S. He nant wavelength with a high extinction ratio in a very large wavelength span (i.e., the quasi-fsr of the MZIcoupler microring), which offers a very large measurement range covering the refractive index change of gases or liquids. 2. STRUCTURE AND THEORY Figure 1 shows the present MZI-coupled microring, which includes a microring and a feedback line. The feedback line is one of the arms of the MZI coupler and the other arm is formed by part of the microring. To analyze the spectrum of this device, we use the transfer matrix method (TMM) [5,15] and obtain the formula for the transmission spectrum at port 4. This transmission at port 4 is given by P= E 4 /E 1 2, where E 4 = k 14 + k 1 4k 4 1 k 14 E 1 1 k 4 1 k 1 4, 1 in which k pq is the coupling ratio relating the electric fields E p,e q at ports p and q, and one has k pq = k pq exp j pq, where pq is the phase delay from port p to port q. For the part of the MZI coupler, the coupling ratios k 14, k 14, k 1 4, and k 1 4 are relating the electric fields at ports 1, 1, 4, and 4 as follows: E 4 E 4 = k 14 k 1 4 k 14 k 1 4 E 1 E 1, where the coupling ratios are given as in which and k 14 = k 12 k 23 k 34 + k 12 k 2 3 k 3 4, k 14 = k 12 k 23 k 34 + k 12 k 2 3 k 3 4, k 1 4 = k 1 2k 23 k 34 + k 1 2 k 2 3 k 3 4, k 1 4 = k 1 2k 23 k 34 + k 1 2 k 2 3 k 3 4, k 12 k 1 2 k 12 k 1 2 k 34 k 3 4 k 34 k K = j K j K 1 K, 1 K = j K j K k 23 = 23 exp j l 23, 1 K, k 2 3 = 2 3 exp j l 2 3. Here is the propagation constant, l 23 and l 2 3 are the lengths of the waveguide section, and K is the power coupling ratio. Therefore, one has k 14 = 1 K 23 exp j l 23 1 K 2 K exp j l 2 3, k 14 = 23 exp j l j K 1 K exp j l 2 3, k 1 4 = 23 exp j l j K 1 K exp j l 2 3, k 1 4 = K 23 exp j l K 2 1 K exp j l 2 3, where l 23 is the length difference between the two arms of the MZI coupler, l 23 =l 23 l 2 3. Usually one can choose a 3 db coupler for the MZI (i.e., K=0.5) and such 3 db couplers could be realized by using a directional coupler or 2 2 MMI coupler [12]. It is well-known that for either directional couplers or MMI couplers, the power coupling ratio K is actually wavelength dependent. In our simulation below the wavelength dependence of K will be included. For a microring resonator (MRR), there are a series of resonant wavelengths MRR corresponding to different orders. As we know, the coupling ratio of an MZI coupler is also wavelength-dependent. This indicates that one will have different coupling ratios for different resonant wavelengths MRR. For any given wavelength, the coupling ratio k 14 of the MZI coupler could be modified in a large range by adjusting the length difference l 23 between its two arms. To achieve a high-q factor we should choose the length difference l 23 to have a large k 14 (i.e., a small coupling coefficient k 14 ) for the considered resonant wavelength MRR0 of the microring. Considering the path from port 1 to port 4, the central wavelength MZI of the MZI coupler for a maximal coupling ratio k 14 is given by the following equation: 2 1 n l 23 = m MZI +1/2 MZI, 2 feedback line l Fig. 1. (Color online) Schematic of the present MZI-coupler microring. l 4 1 where n is the effective index of the MZI arms and m MZI is the interference order. When the central wavelength MZI of the MZI coupler is identical with the resonant wavelength MRR0 of the microring, one has k 14 =1 and a 100% transmission from port 4, i.e., there is no dip at this resonant wavelength. Therefore, in order to have a dip to label the resonant wavelength MRR0, one should introduce a slight deviation between the two wavelengths MZI and MRR0. In this case, the coupling coefficient k 14 is slightly 161

165 D. Dai and S. He Vol. 26, No. 3/March 2009/J. Opt. Soc. Am. B 513 smaller than 100% and consequently a high-q is achieved, i.e., n L 23 = m MZI +1/2 MZI = m MZI +1/2+ MRR0, where is a small fraction. On the other hand, in order to achieve a high extinction ratio, one should have a critical coupling by matching the coupling ratio k 14 and the loss in the microring. In this paper, in order to achieve the critical coupling for the considered resonant wavelength MRR0, we adjust the coupling ratio by optimizing the small fraction in Eq. (3). Since the microring loss is usually very small, the corresponding critical coupling ratio k 14 c should be very close to 1 and the two wavelengths ( MZI and MRR0 ) are different slightly. For the other resonant wavelength except the considered one MRR0, the extinction ratio is usually low because there is no critical coupling ratio. In this way, there is only one resonant wavelength MRR0 with high extinction ratio in a very broad band. When the refractive index of the ambient material on the surface of the sensing area (covering the whole MZIcoupled microring) changes, both the central wavelength MZI of the MZI coupler and the resonant wavelength MRR0 of the microring change with the same wavelength shift = n/n (where n is the change of the effective index of the optical waveguide), i.e., MRR0 = MRR0 + and MZI = MZI +. Therefore, even when the ambient refractive index changes, the coupling coefficient k 14 is almost unchanged and consequently the critical coupling for a high extinction ratio is still available for the shifted resonant wavelength MRR0. Since only the resonant wavelength MRR0 has a high extinction ratio in a very broad band, one can measure the ambient refractive index varying in a large range by measuring the shift of the resonant wavelength MRR0 with a high extinction ratio RESULTS AND DISCUSSIONS In the following part we give a design with the present MZI-coupled microring based on a popular SOI wafer with a 260 nm Si layer n Si =3.445 ona2 m SiO 2 insulator layer n SiO2 = The core width is w co =500 nm and the central wavelength is around 1550 nm. Here we consider the TM polarization, which is preferred for high sensitivity on the change of the ambient refractive index [1]. The effective refractive index is n= and the group index n g is given by n g =n D c, where c is the central wavelength and the dispersion coefficient D = m 1. For the microring, we choose the order m=40 at the central wavelength c of 1550 nm (the resonant wavelength MRR0 is close to c ) and the corresponding bending radius R is about m (with a very low bending loss). First we consider the case with a very small length difference l 23 by choosing m MZI =0 and consequently one has L 23 = 1/2+ MRR0 /n. In this case, due to the small l 23, one should use an MZI with two almost symmetrical arms (different from that shown in Fig. 1) for the practical layout design, and the cavity is similar to a race-track (instead of a standard microring). Here the directional coupler used for the MZI is designed to have a powersplitting ratio of 50:50 (i.e., K=0.5) at the central wavelength c, and the wavelength-dependent power coupling ratio K is achieved by using a beam propagation method (BPM) simulation. In the following calculation, the wavelength dependence of K is included. Our calculation shows that the power coupling ratio K ranges from 0.15 to 0.89 when the wavelength increases from 1.4 to 1.7 m. Figure. 2(a) shows the spectral responses in a small L=0.1dB/cm L=1dB/cm L=2dB/cm (a) wavelength (nm) E 4 /E 1 2 Q (b) Extinction ratio (db) (c) ' MRR0 (nm) = E+07 1.E+06 1.E =0.003 =0.005 =0.007 =0.009 =0.011 =0.013 =0.015 =0.017 L=0.1dB/cm L=1.0dB/cm L=2.0dB/cm L=1.0dB/cm L=0.1dB/cm L=2.0dB/cm L=0.1dB/cm L=1.0dB/cm L=2.0dB/cm (d) Fig. 2. (Color online) Features for the present MZI-coupled microring with m MZI =0 as varies. (a) Transmission spectrum. The curves with difference resonant dips are for the cases of =0.001,0.003,...,0.017 and the dashed curves mark the positions of the resonant wavelengths. (b) Q factor. (c) Extinction ratio. (d) Resonant wavelength MRR0. In these figures, the labels of diamond ( ), square ( ), and triangle ( ) are for the cases of L =0.1, 1.0, and 2.0 db/ cm, respectively. 162

166 514 J. Opt. Soc. Am. B/Vol. 26, No. 3/March 2009 D. Dai and S. He wavelength range around the resonant wavelength MRR0 when choosing different values for. The dashed curves give the mark for the positions of the resonant wavelengths for all the cases with =0.001,0.003,..., Here we consider three cases of L=0.1, 1.0, and 2.0 db/cm (where L is the intrinsic loss of the microring waveguide). For the case with a smaller loss, the spectral response has smaller bandwidth (i.e., a higher Q). On the other hand, when increases, the central wavelength MZI of the MZI coupler deviates more from the resonant wavelength MRR0 and thus the coupling ratio k 14 becomes smaller. Therefore, the Q factor deceases as increases. For the highly sensitive optical sensing, the high-q could be obtained by reducing the intrinsic loss and choosing a small for a large coupling ratio k 14 as shown in Fig. 2(b). For example, for the cases with a low loss of 0.1 db/cm and a moderate low of 1 db/cm, the Q factors are, respectively, as high as and by choosing small. From Fig. 2(a), one also sees that when the length difference L 23 = 1/2+ MRR0 /n is tuning, the extinction ratio varies and the resonant wavelength slightly shifts. Figure 2(c) shows the extinction ratio as varies. Figure 2(c) shows that one obtains a specific value 0 that gives the critical coupling ratio for a high extinction ratio. For the cases of L=0.1, 1.0, and 2.0 db/cm, the specific values of 0 are , 0.009, and , respectively. When increases, the phase delay of the MZI coupler increases, which indicates the effective cavity length of the microring increases. Therefore, the resonant wavelength shifts linearly as varies as shown in Fig. 2(d). From the above analysis, we consider the design of the MZI coupler with the specific value 0 for a high extinction ratio, i.e., 0 = , , and for the cases of L=0.1, 1.0, and 2.0 db/ cm, respectively. Figures 3(a) 3(c) shows the transmission spectrum in a very broad band of [1400, 1700 nm] for these three cases. The coupling ratios k 14 of the MZI coupler with the corresponding 0 are also shown in Fig. 3 Since the coupling ratio k 14 is wavelength-dependent, the extinction ratios at different resonant wavelengths MRR are very different as 10log10 E4/E1 2 1.E+00 1.E (a) L=0.1dB/cm 1.E E E-03 1.E E E-03 1.E-06 (b) L=1.0dB/cm (c) L=2.0dB/cm Wavelength(nm) Fig. 3. (Color online) Transmission spectrum for the present MZI-coupled microring with m MZI =0. (a) L=0.1, (b) L=1.0, and (c) L=2.0 db/cm. Here the bold curves are for the coupling ratios k 14 and the fine lines are for 10 log 10 E 4 /E 1 2. k14 mentioned above. There is a high extinction ratio at the considered resonant wavelength MRR0. When the wavelength deviates from the central wavelength MZI, the coupling ratio decreases and the extinction ratios for the other resonant wavelengths MRR become small. For the case of L=0.1 db/cm, one has only one resonant wavelength MRR0 with a high extinction ratio in the broad band of [1400, 1700 nm]. For the cases with larger losses (e.g., L=1, 2 db/cm), one observes that there are several other resonant wavelengths with relatively high extinction ratios. For example, the cases with L=2 db/cm, one has high extinction ratios of 33.5 db (at nm) and 49.8 db (at nm, which is the considered resonant wavelength). Fortunately the resonant wavelength MRR0 could still be distinguished from other resonant wavelengths when it is shifting with the change of the ambient refractive index. Therefore, when using the present microring for measuring the change of the ambient refractive index, one has a highly sensitivity and large measurement range by measuring the shift of the wavelength MRR0. On the other hand, if it is needed to depress the resonant wavelengths except MRR0, one could choose another interference order m MZI for the MZI coupler. For a different m MZI, one will have different special values 0 for achieving a critical coupling ratio as shown in Fig. 4. From Fig. 4, one sees that the special values 0 increase slightly as the interference order m MZI increases. Here we consider the case of L=2 db/ cm. Figure 5 shows the transmission spectrum for the MZI-coupled microring with different interference orders m MZI (also with the corresponding specific values 0 ). The dashed curves show the wavelength dependence of the coupling ratio k 14. Due to the wavelength dependence of the power coupling ratio K, the powers at the two MZI arms is inbalance. Therefore, the coupling ratio k 14 will not be zero for the wavelengths at which there is a phase-difference between two arms. On the other hand, even though K is wavelength-dependent, we could still have a high coupling ratio k 14 (close to 1.0) at the central wavelength c and thus a high-q and a high extinction ratio could be achieved [see Figs. 5(a) 5(h)]. From Figs. 5(a) 5(h), one sees that the resonant wavelengths (except MRR0 ) are depressed greatly when choosing a larger interference order m MZI. For example, when m MZI =2 or 3, only the desirable resonant wavelength MRR0 has a high extinction ratio [see Figs. 5(c) and 5(d)]. When the order m MZI increases further, the FSR of the MZI coupler decreases and conse L=2.0dB/cm L=1.0dB/cm L=0.1dB/cm m MZI Fig. 4. (Color online) Special values 0 for the cases with different orders m MZI. 163

167 D. Dai and S. He Vol. 26, No. 3/March 2009/J. Opt. Soc. Am. B Power (a) (b) (c) (d) (e) (f) (g) (h) Wavelength(μm) Fig. 5. (Color online) When L=2 db/ cm, the transmission spectrum for the present MZI-coupled microring with (a) m MZI =0, (b) m MZI =1, (c) m MZI =2, (d) m MZI =3, (e) m MZI =4, (f) m MZI =5, (g) m MZI =6, and (h) m MZI =7. Here the dashed curves are for the power coupling ratios k 14 and the solid curves are for E 4 /E 1 2. E 4 / E 1 2 (a) Power Resonant wavelength ' MRR0 (nm) n=0 n=10-6 n= Wavelength (nm) n=0.0 n=0.1 / n=372.5 nm/riu n Fig. 7. (Color online) Resonant wavelength MRR0 as the effective refractive index changes. quently the coupling ratio k 14 has more than one peak in the considered band of [1400, 1700 nm]. Usually in the neighbor region around each peak of k 14, one may have a resonant wavelength with relatively high extinction ratios [see Figs. 5(e) 5(h)]. The wavelength difference between the two adjacent resonant wavelengths with high extinction ratios is defined as the quasi-fsr for the MZIcoupled microring. Therefore, when choosing a large order, the quasi-fsr of the microring decreases (which is determined by the MZI coupler). One can choose an appropriate interference order m MZI to have a very large FSR that provides a large measurement range for optical sensing. For example, we choose m MZI =3 and its corresponding value of 0 = in the following calculation. When the effective index of the optical waveguide changes, the resonant wavelength of the MZI-coupled microring will shift almost linearly. Figure 6(a) shows the spectrum in a small wavelength range when the effective index changes slightly. From Fig. 6, one sees that the shape of the spectrum is almost unchanged when the refractive index changes. An effective index change of n =10 5 introduces a wavelength shift of about 3.73 pm. It is easy to observe such a wavelength shift because of the high-q factor For a smaller change of effective index, e.g., 10 6, the wavelength shift is very small (only about 0.37 pm), which could be measured by using a system with a tunable laser and a photodetector [7]. In Fig. 6(b), we present the calculated spectrums when the effective index has a large change n=0.1,0.2,0.3. From the spectrums, one sees that the quasi-fsr of the present MZI-coupled microring is about nm [see Fig. 6(b)], which is more than ten times the FSR 16.6 nm of the simple microring with a bending radius of about 5 m. Figure 7 shows the resonant wavelength as the refractive index change increases. One sees that the slope / n is about nm/riu (refractive index unit). When n=0.3, the wavelength shift is about 111 nm (still smaller than the quasi-fsr). The large quasi-fsr of the MZI-coupled microring offers a very large measurement range of 0 n 0.48, which covers the refractive index change of gases or liquids. Furthermore, even when the effective index changes greatly n=0.3, the shape of the spectrum is almost the same (e.g., with a high extinction ratio, a high-q, etc). This is helpful for sensing the large changes of the refractive index. 4. CONCLUSION In summary, we have presented an MZI-coupled microring for realizing optical sensing with high sensitivity and a large measurement range. Through TMM calculations, we have given a detailed analysis for the transmission of the present MZI-coupled microring. By optimizing the length difference between the two arms of the MZI coupler, we have obtained the optimal design for the microring with a high-q factor and a high extinction ratio. For the case of L=2 db/ cm, the Q factor is as high as , which is similar to the Q value in [10]. Consequently, the sensitivity of the present MZI-coupled microring is also as high as that of the previous high-q MRR-based sensors. The sensitivity / n (the ratio of n= n= n= k 14 E 4 / E n= FSR=180.35nm 0 n= (b) Wavelength (nm) Fig. 6. (Color online) Spectrum for the case of m MZI =3 and 0 = when (a) there is a small change of the effective refractive index and (b) there is a large change of the effective refractive index. Here the dashed curves are for the coupling ratios k 14 and the solid curves are for E 4 /E

168 516 J. Opt. Soc. Am. B/Vol. 26, No. 3/March 2009 D. Dai and S. He the resonant wavelength shift to the change of the effective refractive index) is about nm/riu. A very small refractive index change of 10 6 introduces a wavelength shift of about 0.37 pm. The simulation results have also shown that it is important to carefully control the length difference l 23. An effective way is to use the thermo-optical effect for compensation or tuning this length difference [8]. Since the coupling ratio of the MZI coupler is wavelength-dependent, one can greatly depress the dips at the resonant wavelengths except the considered one MRR0 by appropriately choosing the interference order of the MZI coupler. In this way, there is only one resonant wavelength MRR0 with a high extinction ratio in a very high wavelength span (i.e., the quasi-fsr of the MZI-coupler microring). For example, when choosing m MZI =3, the quasi-fsr is as large as 180 nm, which is more than 360 times the FSR 0.5 nm of the spiral-ring shown in [10]. Such a large quasi-fsr of the MZI-coupled microring offers a very large measurement range of 0 n 0.48, which covers the refractive index change of gases or liquids. ACKNOWLEDGMENTS This project was partially supported by Zhejiang Provincial Natural Science Foundation of China (J ), and the National Natural Science Foundation of China (NSFC) ( ). REFERENCES 1. A. Densmore, D.-X. Xu, P. Waldron, S. Janz, P. Cheben, J. Lapointe, A. Delâge, B. Lamontagne, J. H. Schmid, and E. Post, A silicon-on-insulator photonic wire based evanescent field sensor, IEEE Photon. Technol. Lett. 18, (2006). 2. G. Nemova and R. Kashyap, Theoretical model of a planar integrated refractive index sensor based on surface plasmon-polariton excitation with a long period grating, J. Opt. Soc. Am. B 24, 2696 (2007). 3. S. Cho and N. M. Jokerst, A polymer microdisk photonic sensor integrated onto silicon, IEEE Photon. Technol. Lett. 18, (2006). 4. R. W. Boyd and J. E. Heebner, Sensitive disk resonator photonic biosensor, Appl. Opt. 40, (2001). 5. C.-Y. Chao and L. J. Guoa, Biochemical sensors based on polymer microrings with sharp asymmetrical resonance, Appl. Phys. Lett. 83, (2003). 6. A. M. Armani and K. J. Vahala, Heavy water detection using ultra-high-q microcavities, Opt. Lett. 31, (2006). 7. A. M. Armani, R. P. Kulkarni, S. E. Fraser, R. C. Flagan, and K. J. Vahala, Label-free, single-molecule detection with optical microcavities, Science 317, (2007). 8. L. Chen, N. Sherwood-Droz, and M. Lipson, Compact bandwidth-tunable microring resonators, Opt. Lett. 32, (2007). 9. F. Xia, L. Sekaric, and Y. Vlasov, Ultracompact optical buffers on a silicon chip, Nat. Photonics 1, (2007). 10. D.-X. Xu, A. Densmore, A. Delâge, P. Waldron, R. McKinnon, S. Janz, J. Lapointe, G. Lopinski, T. Mischki, E. Post, P. Cheben, and J. H. Schmid, Folded cavity SOI microring sensors for high sensitivity and real time measurement of biomolecular binding, Opt. Express 16, (2008). 11. D. Dai and S. He, Highly sensitive sensor with large measurement range realized with two cascaded microring resonators, Opt. Commun. 279, (2007). 12. D.-X. Xu, A. Densmore, P. Waldron, J. Lapointe, E. Post, A. Delâge, S. Janz, P. Cheben, J. H. Schmid, and B. Lamontagne, High bandwidth SOI photonic wire ring resonators using MMI couplers, Opt. Express 15, (2007). 13. W. M. J. Green, R. K. Lee, G. A. DeRose, A. Scherer, and A. Yariv, Hybrid InGaAsP-InP Mach Zehnder racetrack resonator for thermooptic switching and coupling control, Opt. Express 13, (2005). 14. L. Zhou and A. W. Poon, Electrically reconfigurable silicon microring resonator-based filter with waveguide-coupled feedback, Opt. Express 15, (2007). 15. S. Darmawan and M. K. Chin, Critical coupling, oscillation, reflection, and transmission in optical waveguide-ring resonator systems, J. Opt. Soc. Am. B 23, (2006). 165

169 Highly sensitive digital optical sensor based on cascaded high-q ring-resonators Daoxin Dai* Centre for Optical and Electromagnetic Research, State Key Laboratory for Modern Optical Instrumentation, East Building No.5, Zijingang Campus, Zhejiang University, Hangzhou , China Abstract: A digital optical sensor based on two cascaded rings with different free spectral ranges (FSRs) is proposed. Because of their different FSRs, the major peak of the spectral response from the output port shifts digitally when the effective refractive index of ring #1 changes. And the shift of the major peak is equal to multiple FSRs of ring #2. Since it is easy to design a ring with a FSR of nanometers, the present digital optical sensor shows an ultra-high sensitivity (at the order of 10 5 nm/riu) which is over two orders higher than that of a regular single-ring sensor. By using the present digital optical sensor, it becomes convenient to use an integrated optical micro-spectrometer (even with a low resolution) to monitor the peak shift of the spectral response. Therefore, it is promising to realize a low-cost and portable highly-sensitive optical sensor system on a single chip Optical Society of America OCIS codes: ( ) Integrated optics devices; ( ) Sensors. References and links 1. A. Densmore, D.-X. Xu, P. Waldron, S. Janz, P. Cheben, J. Lapointe, A. Delge, B. Lamontagne, J. H. Schmid, and E. Post, A silicon-on-insulator photonic wire based evanescent field sensor, IEEE Photon. Technol. Lett. 18(23), (2006). 2. G. Nemova, and R. Kashyap, Theoretical model of a planar integrated refractive index sensor based on surface plasmon-polariton excitation with a long period grating, J. Opt. Soc. Am. B 24(10), 2696 (2007). 3. S.-Y. Cho, and N. M. Jokerst, A polymer microdisk photonic sensor integrated onto silicon, IEEE Photon. Technol. Lett. 18(20), (2006). 4. C.-Y. Chao, and L. J. Guo, Biochemical sensors based on polymer microrings with sharp asymmetrical resonance, Appl. Phys. Lett. 83(8), 1527 (2003). 5. Q. F. Xu, V. R. Almeida, R. R. Panepucci, and M. Lipson, Experimental demonstration of guiding and confining light in nanometer-size low-refractive-index material, Opt. Lett. 29(14), (2004). 6. D.-X. Xu, A. Densmore, A. Delâge, P. Waldron, R. McKinnon, S. Janz, J. Lapointe, G. Lopinski, T. Mischki, E. Post, P. Cheben, and J. H. Schmid, Folded cavity SOI microring sensors for high sensitivity and real time measurement of biomolecular binding, Opt. Express 16(19), (2008). 7. A. M. Armani, R. P. Kulkarni, S. E. Fraser, R. C. Flagan, and K. J. Vahala, Label-free, single-molecule detection with optical microcavities, Science 317(5839), (2007). 8. P. Rabiei, and W. H. Steier, Tunable polymer double micro-ring filters, IEEE Photon. Technol. Lett. 15(9), (2003). 9. B. Liu, A. Shakouri, and J. E. Bowers, Wide tunable double ring resonator coupled lasers, IEEE Photon. Technol. Lett. 14(5), (2002). 10. P. Cheben, J. H. Schmid, A. Delâge, A. Densmore, S. Janz, B. Lamontagne, J. Lapointe, E. Post, P. Waldron, and D.-X. Xu, A high-resolution silicon-on-insulator arrayed waveguide grating microspectrometer with submicrometer aperture waveguides, Opt. Express 15(5), (2007). 1. Introduction Recently the demands of low-cost, highly sensitive and ultra-compact optical sensors increase rapidly for many areas such as biological, environmental and chemical detections [1 7]. People have developed various integrated optical sensors based on different structures and mechanisms, e.g., Mach-Zehnder interferometers (MZI) [1], surface plasmon sensors [2], microcavities [3 7], etc. Among them, a high-q optical microcavity (including microring/microdisk [3 7]) is becoming one of the most attractive candidates because of the ultra-compact size, high-sensitivity, and easy realization of a sensor array. # $15.00 USD Received 18 Nov 2009; revised 29 Nov 2009; accepted 8 Dec 2009; published 11 Dec

170 For a microring sensor, when the concentration of the target material covering on the surface changes, the effective refractive index of the microring waveguide will change and consequently the resonant wavelength of the microring will shift. In order to monitor the change of the refractive index (or the concentration), one simple way for sensing is to measure the intensity change for a fixed wavelength. In this way, it is possible to have a high detect limit by using a high-q ring resonator, which is usually obtained by minimizing the intrinsic loss and choosing a small coupling coefficient. However, the measurement range is very small because the response approaches zeros very fast as the index-changes. An alternative way for sensing is to measure the shift of the resonance wavelength [4]. In order to measure a small wavelength shift, a regular way is using the combination of a photodetector and a high-precision tunable laser, which is usually very expensive. It is possible to reduce the cost by using a low-cost DFB telecom laser that can be tuned with high resolution using the gain input. However, the tunability range is limited usually. An alternative way to measure the spectral response is using an optical spectrum analyzer (OSA) with a very high resolution. For example, in order to monitor a small refractive index-change of , the OSA should have a resolution as high as about 5 pm. Currently it is still not easy to achieve such a highsolution OSA. Besides, a high-solution OSA is very expensive and cumbersome. It is not convenient for the situation when a low-cost and portable highly-sensitive optical sensing system is required. In this paper, we propose a digital optical sensor based on two cascaded rings with different free spectral ranges (FSRs). One of the two rings is covered by an up-cladding, and the up-cladding on the other ring is removed to form a sample reservoir. Due to their different FSRs, the output port will have a spectral response with a major peak and some minor peaks. When the refractive index increases, the major peak shifts discretely (or digitally) and the shift of the major peak is equal to multiple FSRs of the ring with the up-cladding. This is socalled vernier effect, which has been used for realizing tunable filter [8], lasers [9], etc. In this way, we could have an optical sensing with an ultra-high sensitivity which is many times higher than that of a single-ring sensor. Furthermore, since the FSR is usually at the order of nanometer, the present digital optical sensor makes it convenient to use an integrated-type optical micro-spectrometer (even with a low resolution at the order of nm) to monitor the major-peak shift of the spectral response. For example, one could use the micro-spectrometer based on an arrayed-waveguide grating (AWG) [10] combining with a photodetector array. Therefore, it becomes promising to realize a low-cost and portable optical sensor system with a highly-sensitivity on a single chip. 2. Structure and principle Figure 1 shows the schematic configuration of the present digital optical sensor, which includes two cascaded rings, i.e., ring #1 and ring #2. These two rings have a common bus waveguide, which cascades these two rings. These two rings have different FSRs, which could be realized by choosing different radii (R 1 and R 2 ) for ring #1 and ring #2. In the present optical sensor, we choose R 1 <R 2 and consequently one has FSR1 > FSR2. Because of their different FSRs, the output port will have a spectral response with major peaks locating at the common resonant wavelengths of these two cascaded rings. The whole structure is covered by using an up-cladding except the region of ring #2, where the up-cladding is removed to form a sample reservoir. When the refractive index of the sample in the reservoir changes, the resonant wavelength of ring #2 changes accordingly, i.e., 2 = 2 ( n eff /n eff ), where n eff is the effective index of the fundamental modes in ring #2, n eff is the change of the effective index n eff, 2 is the shift of the resonant wavelength 2 correspondingly. Because ring #1 is covered by the up-cladding, the resonant wavelengths are unchanged. In order to describe the principle of the present digital optical sensor, we show the frequency responses of ring #1 and ring #2 in Fig. 2(a) and 2(b), respectively. Both ring #1 and ring #2 have a series of resonant wavelengths 1(i) and 2(j). When the i-th resonance wavelength 1(i) of ring #1 is coincided with the j-th resonance wavelength 2(i) of ring #2, one # $15.00 USD Received 18 Nov 2009; revised 29 Nov 2009; accepted 8 Dec 2009; published 11 Dec

171 has a common resonance wavelength c(i) as shown in Fig. 2(c). At these common resonance wavelengths c(i), one has a major peak which has a maximal amplitude. And the separation between the adjacent common resonance wavelengths is determined by the difference between the FSRs of ring #1 and ring #2. Cladding Sample reservoir Input Ring #1 R 1 Connection waveguide Sample reservoir R 2 Ring#2 Output (a) (b) Fig. 1. The schematic configuration of the present digital optical sensor based on cascaded rings; (a) the top view; (b) the 3D view [in order to see the structure clearly, we separate the cladding from the substrate only for the view]. (a) 1(i) 1(i+1) FSR1 (b) 2(j) 2(j+1) FSR2 (c) c(i) n=0 n>0 c(i+1) Fig. 2. The schematic spectral responses for the cascaded-rings. When the refractive index of the sample changes slightly ( n>0), the resonant wavelength of ring #2 shifts and the resonant wavelengths 1(i) and 2(j) become separated while the adjacent resonance wavelengths 1(i+1) and 2(j+1) become close. Therefore, the amplitude of the major peak at around = 1(i) decreases while the amplitude of the adjacent minor peak at around 1(i+1) = 1(i) + FSR1 increases. The maximal peak of the output response still locates at the position of = 1(i) when the index-change n eff < n eff0 /2, where neff0 neff ( FSR1 FSR 2 )/ 1( i). (1) When the refractive index of the sample increases further, i.e., n eff > n eff0 /2, the major peak moves to the position of = 1(i+1). When the change of the effective index n eff = n eff0, the adjacent resonant wavelengths 1(i+1) and 2(j+1) become coincided and the common resonant wavelength jumps to the wavelength 1(i+1). Consequently the amplitude of the major peak is close to 1, as shown by the dotted curve in Fig. 2(c). When the refractive index of the sample increases further, the major peak will jump to the next resonant wavelength of ring #1. Therefore, as the refractive index increases, the wavelength max corresponding to the major peak shifts discretely (or digitally). In such a digital way, the shift of the wavelength max is equal to multiple FSRs of ring #1, i.e., max = i FSR1, as the refractive index increases. In this way, the optical sensor has an ultra-high sensitivity S which is given by S / n ( / n )[ /( )] S M. (2) FSR1 eff0 1( i) eff FSR1 FSR1 FSR 2 0 # $15.00 USD Received 18 Nov 2009; revised 29 Nov 2009; accepted 8 Dec 2009; published 11 Dec

172 where M FSR1 /( FSR1 FSR2 ) and S 0 / n eff = 1(i) /n eff (here S 0 is actually the sensitivity of a single ring). From this equation, one sees the sensitivity of the present optical sensor based on cascaded-rings is M times higher than that of a single-ring sensor. And the detect limit (i.e., the minimal measurable index-change) of the present optical sensor is n eff0 given by Eq. (1). When a higher detect limit is desired, one should choose a small difference FSR1 FSR2 between the FSRs of the two rings. The difference FSR1 FSR2 also determines the FSR of the cascaded-ring by ( M 1). (3) FSR The measurement range of the present sensor is then given by n max = FSR /S. Furthermore, the FSR-difference FSR1 FSR2 should be also chosen appropriately according to the resonance linewidth (i.e., the Q-value). Otherwise, there may be no measurable output signal for some refractive index values when the resonance peaks of these two rings do not overlap. For this sake, the FSR-difference FSR1 FSR2 should be small enough. For example, when one chooses FSR1 FSR2 = 3dB (here 3dB is the 3dB bandwidth of a single ring), the major peak will range from ~0.5 to 1.0 as the refractive indexchanges. Consequently, one could always have a measurable output signal. It is possible have a stronger signal (with a peak larger than 0.5) by choosing a smaller FSR-difference (i.e., FSR1 FSR2 < 3dB ) if necessary. When concerning the fabrication, it is important to control the dimensions (the core width, and the radius) of the cascaded rings in order to have a suitable FSR-difference FSR1 FSR2 (which should be close to 3dB as discussed above). 3. Design and result In the following part we give a design with the present digital optical sensor based on a popular SOI (silicon-on-insulator) wafer, which has a 220nm Si layer (n Si = 3.445) on a 2 m SiO 2 insulator layer (n SiO2 = 1.445). The core width of the SOI nanowire is w co = 500nm and the wavelength range is from 1500nm to 1600nm. Here we consider the TM polarization, which is preferred for a high sensitivity on the change of the ambient refractive index [1]. The effective refractive index is n = and for the SOI nanowire with a waterand SiO 2 cladding, respectively. The group index n g is given by n g = n D c, where c is the central wavelength and the dispersion coefficients are D = m 1 and m 1 for the SOI nanowire with a water- and SiO 2 cladding, respectively. For ring #1, we choose the order m = 300 at the wavelength c of 1500nm and the corresponding bending radius R 1 is about m (which guarantees a very low bending loss). Ring #2 has a slightly different bending radius from ring #1 to have a smaller FSR. In the present example, we choose m = 312 and the bending radius R 2 = m. For ring #2, one could choose a slot waveguide to have an enhanced sensitivity when necessary [5]. Here we kept the radius value to four places of decimals in order to get the resonance wavelength at 1500nm as an example. For the fabrication, one should control the core width and the radius, to have a suitable FSRdifference FSR1 FSR2 which should be close to the 3dB-bandwidth 3dB as discussed above. For the present example, the FSRs for ring #1 and ring #2 are FSR1 = 2.331nm and FSR2 = 2.325nm, respectively. The FSR-difference (~6pm) is a little smaller than the resonance linewidth of a single ring ( 3dB = 7.4pm). With such a design, one could always have a measurable output signal (with a peak larger than 0.5) as the refractive index-changes, which will be seen in Fig. 3(b) below. When there are fabrication errors, the resonance wavelength, and the FSR-difference FSR1 FSR will deviate from the designed value. If the FSR-difference FSR1 FSR2 is much smaller than the 3dB-bandwidth 3dB, the extinction ratio between the major peak and the minor peak becomes small, which makes it not easy to distinguish the major peak. On the other hand, if the FSR-difference FSR1 FSR2 is much larger than the 3dB-bandwidth 3dB, there will be no measurable output signal because the overlapping between the resonance peaks of these two rings is too small. Therefore, when concerning to have a relatively larger fabrication tolerance, it is preferred to use the rings with relatively low Q-values (e.g., a relatively large 3dB-bandwidth). FSR1 # $15.00 USD Received 18 Nov 2009; revised 29 Nov 2009; accepted 8 Dec 2009; published 11 Dec

173 Figure 3(a) shows the spectral response at the output port of the cascaded rings when n eff = 0. One sees that there is only one major peak (which has the maximal amplitude) in a very broad wavelength range [here we only show a part from 1500nm to 1600nm in Fig. 3(a)]. This large band makes it allowed to realize a broad measurement range for the refractive index-change. The inset in Fig. 3(a) shows the enlarged view of the major peak, which has a 3dB bandwidth of about 4.8pm (the corresponding Q-value is ). And there are also a series of minor peaks with small amplitudes. For the two adjacent minor peaks (at nm and nm), the amplitudes are about 0.4, which is much smaller than the major peak (~1.0). In order to see how the major peak shifts, Fig. 3(b) shows the spectral responses at the output port of the cascaded rings as the index-change n eff increases with a step of When n eff = 0, the major peak locates at max 1500nm and the two adjacent minor peaks locate at nm and nm. When the refractive index increases, the major peak decreases and one of the adjacent minor peak increases accordingly because the resonance wavelength of ring #2 shifts. For the present example, the major peak and one of the adjacent minor peak become similar when n eff = When the index-change increases further, e.g., n eff = , the peak at nm becomes the major one while the peak at 1500nm becomes the minor one. As the index-change n eff further increases from , the major peak at nm is further enhanced. From Fig. 3(b), one clearly sees how the wavelength max (where the major peak locates) switches as the refractive index-changes. Power Major peak (a) Wavelength (nm) 1600 Power (unit) n eff=0 n eff= n eff= n eff= n eff= n eff= (b) Wavelength (nm) Fig. 3. (a) The response of at the output port of the cascaded rings in the broad band (the inset shows the enlarged view for the major peak); (b) the response at the output port of the cascaded rings when n eff ranges from 0 to In Fig. 4(a), we show the amplitudes of all the peaks (locating at different resonance wavelengths 1(i) ) as the index-change n eff increases. In the present example, the resonance wavelength 1(1) = 1500nm, and the separation between 1(i) and 1(i+1) is around 2.33nm. From Fig. 4(a), one sees that the amplitude for any one peak has a Gaussian-like shape as the indexchange n eff increases. For any given index-change n eff, one will find a major peak which has a larger amplitude than the other peaks (i.e., minor peaks). As the index-change n eff increases, the major peak will be switched. When the amplitude of the major peak becomes maximal, the adjacent minor peaks have minimal amplitude. Consequently one obtains a maximal contrast between the major peak and the minor peaks, which makes it easy to distinguish the major peak. The major peak may have almost the same amplitude as the adjacent minor peak at a certain index-change n eff [see Fig. 3(b)]. In this case, the small contrast makes it not easy to distinguish the major peak. Fortunately, one can easily distinguish these two similar peaks (locating at e.g. 1(i) and 1(i+1) ) from the other minor peaks. According to the position of these two similar peaks, it is easy to determine the indexchange, which is approximately equal to ( n eff(i) + n eff(i+1) )/2, where n eff(i) is the indexchange corresponding to the case with a major peak locating at 1(i). Figure 4(b) shows the wavelength max corresponding to the major peak as the indexchange n eff increases. One sees that the wavelength max changes discretely (which is like a # $15.00 USD Received 18 Nov 2009; revised 29 Nov 2009; accepted 8 Dec 2009; published 11 Dec

174 staircase). The wavelength max shifts 2.33nm when there is a refractive index-change of n eff = This gives an ultra-high sensitivity of about nm/riu, which is several hundreds times higher than the sensitivity of a single-ring-based sensor. We note that the major peak shift may be not sensitive to the refractive index-change when the index-change is smaller than n eff0 [given by Eq. (1)]. On the other hand, as long as the index-change is larger than n eff0, one will observe a significant wavelength shift of the major peak. Therefore, the detection limit is determined by n eff0. The detect limit of the present digital optical sensor is n eff0 = , which could be enhanced further by reducing the difference between the FSRs of these two rings according to Eq. (1). The present cascaded-ring not only has an ultrahigh sensitivity but also a large measurement range because of the ultra-wide FSR. For the present example, the FSR of the cascaded-ring is about several hundreds nanometers estimated by Eq. (3). In this case the measurement range actually might be limited by the bandwidth of the light source. When using a broad-band light source with a bandwidth of = 100nm, a measurement range is about (estimated by n max = /S). Thus, it is important to have a broadband light-source when a larger measurement range is desirable. When using a light-source with a limited bandwidth, it is also possible to have a larger measurement range by choosing smaller FSR for the cascaded rings. max (nm) (1) 1(2) 1(3) 1(5) 1(7) 1(4) 1(6) 1(9) 1(8) 1(10) 1(11) (a) 1530 (b) (b) 1520 max (nm) 1510 n~ ~2.33nm n x n x 10-4 Fig. 4. As the index-change n eff increases, (a) the amplitude of all the peaks locating at different resonance wavelengths 1(i); (b) the wavelength max corresponding to the major peak. Since the wavelength shift of the major peak of the spectral response is at the order of several nanometers when using the present digital optical sensor, it is very convenient to monitor the major peak switching even by using a low resolution integrated microspectrometer based on an AWG [10] combining with a photodetector array. The AWG microspectrometer used here should have a channel spacing equal to the FSR of the ring with the up-cladding. In this way, it is promising to realize a low-cost and portable highly-sensitive optical sensor system on a single chip. 4. Conclusion In summary, we have proposed a digital optical sensor based on cascaded rings. One of the two rings is covered by an up-cladding and the up-cladding on the other ring is removed to form a sample reservoir. The two cascaded rings have different FSRs and consequently the output port will have a spectral response with a major peak and some minor peaks. The proposed optical sensor operates in a digital way, i.e., the wavelength of the major peak switches by a step equal to multiple FSRs of the ring with the up-cladding as the refractive index increases. Therefore, one has an ultra-high sensitivity which is M times higher than that of a single ring. With the present digital optical sensor, one does not need to use a highresolution spectrometer to monitor the peak switching of the spectral response. It is allowed to use a low-resolution integrated optical micro-spectrometer (e.g., based on an AWG [10]) combining with a photodetector array. Consequently it provides a promising way to realize a low-cost and portable highly-sensitive optical sensor system on a single chip. Acknowledgement This project was supported Zhejiang Provincial Natural Science Foundation (No. J ). # $15.00 USD Received 18 Nov 2009; revised 29 Nov 2009; accepted 8 Dec 2009; published 11 Dec

175 December 15, 2010 / Vol. 35, No. 24 / OPTICS LETTERS 4229 Highly sensitive Si nanowire-based optical sensor using a Mach Zehnder interferometer coupled microring Jianwei Wang and Daoxin Dai* Centre for Optical and Electromagnetic Research, State Key Laboratory for Modern Optical Instrumentation, East Building No. 5, Zijingang Campus, Zhejiang University, Hangzhou, , China *Corresponding author: dxdai@zju.edu.cn Received August 16, 2010; revised November 7, 2010; accepted November 27, 2010; posted December 1, 2010 (Doc. ID ); published December 16, 2010 A Mach Zehnder interferometer (MZI) coupled microring is demonstrated experimentally to obtain a high sensitivity as well as a large range for measuring change in refractive index. For the present MZI-coupled microring, there is a major resonance wavelength with a high extinction ratio (16 36 db) in a very large wavelength span. Consequently, a very large quasi-free spectral range (>120 nm) is achieved, which helps to obtain a large measurement range. The MZI-coupled microring sensor is used for measuring the change of the ambient refractive index ranging from 1.0 to 1.538, and the sensitivity is as high as 111 nm/refractive index unit Optical Society of America OCIS codes: , Recently, demand for low-cost, highly sensitive, and compact sensors has increased rapidly in various areas, such as the environment, chemistry, and others [1 6]. People have developed various integrated optical sensors by using different structures, e.g., Mach Zehnder interferometers (MZIs) [1], surface plasmon sensors [2], microcavities [3 6], etc. Among them, a high-q microcavity (including microring/microdisk [3 6]) is one of the most attractive candidates because of its ultracompact size, high sensitivity, and easy realization of a sensor array. For the microcavity-based optical sensor, one usually measures the shift of the resonance wavelength by using a high-resolution optical spectrum analyzer combined with a broadband light source or a tunable laser with a power meter. To achieve the capacity to distinguish a slight shift of the resonance wavelength in a microring, a high-q factor is usually desired; it is obtained by minimizing the intrinsic loss and choosing a small coupling ratio [7]. It is a convenient way to control the coupling coefficient between the microring and its access waveguide by using an MZI coupler, which has been used previously for thermo-optic switches [8], reconfigurable Si microring filters [9], and high-speed modulated hybrid silicon lasers [10]. Recently, we designed an MZI-coupled microring for optical sensing with a high sensitivity as well as a very large measurement range [11]. In this Letter, we demonstrate the experimental results for the MZI-coupled microring optical sensor for measuring the ambient refractive index. Figure 1 shows the schematic configuration of the present MZI-coupled microring, including a microring and a feedback line that is one of the arms of the MZI coupler. To achieve a high-q factor, the length difference ΔLð¼ L 23 L Þ between the two MZI arms is chosen so that we have a small coupling coefficient k 14 0 at the designed wavelength λ MRR0. On the other hand, the coupling ratio k 14 0 should satisfy the critical coupling condition (i.e., matching the loss in the microring) in order to achieve a high extinction ratio at the designed wavelength. Since the coupling ratio k 14 0 is wavelength dependent, it is possible to have a major resonance wavelength with high extinction ratio over a large wavelength span. In this way, the MZI-coupled microring has a large quasi- FSR (free spectral range) [11], which provides a way to realize highly sensitive optical sensing with a large measurement range. When the refractive index of the ambient material on the surface of the sensing window (covering the whole MZI-coupled microring) changes, both the central wavelength λ MZI of the MZI coupler and the resonance wavelength λ MRR0 of the microring change with the almost same wavelength shift [11]. Therefore, when the ambient refractive index changes, the coupling coefficient k 14 0 at the resonance wavelength λ MRR0 is almost unchanged. Consequently the critical coupling for a high extinction ratio is still satisfied at the shifted resonance wavelength λ MRR0. Because of the large quasi-fsr, the measurement range for the change of the ambient refractive index is very large. This is achieved by monitoring the shift of the major resonance wavelength λ MRR0 [11]. In our design and fabrication, we choose the popular silicon on insulator (SOI) wafer with a 220 nm Si layer on a 2 μm SiO 2 insulator layer. The core width of the Si nanowire is w co ¼ 500 nm, and the bending radius of the microring is R ¼ 2 μm. To shorten the couple length, the width of the Si nanowires in the coupling regions is tapered down to w DC ¼ 400 nm with a 1.5-μm-long taper, as shown in Fig. 1. The gap width of the directional coupler is G ¼ 150 nm, according to the resolution of the deep-uv lithography process. The length of the coupling region is L DC ¼ 7:5 μm. The optimized length difference for the MZI coupler is ΔL ¼ 9:528 μm. In this case, the Fig. 1. (Color online) Configuration of the present MZIcoupled microring /10/ $15.00/ Optical Society of America 172

176 4230 OPTICS LETTERS / Vol. 35, No. 24 / December 15, 2010 resonance wavelength λ MRR0 is around 1550 nm for the TE polarization. The MZI-coupled microring based on SOI nanowires was fabricated using the deep-uv (248 nm) lithography at IMEC (Interuniversity Microelectronics Centre, Belgium). Figure 2(a) shows the scanning electron microscope (SEM) image for the fabricated MZI-coupled microring. Grating couplers were used to have an efficient coupling between the fibers and silicon nanowires [see the inset of Fig. 2(a)]. Figure 2(b) shows the measured spectral response of the fabricated MZI-coupled microring when covered by deionized (DI) water, as an example. This spectral response is normalized by the transmission of the straight waveguide with input/output grating couplers. One sees that there is a major resonance wavelength λ MRR0 at around 1540 nm with a high extinction ratio of over 25 db in the wavelength range from 1520 nm to 1630 nm. The wavelength range shown here is limited by the tunable range of the laser source. The other resonance wavelengths in this wavelength range ( nm) are distinctly depressed. The Q factor ( 3900) is not as high as expected, which is due to the loss of the microring and the deviation of the coupling coefficient k 14 0 resulting from fabrication errors. To demonstrate that the MZI-coupled microring is able to measure the concentration change of the ambient materials, we first use aqueous solutions of NaCl with different concentrations (i.e., a small change of refractive index). Before we did the measurement for new NaCl solution, we measured the result for DI water, which is used as the reference for calibration. This helps to avoid any influence of variations in incidental factors (e.g., temperature variation). All measurements were performed three times to verify their reliability and repeatability. Figure 3(a) shows the measured transmission response of the MZI-coupled microring when the covered NaCl solution has different concentrations. The ratio of the refractive index change to the concentration change for the aqueous solution of NaCl is about refractive index units (RIU)/1% at 20 [12]. In our experiment, the concentration varies from 0% to 5% with a step of 1% and the corresponding refractive index ranges from to From Fig. 3(a), one sees that the major resonance wavelength λ MRR0 increases as the concentration of the NaCl solution increases, and the shape of the spectrum is almost the same (i.e., with a high extinction ratio of 25 db), as predicted. From Fig. 3(b), one sees that the sensitivity of the MZI-coupled microring sensor is about 111:1 nm/riu. It is possible to improve the sensitivity further by using TM polarization [1,11]. We also designed and fabricated MZI-coupled microrings with different parameters for the MZI coupler, e.g., L DC ¼ 1 μm. With this design, we also achieve a high extinction ratio and a very large quasi-fsr, as shown in Fig. 4(a). To show that the present MZI-coupled microring sensor has the capacity to measure a large range of the refractive index change, here we used different organic liquids with very different refractive indices. Table 1 shows the refractive indices of the organic liquids used in our experiment, e.g., C 2 H 6 O, C 4 H 9 O, C 6 H 12,C 6 H 6, and C 7 H 8 O[12]. Figure 4(a) shows the measured transmission responses of MZI-coupled microring covered with these organic liquids. We note that the extinction ratio changes in some degree as the ambient refractive index varies. Figure 4(b) shows the extinction ratios extracted from Fig. 4(a). When the refractive index ranges from to 1.501, Fig. 2. (Color online) (a) SEM image for the fabricated MZIcoupled microring. Inset, TE grating coupler. (b) Measured transmission response of MZI-coupled microring with deionized H 2 O cladding. Fig. 3. (Color online) (a) Measured transmission responses of the MZI-coupled microring covered the aqueous solution of NaCl with different concentrations. (b) The major resonance wavelength λ MRR0 shifts as the concentration varies. 173

177 December 15, 2010 / Vol. 35, No. 24 / OPTICS LETTERS 4231 Table 1. Refractive Indices of Liquids at 1.55 μm Liquids n Deionized H 2 O C 2 H 6 O C 4 H 9 O C 6 H C 6 H C 7 H 8 O Fig. 4. (Color online) (a) Measured transmission responses of the MZI-coupled microring covered with different liquids shown in Table 1. (b) Resonance wavelength λ MRR0 and the extinction ratio. the extinction ratio is as high as 36 db. When the refractive index is out of this range, the extinction ratio decreases slightly. To explain it, we use a threedimensional finite-difference time-domain method to calculate the coupling ratio of the directional coupler. The simulation shows that the power coupling ratio increases from to as refractive index changes from 1.0 to This introduces a deviation in the coupling ratio of k 14 0 from the idea value, satisfying the critical coupling condition. Furthermore, when ambient refractive index increases, the index contrast of the Si nanowire decreases and the resonance wavelength becomes long. Since a lower index contrast or longer wavelength will introduce a larger bending loss, the critical coupling condition is not preserved, and consequently the extinction ratio decreases. Fortunately, one can still distinguish the major resonance wavelength λ MRR0. Therefore, the ultralarge quasi-fsr (>120 nm) of the MZI-coupled microring enables a large dynamic range for measuring the change of the refractive index (1 <n<1:538). For a microring with a large bending radius (e.g., 10 μm or more), its FSR is quite small, which will limit the measurement range. By using the present MZI-coupled microring, a large measurement range could be achieved even when the microring radius is quite large. In Fig. 4(b), we also show that the shifts of the resonance wavelength as the ambient refractive index increases from 1.0 to by using different liquids shown in Table 1. Here the wavelength shift is with reference to the resonance wavelength when covered by DI water (H 2 O). The linearity of the Δλ MRR0 =Δn curve shows that the MZI-coupled microring sensor works well even when the refractive index of ambient liquid changes significantly. In summary, we have experimentally demonstrated an MZI-coupled microring sensor with a high sensitivity as well as a large measurement range. The MZI-coupled microring has an ultralarge quasi-fsr (>120 nm). This makes it available for a large-range measurement. In our experiment, the index ranges from 1.0 to by using NaCl solution and different organic liquids. It has been shown that the resonance wavelength shifts linearly almost as the index changes and the sensitivity is about 110 nm/riu. The present MZI-coupled ring could be used for many applications of optical sensing, e.g., measuring the concentration of gas or liquid. Since Si has a relatively large thermal-optical coefficient, the MZI-coupled microring sensor is not temperature insensitive, i.e., the resonance wavelength will shift as the temperature changes, which is similar to the case of conventional microrings based on Si nanowires. To avoid the influence of temperature variation, one could keep the temperature unchanged or introduce a careful calibration. On the other hand, since the wavelength shift of the MZI coupler is almost the same as that of the microring, the critical coupling condition will not be violated as the temperature changes. Thus, one could still obtain a high extinction ratio as the temperature changes, which is good for temperature sensing. This project was partially supported by Zhejiang Provincial Natural Science Foundation (R ) and the National Natural Science Foundation of China (NSFC) ( ). References 1. D.-X. Densmore, P. Xu, S. Waldron, P. Janz, J. Lapointe Cheben, A. Delâge, B. Lamontagne, J. H. Schmid, and E. Post, IEEE Photon. Technol. Lett. 18, 2520 (2006). 2. G. Nemova and R. Kashyap, J. Opt. Soc. Am. B 24, 2696 (2007). 3. S. Cho and N. M. Jokerst, IEEE Photon. Technol. Lett. 18, 2096 (2006). 4. R. W. Boyd and J. E. Heebner, Appl. Opt. 40, 5742 (2001). 5. C.-Y. Chao and L. J. Guoa, Appl. Phys. Lett. 83, 1527 (2003). 6. A. M. Armani, R. P. Kulkarni, S. E. Fraser, R. C. Flagan, and K. J. Vahala, Science 317, 783 (2007). 7. L. Chen, N. Sherwood-Droz, and M. Lipson, Opt. Lett. 32, 3361 (2007). 8. W. M. J. Green, R. K. Lee, G. A. DeRose, A. Scherer, and A. Yariv, Opt. Express 13, 1651 (2005). 9. L. Zhou and A. W. Poon, Opt. Express 15, 9194 (2007). 10. D. Dai, A. Fang, and J. E. Bowers, New J. Phys. 11, (2009). 11. D. Dai and S. He, J. Opt. Soc. Am. B 26, 511 (2009). 12. D. R. Lyde, ed., Handbook of Chemistry and Physics (CRC Press, ). 174

178 842 IEEE PHOTONICS TECHNOLOGY LETTERS, VOL. 23, NO. 13, JULY 1, 2011 Cascaded-Ring Optical Sensor With Enhanced Sensitivity by Using Suspended Si-Nanowires Jing Hu and Daoxin Dai, Member, IEEE Abstract A cascaded-ring optical sensor with Vernier effect is demonstrated experimentally by using Si nanowires. The Vernier effect helps to obtain ultrahigh sensitivity. In order to enhance the sensitivity further, a suspended Si nanowire is used for the sensingringbyremovingthesio insulator underneath with a wet-etching process. The measurement result shows that the sensitivity of the demonstrated cascaded-ring optical sensor is up to nm/riu experimentally. The detection limit for the index change is about. Index Terms Cascaded, nanowire, ring, Si, suspended, Vernier. I. INTRODUCTION T HE demand for low-cost, highly sensitive and compact optical sensors is increasing rapidly for many areas such as environmental and biochemical detections. Ring resonator is a good option for sensing due to its compactness, robustness, as well as low cost. For a ring-based sensor, one usually use the way of measuring the resonance wavelength shift. In order to measure a small wavelength shift, usually there are two ways. One is using the combination of a photodetector and a high-precision tunable laser. The other one is using an optical spectrum analyzer (OSA) with high resolution. Both these two ways are expensive and not convenient for low-cost and portable highly-sensitive optical sensing system. A potential solution is to use an integrated-type OSA. However, the resolution of an integrated OSA is usually relatively low, e.g., 0.1 nm 1 nm [1], which limits the detection limit of the optical sensing system. In order to make an integrated OSA available for integrated optical sensor, an option is using the recently proposed optical sensor based on cascaded highring-resonators, which has an ultrahigh sensitivity due to the Vernier effect [2] [4]. By using such a structure, a small refractive index change will introduce a signi cant wavelength shift. Therefore, a low-resolution OSA is enough to distinguish the spectral response change due to a small variation of refractive index. In [3], the experimental result was demonstrated for Manuscript received November 19, 2010; revised March 21, 2011; accepted March 26, Date of publication April 05, 2011; date of current version June 02, This project was supported in part by the Zhejiang Provincial Natural Science Foundation (R ), and in part by the National Science Foundation of China ( ). The authors are with the Centre for Optical and Electromagnetic Research, State Key Laboratory of Modern Optical Instrumentation, Zhejiang Provincial Key Laboratory for Sensing Technologies, Zhejiang University, Hangzhou , China ( dxdai@zju.edu.cn). Color versions of one or more of the gures in this letter are available online at Digital Object Identi er /LPT Fig. 1. Microscopic picture for the fabricated cascaded-ring sensor with suspended Si-nanowire. the cascaded-ring sensor by using shallowly-etched silicon-oninsulator (SOI) ridge waveguides. The reported sensitivity is about 1300 nm/riu (refractive index unit) when operating at TE (transverse electric) polarization. Since TM (transverse magnetic) polarization has higher sensitivity than TE polarization, recently the cascaded-ring sensor operating at TM polarization by using SOI nanowires was demonstrated experimentally and the sensitivity is about 2169 nm/riu [5]. In this manuscript, a cascaded-ring optical sensor based on suspended SOI nanowires are demonstrated experimentally. The suspended SOI nanowire is used to improve the sensitivity further. Due to the enhancement effect in a high index-contrast waveguide [6], the suspended SOI nanowire has sensitivity of more than 1, which is more than double of that of the conventional SOI nanowire. In comparison with the nano-slot waveguide in [7], the suspended SOI nanowire used here is also more sensitive while the fabrication is easier and the loss is lower. Therefore, by combining the Vernier effect and the suspended waveguide structure, our cascaded-ring optical sensor shows very high sensitivity and small detection limit. II. STRUCTURE AND DESIGN The SOI wafer used here has a 220 nm-thick Si layer and a 2 m-thick buried oxide layer. The Si nanowire is 500 nm wide to be single-mode. Since the present SOI nanowire is very thin ( 220 nm), the evanescent eld for TM polarization is stronger than TE polarization [8]. Consequently, we choose TM polarization in our design and experiment. Fig. 1(a) shows the picture for the fabricated cascaded-ring sensor. Ring #1 and ring #2 have different radii for different free spectral ranges (FSRs), i.e.,,and. Thus the spectral response at the drop port has a major resonance wavelength with the highest power level [2]. In the present design, ring #2 is the sensing ring, which is exposed to the liquid sample to be measured. When the refractive index of the sample changes, this major resonance wavelength will shift by multiple FSRs of ring #1 due to the Vernier effect, which consequently gives an ultrahigh sensitivity [2] /$ IEEE 175

179 HU AND DAI: CASCADED-RING OPTICAL SENSOR WITH ENHANCED SENSITIVITY 843 Fig. 3. SEM picture of the ring sensor with suspended Si nanowires. The inset is the enlarged view for the suspended Si nanowires. Fig. 2. Calculated sensitivity for (a) the conventional Si nanowires, (b) the suspended Si nanowires. In order to enhance the sensitivity further, we use a suspended Si nanowire for the sensing ring (#2). Fig. 2(a) and (b) show the calculated sensitivities of a conventional Si nanowire (with a SiO insulator layer) and a suspended Si nanowire. From these gures, one sees that the conventional Si nanowire has a sensitivity of about (at 1550 nm). The sensitivity for the suspended Si nanowire is as high as (at 1550 nm), which is even higher than that for a Si nano-slot waveguide ( [7]). Consequently, when using the suspended Si nanowire, the bulk sensitivity for a single ring sensor is up to 515 nm/riu, which is even much higher than that for the case of using Si nano-slot waveguides [7]. For the present cascaded-ring sensor with suspended Si nanowires, we choose the following parameters according to the theory shown in [2]: the bending radii mand m, the length of the coupling region between the ring and the access waveguides is m. The FSRs for ring #1 and ring #2 are about 2.18 nm and 2.10 nm respectively. III. RESULTS AND DISCUSSION The sensor chip was fabricated partially by deep-uv lithography at IMEC. A 600 nm-thick SiO layer was deposited to cover the whole chip by using the PECVD technology. Positive photoresist (RZJ304-25) was then used to form the pattern of the sample window. The sample window has two curved regions (which are 8 mwide)asshowninfig.1.inorderto obtain the support for the suspended Si nanowires of ring #2, the coupling regions between ring #2 and its access waveguides are protected by photoresist during the wet etching. Finally, by using an HF wet etching process, the SiO up-cladding as well as the SiO insulator layer beneath in the window region were removed. Consequently the sensing ring #2 becomes suspended partially, as shown in Fig. 3. For the characterization of the fabricated cascaded-ring sensor, we use a low-resolution (0.1 nm) OSA and a broadband ampli ed spontaneous emission (ASE) laser. The ASE laser source has a peak power of 22.5 dbm at the central wavelength of 1552 nm and the 3 db bandwidth is about 43 nm. A ber-type polarization controller (PC) is used to obtain the desired TM-polarized light. Grating couplers are used to couple light between bers and the chip and the coupling loss of about 7 db per facet. In order to obtain the liquid samples with different refractive indices in the measurement, salt solutions with different concentrations were used. Fig. 4(a) shows the measured spectral responses at the drop port. The concentrations of the salt solutions are 0 wt% (DI water), 0.04 wt%, 0.06 wt%, and 0.11 wt% respectively. Before switching to new salt solution with a different concentration, deionized (DI) water was used to clean the sensor chip, which helps to remove the residual salt solution inside the sample reservoir. The spectral responses for measuring the DI water after cleaning are also shown in Fig. 4(a). We note that the major peak wavelengths corresponding to the DI water sample are different slightly. This small difference might be because the sample reservoir was not cleaned very completely. On the other hand, this indicates the present sensor is very sensitive to the index change. Therefore, in order to avoid the error due to the calibration when measuring small index change, one should clean the sample reservoir very carefully. From Fig. 4(a), one sees that the major wavelength shifts to the longer wavelength for higher concentration. For example, when the concentration increases from 0.04 wt% to 0.06 wt%, the wavelength shifts from nm to nm. For the present cascaded-ring sensor, the measurement range is limited by its quasi-fsr, which is given by the difference between the two adjacent major wavelengths. Due to the limitation of the homemade ASE light source used, 176

180 844 IEEE PHOTONICS TECHNOLOGY LETTERS, VOL. 23, NO. 13, JULY 1, 2011 detection limit for the present cascaded-ring sensor is estimated to be about RIU. IV. CONCLUSION We have demonstrated a cascaded-ring optical sensor with suspended Si nanowires experimentally. By utilizing the Vernier effect [2] [4], the cascaded-ring optical sensor shows an ultrahigh sensitivity. The suspended Si nanowire has been also used to enhance the sensitivity further. Our experimental results have shown that the fabricated cascaded-ring sensor based on suspended Si nanowires provides sensitivity as high as about nm/riu and the detection limit is about. Therefore, a small refractive index change will introduce a signi cant wavelength shift. This makes it possible to detect the small index change by using a low-resolution integrated-type OSA, which provides a way to realize low-cost optical sensor system. When using an optical sensor with an ultrahigh sensitivity, it is very important to minimize the environmental in uences (e.g., temperature variation) by using a temperature control, introducing novel athermal designs, or a temperature compensation method [10]. Fig. 4. Measurement results for the cascaded-ring sensor with suspended Si nanowires using salt solutions with different concentrations (0 wt%, 0.04 wt%, 0.06 wt%, and 0.11 wt%). (a) Spectral responses at the drop port; these curves in (a) are shifted in the Y-axis for clarity and the unit is nanowatts (nw). (b) Wavelength shift as the solution concentration changes. the major peak over a quasi-fsr is not signi cant. From the result for the case with the 0.06 wt% salt solution shown in Fig. 4(a), one sees that the two adjacent major wavelengths and are nm and nm, respectively. Consequently the quasi-fsr is about 37 nm. Wealsonotethat the wavelength shift for the 0.11 wt% saltsolution is larger than a quasi-fsr, as shown in Fig. 4(b). Therefore the measurement range of the present cascaded ring sensor is limited by the quasi-fsr, which is similar to the conventional single-ring sensor. In Fig. 4(b) the major wavelength is shown as the sample concentration ranges from0to0.11wt%.by ttingthe data in Fig. 4(b), the slope of the curve is about 330 nm/wt%. Since the refractive index change due to a 0.02 wt% concentration change is about RIU [9], the estimated sensitivity is about nm/riu. Accordingto[2],the detection limit of the cascaded-ring sensor is given by ( nm in our design). Therefore, the REFERENCES [1] P. Cheben, J. H. Schmid, A. Delâge, A. Densmore, S. Janz, B. Lamontagne, J. Lapointe, E. Post, P. Waldron, and D.-X. Xu, A high-resolution silicon-on-insulator arrayed waveguide grating microspectrometer with submicrometer aperture waveguides, Opt. Express, vol. 15, no. 5, pp , Mar. 5, [2] D. X. Dai, Highly sensitive optical sensor based on cascaded high-q ring-resonators, Opt. Express,vol.17, no. 26, pp , Dec. 21, [3] L.Jin,M.Y.Li,andJ.J.He, Highly-sensitive silicon-on-insulator sensor based on two cascaded micro-ring resonators with Vernier effect, Opt. Commun., vol. 284, no. 1, pp , [4] H.X.Yi,D.S.Citrin,Y.Chen,andZ.P. Zhou, Dual-microring-resonator interference sensor, Appl. Phys. Lett., vol. 95, no. 19, p , Nov. 12, [5] T. Claes, W. Bogaerts, and P. Bienstman, Experimental characterization of a silicon photonic biosensor consisting of two cascaded ring resonators based on the Vernier-effect and introduction of a curve tting method for an improved detection limit, Opt. Express, vol. 18, no. 22, pp , Oct. 25, [6] G.J.Veldhuis,O.Parriaux,H.J.W. M. Hoekstra, and P. V. Lambeck, Sensitivity enhancement in evanescent optical waveguide sensors, J. Lightw. Technol., vol. 18, no. 5, pp , May [7] J. T. Robinson, L. Chen, and M. Lipson, On-chip gas detection in silicon optical microcavities, Opt. Express, vol. 16, no. 6, pp , Mar. 17, [8] A.Densmore,D.X.Xu,P.Waldron, S. Janz, P. Cheben, J. Lapointe, A.Delâge,B.Lamontagne,J.H.Schmid, and E. Post, A silicon-oninsulator photonic wire based evanescent eld sensor, IEEE Photon. Technol. Lett., vol.18,no. 21, pp , Dec. 2, [9] H.P.HoaandW.W.Lam, Application of differential phase measurement technique to surface plasmon resonance sensors, Sens. Actuators B, vol. 96, no. 3, pp , Dec. 1, [10] K. B. Gylfason, C. F. Carlborg, A. Kazmierczak, F. Dortu, H. Sohlström,L.Vivien,C.A.Barrios,W.Wijngaart,andG.Stemme, On-chip temperature compensation in an integrated slot-waveguide ring resonator refractive index sensor array, Opt. Express, vol. 18, no. 4, pp , Feb. 1,

181 December 15, 2013 / Vol. 38, No. 24 / OPTICS LETTERS 5405 Suspended ultra-small disk resonator on silicon for optical sensing Xiaokun Wang, Xiaowei Guan, Qiangsheng Huang, Jiajiu Zheng, Yaocheng Shi, and Daoxin Dai* Centre for Optical and Electromagnetic Research, State Key Laboratory for Modern Optical Instrumentation, Zhejiang Provincial Key Laboratory for Sensing Technologies, Zhejiang University, Zijingang Campus, Hangzhou , China *Corresponding author: dxdai@zju.edu.cn Received September 13, 2013; revised November 1, 2013; accepted November 13, 2013; posted November 18, 2013 (Doc. ID ); published December 11, 2013 An ultra-small disk resonator consisting of a suspended silicon disk with a submicron bending radius sitting on an SiO 2 pedestal is demonstrated experimentally. An asymmetrical suspended rib waveguide is integrated as the access waveguide for the suspended submicron disk resonator, which is used to realize an ultra-small optical sensor with an improved sensitivity due to the enhanced evanescent field interaction with the analyte. The present optical sensor also has a large measurement range because of the ultra-large free-spectral range of the submicron-disk resonator. As an example, a suspended submicron disk sensor with a bending radius of 0.8 μm is designed, fabricated, and characterized. The concentration of NaCl aqueous solution and organic liquids is measured with the suspended submicron-disk sensor, and the measured sensitivity is about 130 nm RIU, which agrees well with the simulation value Optical Society of America OCIS codes: ( ) Guided waves; ( ) Integrated optics devices; ( ) Waveguides. Silicon-photonic-integrated devices have been extensively investigated for many applications (optical interconnect [1], optical sensing [2,3], etc.) because of CMOS compatibility and ultra-compactness. Among various silicon-photonic-integrated devices, an optical microcavity is well known as a versatile element to realize various functionality components, including optical modulators [4] and optical filters [5] as well as optical sensors [6,7]. The optical sensors based on optical microcavities have attracted lots of attention since there is a field enhancement in the microcavity when operating at the resonance wavelength [2,3]. It is well known that small size is universally desirable for most applications of microcavities [8]. In [8], a silicon microring resonator with 1.5 μm radius was demonstrated for the application of optical modulators. Similarly, for optical-sensing applications, there are also some benefits with small microcavities. First, a smaller microcavity sensor has a larger free-spectral range (FSR) so that a larger measurement range is available. Second, the sample volume to be measured is less when using a smaller microcavity sensor. Third, one can integrate more sensor elements in a single chip to have a sensor array with a higher integration density. A photonic crystal microcavity could be used for optical sensors with a small footprint and small mode volume [9]. A drawback is that a photonic crystal cavity usually has high excess loss, e.g., 17 db as shown in [10]. A simple way to have a low-loss optical microcavity is using a conventional optical-cavity waveguide with improved light confinement. For the case with a siliconon-insulator (SOI) platform, which is the most popular for silicon photonics, one can make a suspended silicon optical cavity by replacing the buried oxide (BOX) with another lower-index material (e.g., air). A disk resonator is considered here since it is one of the best options to support a suspended structure among various optical cavities. Furthermore, a microdisk resonator is also helpful to have low loss and a high Q value [11,12]. A high-q-suspended microdisk resonator without any access waveguide integrated has been demonstrated previously [13,14]. In that case, one usually has to use a tapered microfiber to couple light into the resonator, which is not reliable and convenient. It is also not ideal to be extended to form an array by cascading several resonators. A suspended GaAs microdisk resonator with an access waveguide has been demonstrated previously [15]. In this Letter, we demonstrate a suspended silicon ultrasmall disk resonator with an access waveguide. The disk resonator has a submicron bending radius (R <1 μm) to realize a submicron optical sensor with a large measurement range for measuring the concentrations of NaCl solutions and different organic liquids. Figure 1 shows the schematic configuration of the present suspended submicron-disk resonator for optical sensing. It can be seen that there is a suspended submicron disk sitting on a SiO 2 pedestal. An asymmetrical suspended rib waveguide is placed at the side as the access waveguide so that the measurement is convenient and robust. It is also easy to achieve a sensor array by cascading several resonators. When using the suspended disk resonator as an optical sensor to measure Fig. 1. Present suspended silicon submicron-disk resonator with a suspended access waveguide /13/ $15.00/ Optical Society of America 178

182 5406 OPTICS LETTERS / Vol. 38, No. 24 / December 15, 2013 the refractive index of gas or liquid, the sensitivity is improved intrinsically due to the enhanced evanescent field interaction with the analyte in comparison with the regular unsuspended disk resonator with BOX beneath. In addition, the suspended structure is helpful to reduce the bending loss so that one can realize a submicron-disk resonator, which has an ultra-large FSR and thus a large measurement range for optical sensing. Regarding that the bending loss becomes dominant for a submicron-disk resonator [8], we calculate the complex effective refractive index n eff and the field profiles of the whispering-gallery mode of a submicron-disk resonator by using a finite-element method. The bending loss for a 90 bending is then given by L 20 lg exp n im k 0 Rπ 2, where k 0 is the wavenumber (k 0 2π λ), R is the bending radius, n im is the imaginary part for the complex effective index n eff. Figure 2(a) shows the calculated bending loss L of the fundamental modes (TE 0 and TM 0 ) as well as the first higher-order modes (TE 1 and TM 1 )ofa suspended microdisk resonator as the radius R varies. In order to give a comparison, the result for an unsuspended microdisk resonator with BOX is also given, as shown in Fig. 2(b). For the present calculation, the cladding is air (n c 1) or deionized (DI) water (n 1.316). The SOI wafer has a 340 nm thick top silicon layer and a 1 μm thick SiO 2 insulator layer (which is thick enough to guarantee a low substrate leaky loss). The refractive indices of silicon and SiO 2 are and 1.445, respectively. And the operation wavelength is 1550 nm. Figure 2 shows that the suspended microdisk resonator has lower loss than the unsuspended one, which is due to the improved refractive index contrast. The comparison between Figs. 2(a) and 2(b) also shows that the bending loss for TE mode is lower than that for TM mode, which is due to the higher confinement ability for TE mode. As is known, a microdisk resonator usually supports the higher-order mode resonance, which is undesired for many applications, including optical sensing considered here. Fortunately, the higher-order modes (TE 1 and TM 1 ) have a large loss for the present submicron-disk resonator with a bending radius of less than 0.8 μm, as shown in Figs. 2(a) and 2(b). Therefore, the resonance for the higher-order modes is depressed significantly, which will be verified from the measured spectral responses below. For the disk with a larger radius, the Q value of the diskresonator improves, while multimode effects become severer because the higher-order modes are supported well with a low bending loss, as shown in Fig. 2(a). Furthermore, regarding that the FSR is inversely proportional to the bending radius, one can have a larger FSR by choosing a smaller bending radius. Therefore we choose R 0.8 μm in the following design. The intrinsic Q-value of a submicron-disk resonator is calculated by [16] Q i 2πn g αλ 0 n g 2n im ; (1) where n g is the group index. It is expected that the suspended submicron-disk resonator has a higher Q-value than the unsuspended one because of the lower bending loss [Fig. 2(a)]. For a suspended submicron-disk resonator with R 0.8 μm, the calculated intrinsic Q-values are about 12,000 and 1955, respectively, for TE and TM polarizations. When the suspended submicron-disk resonator is covered by, e.g., DI water (n 1.316), the Q-values for the TE and TM modes degrade to 680 and 300, respectively. The Q-value degradation is due to the increased bending loss as shown in Fig. 2(a). When using the submicron-disk resonator for optical sensing, the sensitivity is determined by the device sensitivity S d λ c n eff and the waveguide sensitivity S w n eff n c [17], i.e., S λ c n c λ c n eff n eff n c S d S w ; (2) where λ c is the resonant wavelength, and n c is the cladding index. One sees that the sensitivity S can be improved by enhancing either the device sensitivity S d or the waveguide sensitivity S w. For disk resonators, one has S d λ c n eff λ c n g. Note that the group index n g usually changes slightly as the waveguide dimension varies. For the present SOI nanowire, the group index n g varies slightly from 4.58 to 4.44 when the waveguide width increases from 300 to 500 nm. As a consequence, the device sensitivity S d does not change notably by optimizing the waveguide dimension. In this Letter, we focus on improvement of the waveguide sensitivity S w by introducing a suspended waveguide, which has enhanced evanescent field interaction with analyte. This can be seen from Fig. 3, which shows the calculated field profile for the TM 0 mode of the suspended and unsuspended submicron-disks covered by DI water when R 0.8 μm. For the suspended disk, the mode confinement factor in silicon is about 66%. The calculated waveguide sensitivities for the suspended and unsuspended submicron-disk resonator are S w and 0.203, respectively. Their device sensitivities are S d 457 and 462 nm RIU. Their sensitivities are S 150 and Fig. 2. Calculated bending losses of the TE 0,TM 0,TE 1, and TM 1 modes in a submicron-disk resonator when the cladding is air (thick curves) or DI water (thin curves). (a) Suspended. (b) Unsuspended. Fig. 3. Profile for the TM 0 mode in a submicron disk when R 0.8 μm. (a) Unsuspended. (b) Suspended. 179

183 December 15, 2013 / Vol. 38, No. 24 / OPTICS LETTERS nm RIU, respectively. It can be seen that the sensitivity is improved by 60%. The fabrication was started with a SOI wafer with a 340 nm thick top silicon layer and a 1 μm thick buried SiO 2 layer. A double-etching process was carried out to form the asymmetrical access optical waveguide and the submicron disk. In our case, the patterns were formed with positive E-beam lithography-resist ZEP- 520A by using a Raith150-II machine, and a dry etching process is implemented by using an STS inductively coupled plasma system. A third etching process was carried out to fabricate grating couplers for efficient fiberchip coupling [18]. Here the grating coupler working for TM polarization is designed and fabricated with a grating period of 810 nm, a duty cycle of 0.5, and an etching depth of 170 nm. And the coupling efficiency is estimated to be 28% at the central wavelength. A 300 nm thick SiO 2 layer is then deposited on the top to protect the silicon layer. A thin chromium layer ( 50 nm) was deposited and patterned as the hard mask in the following SiO 2 wet-etching process. Finally, the SiO 2 layer is corroded with the buffered SiO 2 etchant (a mixture of NH 4 F, CH 3 COOH, DI water, and ethylene glycol), and the wet-etching depth is about 400 nm. Figure 4(a) shows the scanning electron microscopy (SEM) picture of the fabricated submicron-disk resonator whose bending radius is about R 0.8 μm. From this figure, it can be seen clearly that the silicon submicrondisk is sitting on a SiO 2 pedestal. For the asymmetrical access waveguide coupling to the submicron disk, the slab height h slab is about 100 nm, and the rib width w rib is about 305 nm. The coupling gap is about 65 nm, as shown in Fig. 4(b). We note that there is a polarization rotation effect in the asymmetric silicon access waveguide due to the mode hybridization. In order to minimize the influence of the polarization rotation, the coupling region is designed to satisfy the critical coupling condition for the TM 0 mode only while the critical coupling condition does not satisfy for the TE 0 mode. In this way, only the resonance for the TM 0 mode of the disk resonator becomes significant, as observed in the measured spectral responses shown below. And the grating coupler at the output end also plays a role of polarizer so that the TE 0 mode is filtered out. In order to characterize the fabricated submicron-disk resonator, we use a tunable laser (Agilent 81600B) as the light source. The polarization of the light output from the tunable laser is adjusted by the polarization controller. A vertical coupling system with grating couplers was used to improve the fiber-chip coupling efficiency, and the response of the device at the output port is detected by the power meter (Aglient 81635). The spectral response of the fabricated submicron-disk resonator is measured when it is covered by the NaCl solution with different concentrations, i.e., c 0 25%. The corresponding refractive index of NaCl solution changes from to Before switching to measure the new salt solution with a different concentration, DI water was used to clean the sensor chip, which helps to remove the residual salt solution inside the sample reservoir [7]. Figure 5 shows the measured spectral response of the fabricated submicron-disk resonator when covered by the NaCl solution with different concentrations. The overall insertion loss is about 22 db, which is mainly from the coupling loss of the grating coupler and the mode conversion loss. These spectral responses are normalized by the transmission of the straight waveguide. The wavelength range shown here is limited by the bandwidth of the grating coupler, while the theoretical FSR of the submicron disk is estimated to be around 130 nm to enable a broad measurement range. Figure 5 shows a major resonant wavelength λ MRR0 with a high extinction ratio of >20 db in the range of nm. The loaded Q-value is about 100, which is comparable with the theoretical value of 112 obtained from a 3D-FDTD simulation. The extinction ratio and Q-value decrease with the increase of the NaCl solution concentration, which should be due to increased radiation loss and over-coupling of the disk-resonator caused by the increment of ambient refractive index. The inset of Fig. 5 shows the resonance wavelength λ MRR0 shifts as the concentration varies. It can be seen that the sensitivity of the suspended submicron-disk resonator is about 130 nm RIU, which is close to the theoretical value of 150 nm RIU. As a comparison, the ring resonator-based optical sensor demonstrated in [19] has a sensitivity of 70 nm RIU. In [20], the detection limit (DL) is given as DL r S, where r is the sensor resolution (the minimal detectable change of the resonant wavelength). According to [19], a wavelength shift of 1 15 of the peak width Δλ peak is usually measurable. In our case, one has Δλ peak 1.5 nm and S 130 nm RIU. Thus the estimated detection limit for the refractive index is about RIU Fig. 4. SEM pictures of the suspended submicron-disk (R 0.8 um). (a) Tilt view. (b) Top view. Fig. 5. Measured transmission spectrums of the suspended submicron-disk resonator covered by NaCl solution with different concentrations (0% 25%). Inset: the resonant wavelength shifts as the concentration varies. 180

184 5408 OPTICS LETTERS / Vol. 38, No. 24 / December 15, 2013 organic liquids. It has been shown that the present suspended submicron-disk optical sensor has an improved sensitivity ( 130 nm RIU) due to the enhanced evanescent field. This project was supported by a 973 project (2011CB503700), NSFC project ( ), Zhejiang provincial NSF (LY12A04010), and the Fundamental Research Funds for the Central Universities. Fig. 6. Measured transmission spectrums of the suspended submicron-disk sensor covered with different organic liquids. Inset: the resonant wavelength shifts as the refractive index of organic liquid varies. (corresponding to the concentration change of 0.4%). An improved DL can be achieved when using the present suspended submicron-disk resonator for gas sensing because of the improved Q-value. The present submicron-disk sensor also is used to measure the refractive indices of different organic liquids, including DI water (n 1.316) [7], methanol (n 1.326) [21], ethanol (n 1.354) [7], and isopropyl alcohol (IPA, n 1.364) [22]. The measured transmission responses are shown in Fig. 6. It can be seen that the Q-value and the extinction ratio are similar to those shown in Fig. 5. The inset of Fig. 6 shows the resonance wavelength λ MRR0 shifts as the refractive index varies. It can be seen that the sensitivity of the suspended submicron-disk resonator is about 130 nm RIU, which is consistent with the measurement result for a salt solution. In summary, we have demonstrated an ultra-small optical sensor by using a suspended-silicon submicron-disk resonator sitting on an SiO 2 pedestal. An asymmetrical suspended rib waveguide is introduced to work as the access waveguide of the suspended submicron-disk resonator, so that it is convenient to couple light into/out from the resonator. We have designed and fabricated a suspended submicron-disk sensor with R 0.8 μm, which has a very high extinction ratio (>30 db) and a moderate Q-value ( 10 2 ). It also has an ultra-large FSR so that a large measurement range is available. The present submicron-disk sensor has been used to measure the concentration of NaCl aqueous solutions and some References 1. R. Soref, IEEE J. Sel. Top. Quantum Electron. 12, 1678 (2006). 2. D. X. Xu, A. Densmore, A. Delâge, P. Waldron, R. McKinnon, S. Janz, J. Lapointe, G. Lopinski, T. Mischki, E. Post, P. Cheben, and J. H. Schmid, Opt. Express 16, (2008). 3. Z. Xia, Y. Chen, and Z. Zhou, IEEE J. Quantum Electron. 44, 100 (2008). 4. Q. Xu, B. Schmidt, S. Pradhan, and M. Lipson, Nature 435, 325 (2005). 5. D.-X. Xu, A. Densmore, P. Waldron, J. Lapointe, E. Post, A. Delâge, S. Janz, P. Cheben, J. H. Schmid, and B. Lamontagne, Opt. Express 15, 3149 (2007). 6. T. Lei and A. W. Poon, Opt. Express 19, (2011). 7. J. Wang and D. Dai, Opt. Lett. 35, 4229 (2010). 8. Q. Xu, D. Fattal, and R. G. Beausoleil, Opt. Express 16, 4309 (2008). 9. K. Yao and Y. Shi, Opt. Express 20, (2012). 10. S. H. Mirsadeghi, E. Schelew, and J. F. Young, Appl. Phys. Lett. 102, (2013). 11. H. Lee, T. Chen, L. Jiang, K. Y. Yang, S. Jeon, O. Painter, and K. J. Vahala, Nat. Photonics 6, 369 (2012). 12. M. Soltani, Q. Li, S. Yegnanarayanan, and A. Adibi, Opt. Express 18, (2010). 13. J. Shainline, S. Elston, Z. Liu, G. Fernandes, R. Zia, and J. Xu, Opt. Express 17, (2009). 14. M. Borselli, T. J. Johnson, and O. Painter, Appl. Phys. Lett. 88, (2006). 15. S. Koseki, B. Zhang, K. De Greve, and Y. Yamamoto, Appl. Phys. Lett. 94, (2009). 16. P. Rabiei, W. H. Steier, C. Zhang, and L. R. Dalton, J. Lightwave Technol. 20, 1968 (2002). 17. C.-Y. Chao and L. Guo, J. Lightwave Technol. 24, 1395 (2006). 18. Z. Wang, Y. Tang, L. Wosinski, and S. He, IEEE Photon. Technol. Lett. 22, 1568 (2010). 19. K. De Vos, I. Bartolozzi, E. Schacht, P. Bienstman, and R. Baets, Opt. Express 15, 7610 (2007). 20. I. M. White and X. Fan, Opt. Express 16, 1020 (2008). 21. W. Liang, Y. Huang, Y. Xu, R. K. Lee, and A. Yariv, Appl. Phys. Lett. 86, (2005). 22. C. Kim and C. Su, Meas. Sci. Technol. 15, 1683 (2004). 181

185 High-sensitivity liquid refractive-index sensor based on a Mach-Zehnder interferometer with a double-slot hybrid plasmonic waveguide Xu Sun, 1,2,* Daoxin Dai, 2,3 Lars Thylén, 1,2,4,5 and Lech Wosinski 1,2 1 School of Information and Communication Technology, KTH Royal institute of Technology, , Kista, Sweden 2 JORCEP, Joint Research Center of Photonics of the Royal Institute of Technology (Sweden) and Zhejiang University, China 3 Centre for Optical and Electromagnetic research, State Key Laboratory for Modern Optical Instrumentation, Zhejiang University, Zijingang Campus, Hangzhou, , China 4 Dept. of Theoretical Chemistry and Biology, KTH Royal Institute of Technology, Stockholm, Sweden 5 Hewlett-Packard Laboratories, Palo Alto, CA 94304, USA * xus@kth.se Abstract: A Mach-Zehnder Interferometer (MZI) liquid sensor, employing ultra-compact double-slot hybrid plasmonic (DSHP) waveguide as active sensing arm, is developed. Numerical results show that extremely large optical confinement factor of the tested analytes (as high as 88%) can be obtained by DSHP waveguide with optimized geometrical parameters, which is larger than both, conventional SOI waveguides and plasmonic slot waveguides with same widths. As for MZI sensor with 40 m long DSHP active sensing area, the sensitivity can reach as high value as 1061nm/RIU (refractive index unit). The total loss, excluding the coupling loss of the grating coupler, is around 4.5dB Optical Society of America OCIS codes: ( ) Integrated optics; ( ) Sensors; ( ) Waveguides. References and links 1. S. Balslev, A. M. Jorgensen, B. Bilenberg, K. B. Mogensen, D. Snakenborg, O. Geschke, J. P. Kutter, and A. Kristensen, Lab-on-a-chip with integrated optical transducers, Lab Chip 6(2), (2006). 2. J. Wang and D. Dai, Highly sensitive Si nanowire-based optical sensor using a Mach-Zehnder interferometer coupled microring, Opt. Lett. 35(24), (2010). 3. Q. Liu, X. Tu, K. W. Kim, J. S. Kee, Y. Shin, K. Han, Y. Yoon, G. Lo, and M. K. Park, Highly sensitive Mach- Zehnder interferometer biosensor based on silicon nitride slot waveguide, Sens. Actuators B Chem. 188, (2013). 4. F. Prieto, B. Sepulveda, A. Calle, A. Llobera, C. Domynguesz, A. Abad, A. Montoya, and L. M. Lechuga, An integrated optical interferometric nanodevice based on silicon technology for biosensor applications, Nanotechnology 14(8), (2003). 5. A. Densmore, D.-X. Xu, P. Waldron, S. Janz, P. Cheben, J. Lapointe, A. Delge, B. Lamontagne, J. H. Schmid, and E. Post, A silicon-on-insulator photonic wire based evanescent field sensor, IEEE Photonics Technol. Lett. 18(23), (2006). 6. J. Gonzalo Wangüemert-Pérez, P. Cheben, A. Ortega-Moñux, C. Alonso-Ramos, D. Pérez-Galacho, R. Halir, I. Molina-Fernández, D. X. Xu, and J. H. Schmid, Evanescent field waveguide sensing with subwavelength grating structures in silicon-on-insulator, Opt. Lett. 39(15), (2014). 7. L. Jin, M. Li, and J. He, Highly-sensitive silicon-on-insulator sensor based on two cascaded micro-ring resonators with vernier effect, Opt. Commun. 284(1), (2011). 8. H. Li and X. Fan, Characterization of sensing capability of optofluidic ring resonator biosensors, Appl. Phys. Lett. 87(1), (2010). 9. H. Yamada, T. Chu, S. Ishida, and Y. Arakawa, Si photonic wire waveguide device, IEEE J. Sel. Top. Quantum Electron. 12(6), (2006). 10. Q. Xu, V. R. Almeida, R. R. Panepucci, and M. Lipson, Experimental demonstration of guiding and confining light in nanometer-size low-refractive-index material, Opt. Lett. 29(14), (2004). 11. F. Qiu, A. M. Spring, D. Maeda, M. Ozawa, K. Odoi, A. Otomo, I. Aoki and S. Yokoyama, A hybrid electrooptic polymer and TiO2 double-slot waveguide modulator, Sci. Rep. 5, 8561 (2015). 12. G. D. Osowiecki, E. Barakat, A. Naqavi, and H. P. Herzig, Vertically coupled plasmonic slot waveguide cavity for localized biosensing applications, Opt. Express 22(17), (2014). 13. M. Z.Alam, J. Meier, J. S. Aitchison, and M.Mojahedi, Super mode propagation in Low Index Medium, in CLEO/QELS (OSA, 2007), paper JThD112. # Received 8 Jul 2015; revised 24 Aug 2015; accepted 16 Sep 2015; published 22 Sep 2015 (C) 2015 OSA 5 Oct 2015 Vol. 23, No. 20 DOI: /OE OPTICS EXPRESS

186 14. R. F. Oulton, V. J. Sorger, D. A. Genov, D. F. P. Pile, and X. Zhang, A hybrid plasmonic waveguide for subwavelength confinement and long-range propagation, Nat. Photonics 2(8), (2008). 15. D. Dai, Y. Shi, S. He, L. Wosinski, and L. Thylen, Silicon hybrid plasmonic submicron-donut resonator with pure dielectric access waveguides, Opt. Express 19(24), (2011). 16. F. Lou, D. Dai, L. Thylen, and L. Wosinski, Design and analysis of ultra-compact EO polymer modulators based on hybrid plasmonic microring resonators, Opt. Express 21(17), (2013). 17. F. Lou, L. Thylen, and L. Wosinski, Ultra-sharp Bends Based on Hybrid Plasmonic Waveguides, 40th European Conference ECOC, Cannes, France, Sept , D. Dai and S. He, Low-loss hybrid plasmonic waveguide with double low-index nano-slots, Opt. Express 18(17), (2010). 19. S. Choi and J. T. Kim, Vertical coupling characteristics between hybrid plasmonic slot waveguide and Si waveguide, Opt. Commun. 285(18), (2012). 20. L. Lu, F. Li, M. Xu, T. Wang, J. Wu, L. Zhou, and Y. Su, Mode-selective hybrid plasmonic bragg grating reflector, IEEE Photonics Technol. Lett. 24(19), (2012). 21. C. Bohren and D. Huffman, Absorption and Scattering of Light by Small Particle, (Wiley, 1983), Chap D. R. Lide, ed., Handbook of Chemistry and Physics, (CRC, 2008), Chap O. Parriaux and G. J. Veldhuis, Normalized Analysis for the Sensitivity Optimization of Integrated Optical Evanescent-Wave Sensors, J. Lightwave Technol. 16(4), (1998). 24. Y. Tang, Z. Wang, L. Wosinski, U. Westergren, and S. He, Highly efficient nonuniform grating coupler for silicon-on-insulator nanophotonic circuits, Opt. Lett. 35(8), (2010). 25. F. Dell Olio and V. M. N. Passaro, Optical sensing by optimized silicon slot waveguides, Opt. Express 15(8), (2007). 1. Introduction Integrated optical sensors [1], showing the abilities of high sensitivity, miniaturization and mass production, play increasingly important role in chemical and biomedical analyses. Various optical sensing elements, e. g., Mach-Zehnder interferometers (MZI) [2 6], ring or disk resonators [7, 8], Bragg gratings [9], have been proposed and evaluated during the past years. The changes of the guided-mode effective index (n eff), affected either by changing of refractive indices of tested analytes (homogenous sensing) or by thin-layer receptors fixed on the surface of the waveguides (surface sensing), are readout by different optical measurement methods depending on sensor architectures. For most integrated optical sensors, waveguide optimization is the key design task to maximize the sensitivity, e. g. dielectric waveguides [5] and sub-wavelength grating waveguides [6]. Especially sub-wavelength grating waveguides are interesting as the analyte can directly infiltrate the area with high light confinement when the field delocalization is correctly engineered. Slot waveguides, including dielectric slot waveguides [3, 10, 11] and plasmonic slot waveguides [12], have been intensively investigated in order to achieve enhanced optical sensitivity. Differently from conventional Si nanowires, slot waveguides can confine optical mode inside the nano-slot due to high indexcontrast (dielectric slot waveguide) or surface plasmonic enhancement (plasmonic slot waveguide). By optimizing the geometrical parameters, ultra-high sensitivity can be obtained. Compared to dielectric slot waveguides, plasmonic slot waveguides can support subwavelength optical modes, but in the expense of large propagation losses. Hybrid plasmonic (HP) waveguides [13, 14], however, can support a mixture between plasmonic and photonics modes, and allow for sub-wavelength confinement with relative low propagation losses. This has attracted a lot of attention for realizing ultra-compact photonic integrated circuits [15 17]. Additionally, the ultra-high optical confinement factor in the low-index region, due to both, high index contrast and plasmonic enhancement, is also very promising to provide great performances for optical sensing applications. However, in the most often realized HP waveguide geometries [13 18], where the oxide material (e.g. SiO 2) rather than open slot is placed between metal and high refractive index material, only few percent of an optical mode is evanescently confined by the covering analyte, which does not show the capacity of high sensitivity. In this paper, we introduce a novel double-slot HP (DSHP) waveguide with two open nano-slots between a high-index layer (Si ridge) and two metal strips (Ag), which is suitable to be filled with test analytes. Similar structures for other applications have been proposed in [18 20], but not yet been realized experimentally. The present DSHP waveguide supports quasi-te polarization mode and can operate compatibly with conventional SOI optical # Received 8 Jul 2015; revised 24 Aug 2015; accepted 16 Sep 2015; published 22 Sep 2015 (C) 2015 OSA 5 Oct 2015 Vol. 23, No. 20 DOI: /OE OPTICS EXPRESS

187 devices. Highly-efficient grating couplers can be adapted at both ends of the device in order to obtain high coupling efficiency between optical fibers and the sensor chip. In this paper, exhaustive investigations have been made to optimize the optical confinement factor of the region filled by the tested liquids, which show the capability of highly-efficient sensing in sub-wavelength scale. Employing such a DSHP waveguide as a sensing element in one arm of an MZI, optical sensors have been realized with high sensitivity when testing the chemical liquid with different concentrations. Further applications, e. g. ultra-compact highly-efficient electro-optics (EO) modulators to realize high-density optical communication chips and photonic interconnects, have been also discussed. 2. Double-slot hybrid Plasmonic waveguide 2.1 Schematic of the DSHP waveguide Figure 1(a) shows the schematic of the DSHP waveguide, which consists of a SOI nanowire located in the middle of the plasmonic slot waveguide (we use Ag as the plasmonic material in this paper). Two narrow slots between Ag strips and Si nanowire are forming the hybrid guided-modes between photonics (Si-slot materials) and plasmonics (slot materials-ag). Ag tapers are used to perform the photonic to hybrid plasmonic mode conversion. Normally, the width of Si ridge of the DSHP waveguide is narrower than the bus waveguide (SOI waveguide, set to 400nm), hence Si tapers (not shown in this paper) are also applied to connect the bus waveguide to the DSHP waveguide. Fig. 1. (a) Schematic of the double-slot hybrid plasmonic (DSHP) waveguide coupled to SOI waveguides at both ends. (b) Cross-section view of the DSHP waveguide covered by test liquid. The widths of Si ridge and slots are denoted as w Si and w slot, respectively. The silver pads and Si ridge have identical height h WG. (c) Mode profile of the DSHP waveguide, where w slot = 150nm, w Si = 165nm and h WG = 250nm. The covering material is 100% 2-propanol (IPA). The cross-section view is shown in Fig. 1(b): SiO 2 material is used for the buffer layer, and liquid to be tested is covering the waveguide. The heights of the silver strips and the Si ridge are identical and set as h WG = 250nm. The widths of the nano-slot and the Si ridge are denoted as w slot and w Si, respectively. The mode profile is shown in Fig. 1(c), which is accomplished by finite-element-method (FEM)-based software, COMSOL Multiphysics. The geometric parameters are set to: w Si = 165nm, w slot = 150nm and h WG = 250nm. The # Received 8 Jul 2015; revised 24 Aug 2015; accepted 16 Sep 2015; published 22 Sep 2015 (C) 2015 OSA 5 Oct 2015 Vol. 23, No. 20 DOI: /OE OPTICS EXPRESS

188 thicknesses of covering liquids and buffer layers are set as 3 m, so the influences of simulation boundaries can be ignored. In the simulation work, the refractive indices of Si and SiO 2 are and 1.45, respectively, for the operation wavelength of 1550nm. The permittivity of silver is calculated by Durde model [21]: 2 ω p ε = ε 2 ω + jωγ (1) where ε = 3.1, 14 ω = and γ = rad / s. In this paper, the liquids to 14 p rad / s be tested are the aqueous solutions of 2-propanol (IPA), whose refractive indices are taken from [22], as illustrated in Table 1. Table 1. Refractive indices of aqueous solution of 2-propanol [22] C 100% 80% 60% 40% 20% 10% 0 n Due to the high-index contrast (between the Si core region and the IPA cover layer) and plasmonic optical enhancement (Ag-IPA), there is a large interaction between optical mode and the covering material. Next, we will analyze and optimize the optical performance of the described DSHP waveguide with different geometrical parameters. 2.2 Model investigation In order to study the influence of nano-slots, we fixed the w Si with different values (100nm, 200nm, 300nm and 400nm), and gradually increase w slot from 20nm to 200nm. The effective refractive indices (n eff) versus w slot are shown in Fig. 2(a). One can see that the n eff decreases with increasing of w slot, and gradually tends to the value of SOI waveguides without the influences of plasmonic materials, when w slot is large enough (normally larger than 500nm, not shown in this figure). The larger n eff of the DSHP waveguide with narrower slots indicates that the DSHP waveguide provides a larger optical confinement compared with conventional SOI waveguide, however, in the expanse of larger propagation loss, as shown in Fig. 2(b). The trade-off between optical confinement factor and propagation loss in plasmonic and HP waveguides can be chose depending on the applications [14 17]. The optical confinement factor is defined by the power confined in particular area divided by the total power: 2 2 Γ= Exy (, ) dxdy/ Exy (, ) dxdy, (2) area which is a key property of optical waveguide in homogeneous sensing applications [23]: the waveguide sensitivity ( neff / nliquid ) is proportional to the optical confinement factor in tested liquids (IPA in this paper), IPA. As shown in Fig. 2(c), IPA increases with narrower slot (smaller w slot) due to the larger plasmonic optical enhancement. While with larger w slot, the DSHP waveguide tends to SOI waveguide with smaller IPA, and simultaneously, Si increases due to lower influence of Ag, as shown in Fig. 2(d). Besides, the value of IPA is generally larger for DSHP waveguides with smaller w Si, which act similarly as SOI waveguide: the optical mode is less confined in Si, but evanescently confined in covered liquids. However, one can observe from the results of DSHP waveguides with 100nm and 200nm w Si: as for w slot larger than 120nm, IPA of waveguide with w Si = 200nm is larger than the one with w Si = 100nm, this indicates that the tendency of IPA is not simply influenced by a photonics mode, but by some more complicated hybrid influences between photonics and plasmonics, which will be discussed in the following sections. # Received 8 Jul 2015; revised 24 Aug 2015; accepted 16 Sep 2015; published 22 Sep 2015 (C) 2015 OSA 5 Oct 2015 Vol. 23, No. 20 DOI: /OE OPTICS EXPRESS

189 Fig. 2. Performances (effective refractive index, loss and confinement factors) of double-slot hybrid plasmonic waveguides for different widths of Si ridge and slot. (a) Effective refractive index (n eff) changed with slot width (w slot). (b) Loss in the units of db/ m versus w slot. (c) and (d) Confinement factors in covering IPA and Si with different w slot. From the analysis above, IPA of DSHP waveguide is larger than for conventional SOI waveguide, which is caused by both, high index contrast and plasmonic optical enhancement, or in other words, the sensitivity DSHP waveguide is larger due to the proportional relationship between optical confinement factor and sensitivity. However, the results above are based on fixed width of Si ridge, and it is difficult to give an optimized ratio between those two modes. Thus, a q factor, which represents the width ratio of Si nanowire to the total width of DSHP waveguide, q = w Si/w, is defined. One needs to note that when q = 0 or 1, the optical waveguide is typically plasmonic slot waveguide with slot material as IPA or Si. The mode profile of DSHP waveguide with q factors of 0, 0.5 and 1 are shown in Fig. 3(a), (b) and (c), respectively. Figure 3(d) shows the n eff variations with different q values, and when the total widths of DSHP waveguide w changes from 200nm to 700nm with a step of 100nm. The n eff increases with the width ratio of Si ridge (q), which is caused by: (1) the large refractive index of Si causes the high n eff of the propagation mode; (2) with a higher q value, w slot is smaller, which results in a larger IPA as we discussed in Fig. 2(c). The former one is the explanation coming from the aspect ratio of photonics modes, while the latter one is from plasmonic optical enhancement. However, due to the interactions between the two modes, the increase of n eff is more complicated than simple linear growth. As for the propagation loss, as shown in Fig. 3(e), there exist optimized lowest values for DSHP waveguide (0<q<1), when w is larger than 200nm, which is lower than purely plasmonic slot waveguide (q = 0 or 1). Together with the results shown in Fig. 2(b), we can conclude that the propagation loss of DSHP waveguide is higher than conventional SOI waveguide and lower than plasmonic slot waveguide, which indicates that the mode confined # Received 8 Jul 2015; revised 24 Aug 2015; accepted 16 Sep 2015; published 22 Sep 2015 (C) 2015 OSA 5 Oct 2015 Vol. 23, No. 20 DOI: /OE OPTICS EXPRESS

190 in DSHP waveguide is a mixture between loss-less photonics and lossy plasmonic modes. Additionally, similarly to other types of plasmonic waveguides, with a wider width of the waveguide, the propagation loss is lower, which can be explained by the fact that the influence of plasmonic material (silver in this paper) is significantly reduced, when the effective area of confined mode is larger. When w decreases down to 200nm, the conventional Si nanowire hardly supports photonics mode due to diffraction limit, and the DSHP waveguide acts similarly to plasmonic slot waveguide (plasmonic mode dominates the propagation), without optimized value for loss. Fig. 3. (a), (b) and (c) mode profiles of 300nm wide DSHP waveguide with Si width ratio (q) of 0, 0.5 and 1, respectively. (d) and (e) n eff and loss (db/ m) versus q factor. (f), (g) and (h) confinement factors in covering 2-propanol ( IPA), slot ( slot) and Si ridge ( Si) with different q factors. n eff and values are given for widths of DSHP waveguide w from 200nm to 700nm with a step of 100nm. Figure 3(f) shows the optical confinement factors of covering IPA material. Similarly to propagation loss, optimized IPA values can be obtained, which can reach as high as 88% confinement for the DSHP waveguide with the width of 200nm. Special attention needs to be paid, when the width of the DSHP goes down to 200nm, the optimized q factor still exists, which is different from the analysis of propagation loss in Fig. 3(d). That is to say that even though photonic mode disappears when the waveguide dimension decreases below diffraction limit, the high-index of Si material can also play a role in increasing the IPA. Moreover, the confinement factors of the nano-slot ( slot) (the optical power concentrated in the slot), shown in Fig. 3(g), are also investigated, which are about 10% lower than respective IPA, that includes, both slot and top IPA layer. This means that the most of optical field is concentrated in the nano-slot and the remaining 10% is leaking to the top IPA layer # Received 8 Jul 2015; revised 24 Aug 2015; accepted 16 Sep 2015; published 22 Sep 2015 (C) 2015 OSA 5 Oct 2015 Vol. 23, No. 20 DOI: /OE OPTICS EXPRESS

191 (similar amount is also leaking to the SiO 2 substrate). In the further discussion about the electro-optics (EO) modulator we will consider the values for slot. The confinement factors of Si ( Si) changes inversely proportional compared to IPA and slot, as shown in Fig. 3(h). Summarizing the analysis above, we can conclude that DSHP waveguide has better performance in the aspects of propagation loss and sensitivity than pure plasmonic slot waveguide. The optimized q factors for propagation and sensitivity are different, which need careful design to satisfy the requirement of particular applications. 3. Experimental results As we discussed above, the guided-mode of the DSHP waveguide is extremely sensitive to the refractive index change of the tested liquids, which results in a phase change. In order to transfer the phase change into measureable intensity signals, resonant cavities (like ring/disk resonators or MZIs), can be used. In this paper, we design and fabricate an MZI with a DSHP waveguide as an active sensing arm to experimentally evaluate the performance of the DSHP waveguide for homogenous sensing. Fig. 4. Characterization setup and schematic of the Mach-Zehnder Interferometer employing double-slot hybrid plasmonic waveguide as a sensing arm. Two grating couplers are fabricated at each end of the device, which are used for coupling light from/to optical fiber. The subfigure shows the details of the sensing area, which contains taper designs for both Ag pads and Si ridge. 3.1 MZI sensor with a DSHP waveguide The designed MZI employing a DSHP waveguide in one arm as an active sensing area is shown in Fig. 4. Due to the notable propagation loss introduced by the sensing arm, an asymmetric Y-splitter is applied to improve extinction ratio. The Y-splitter is composed of a straight and S-shaped bent wires with bending radius of 5 m (denoted as r ref), which are connected at the input/output ends. Compared to typical 3dB splitter, the designed Y-splitter is estimated to give more optical power to the sensing arm, which can compensate the coupling and propagation losses of the DSHP waveguide sensing area. The length of the reference arm, L ref, is 67 m with a width of 400nm (w ref = 400nm). As for the sensing arm, the DSHP sensing area is inserted between the input and output SOI waveguides, which have the same widths as the reference arm. The lengths of the input and output SOI waveguides, # Received 8 Jul 2015; revised 24 Aug 2015; accepted 16 Sep 2015; published 22 Sep 2015 (C) 2015 OSA 5 Oct 2015 Vol. 23, No. 20 DOI: /OE OPTICS EXPRESS

192 L input and L output, are both 20 m. Si tapers are used as the couplers between the SOI waveguides and the DSHP waveguide sensing area, as shown in the sub-figure. As for the sensing area, two Ag pads are put aside the Si ridge to form the DSHP waveguide, and the tapers of Ag pads are used to decrease the coupling loss from SOI waveguide to DSHP waveguide. Taking into account optical confinement factor, propagation loss and fabrication difficulties, the parameters for the DSHP waveguide are chosen as: w Si = 165nm and w slot = 150nm (w = 465nm and q = 0.355), which will give about 78% IPA and 0.01dB/ m propagation loss according to the simulation results shown in Fig. 3. The length of the DSHP waveguide is varied from 20 m to 40 m with a step of 10 m, which is denoted as L DSHP. One should notice that when the length of the DSHP waveguide decreases, a part of Si ridge with 165nm width will be without metal on both sides, which will also support optical propagation with a relative large loss (near cut-off width). The length of this part is denoted as L ridge, which ranges from 15 m to 5 m depending to the length of the DSHP waveguide. The total effective length difference between the two arms is then: Δ l = n (2π r + L 2 L ) 2 n ( ldl ) 2 n ( ldl ) n L, eff eff, ref ref ref in eff, taper eff, ridge eff, DSHP DSHP Ltaper Lridge (3) where n eff,ref and n eff,dshp are the effective refractive indices of the reference Si nanowire with 400nm widthand the DSHP waveguide, respectively. n eff,taper(l) and n eff,ridge(l) are the effective refractive indices of Si tapers and the Si ridges with Ag tapers at different positions. 3.2 Fabrication and measurement setup The fabrication process starts from commercial Silicon-on-insulator (SOI) wafer with 250nm crystalline Si on top of 3 m thick SiO 2 buffer layer. After patterning the Si structure with e- beam lithography (EBL), Inductively Coupled Plasma (ICP) dry etching with 10% over etch is performed, which is processed by C 4F 8-SF 6 gas mixture under low temperature (~10 C). Then, after removal of e-beam resist, the second E-beam exposure and etching process are performed to fabricate the highly efficient non-uniform grating couplers [24]. The etching depth is around 80nm. Finally, the pattern of silver pads is introduced by the third E-beam exposure. After patterning, 20nm Ti and 230nm Ag layers are evaporated by metal evaporation tool, where the Ti layer is used to increase the adhesive strength between silver and substrate material (SiO 2). Then, metal lift-off process is used to open the silver pads. The optical characterization is carried out by grating coupler setup: an input optical fiber connected to continuous wave (CW) tunable laser with wavelength range of nm is placed above the grating coupler at one end of a tested device; another optical fiber connected to optical spectrum analyzer (OSA) is placed at the other end of the device. Polarization controller is also used before input into the device, to achieve the characterization with only TE mode. The test liquids (different concentrations of IPA in water) are directly dropped onto the surface of the tested sample. The transmission response of the tested device is then obtained after adjusting the positions of input and output optical fibers. # Received 8 Jul 2015; revised 24 Aug 2015; accepted 16 Sep 2015; published 22 Sep 2015 (C) 2015 OSA 5 Oct 2015 Vol. 23, No. 20 DOI: /OE OPTICS EXPRESS

193 3.3 Characterization results Fig. 5. SEM top view of fabricated device with added monochrome color to enhance contrast. The sub-figure is the close-view of the double-slot hybrid plasmonic waveguide. The widths of Si ridge and slots are 165nm and 150nm, respectively. The white bright elements with tapers are Ag pads (w Ag = 1μm). The scanning electron microscope (SEM) top-view of the MZI sensor is shown in Fig. 5. False monochrome color is added to the picture in order to enhance contrast. The lower redwire is Si reference arm, with a width of 400nm, and the upper narrower one is Si ridge of DSHP waveguide (w Si = 165nm). The white bright elements with tapers are Ag pads (w Ag = 1μm). The black substrate is SiO 2 buffer layer. Grating couplers (not shown in the figure) are placed at each end of the sensor and give around 50% coupling efficiency (estimated result) between optical fiber and the device. The measurement is accomplished by infiltrating the fabricated sample with different concentrations of IPA. Figure 6 (a) shows the measured transmission response of MZI sensor with 30 m long DSHP waveguide covered by 100% (black curves) and 60% IPA in water (red curves). The refractive indices of 100% and 60% IPA are and [22], respectively. The reference level is the transmission response of the straight waveguide with input/output grating couplers, which is normalized to 0dB (green dashed line). Sinusoidal fitting curves are applied in order to clearly show the transmission properties. One can see that the resonant wavelength ( res) of MZI sensor decreases with the refractive indices of the covering material (from 100% to 60% IPA), which can be easily understood by the basic principles of MZI sensor, where the resonant wavelength, res = l eff/m, is proportional to the effective length difference. When the refractive index of the covering material decreases, the effective refractive indices of the elements in sensing arm will decrease more than those in the reference arm (due to higher sensitivity of the DSHP waveguide), which will consequently lead to the decreasing of the effective length difference, according to Eq. (3). Hence, the resonant wavelength res will shift to the left (shorter wavelengths) when covered with lower refractive index material. The free-spectral-range (FSR) of the interferometer is about 10nm, and the extinction ratio is around 5dB, when infiltrated with 100% IPA. Compared to the reference level (grating coupler, 0dB), the total loss, excluding the grating coupler loss, is about 4.5dB. # Received 8 Jul 2015; revised 24 Aug 2015; accepted 16 Sep 2015; published 22 Sep 2015 (C) 2015 OSA 5 Oct 2015 Vol. 23, No. 20 DOI: /OE OPTICS EXPRESS

194 Fig. 6. (a) Output power of the DSHP MZI sensor. The reference level (green) is the transmission response of the straight waveguide with input/output grating couplers, which is normalized to 0dB. The black and red dashed curves are measured results when the sensor is infiltrated with 100% 2-propanol and 60% 2-propanol, respectively. Solid curves are sinusoidal fitting curves according to the measured results. (b) Normalized output power of the MZI sensor with 30 m long DSHP waveguide for different IPA concentrations. Figure 6(b) shows the normalized output powers of the MZI sensor with 30 m long DSHP waveguide. The different color curves are the measured results for various concentrations of IPA in water (ranges from 100% to 10%). From the fitted sinusoidal curves for the MZI's responses, one can easily read the resonant wavelengths for the tested liquid with different concentrations and the sensitivity is given by λres λ n res eff S = =, (4) n n n liquid eff liquid where λres / neff is the resonant wavelength shift produced by the MZI sensor when the effective refractive index of sensing waveguide is changed, which is depended on the architecture of the designed sensors; the neff / nliquid is the sensitivity of the sensing waveguide, which is proportional to the optical confinement factor of covering liquids, as we discussed in the former sections. Figures 7(a)-7(c) show the transmission responses of the MZI sensors with 20 m, 30 m and 40 m-long DSHP waveguides respectively covered with 100% (black curves) and 60% IPA (red curves). One can clearly observe that the wavelength shifts are increased with the length of DSHP waveguide, which ranges from 1.2nm (for the design with a 20 m-long DSHP waveguide) to 6.4nm (for the design with a 40 m-long DSHP waveguide). Figure 7(d) shows the wavelength shifts versus refractive index of covering liquids (100% to 10% IPA). The corresponding sensitivities read from fitting lines are 153nm/RIU, 406nm/RIU and 1061nm/RIU. By simulating the n eff differences of Si ridge and DSHP waveguide merged in 100% and 60% IPA ( n eff,ridge = and n eff, DSHP = ), without consideration of the phase-shift provided by Si and DSHP tapers, the phase change of the sensing arm with and without 40 m DSHP waveguide is 0.23 (2 ) and 0.04 (2 ), respectively. In the experimental results, the large difference of phase changes is demonstrated. However, the phase changes are not only provided by the n eff differences of the sensing arm, but also provided by: the phase shifts caused by DSHP and Si tapers, the dispersion of MZI sensor, fabrication roughness and alignment error of Ag pads, which altogether result in a larger phase-shift, about 0.55 (2 ) for 40 m DSHP waveguide, than the estimated results. # Received 8 Jul 2015; revised 24 Aug 2015; accepted 16 Sep 2015; published 22 Sep 2015 (C) 2015 OSA 5 Oct 2015 Vol. 23, No. 20 DOI: /OE OPTICS EXPRESS

195 Fig. 7. (a), (b) and (c) wavelength shifts with 100% IPA and 60% IPA for different lengths (20 m, 30 m and 40 m) of the double-slot hybrid plasmonic (DSHP) waveguide sensing area. (d) wavelength shift versus refractive index of test liquids, linear fittings are used to calculate the sensitivity of MZI sensors. 4. Potential application of the DSHP waveguide for an EO modulator Besides the optical liquid sensor application, the present structure is also a promising solution for an ultra-compact highly-efficient optical modulator when the nano-slots are filled with an active nonlinear material. Particularly, for EO modulators, the plasmonic material (silver or gold) pads can be also used as electrodes, which will provide a strong electric field even with low bias voltage because of the narrow distance between two metal pads. Differently from optical sensors, the modulation efficiency of an EO modulator depends on the interaction between optical and modulating radiofrequency (RF) signals. Normally, only the optical confinement factor of materials filled into the nano-slot ( slot) dominants the performance of an EO modulator. As we discussed in Fig. 3, the slot can reach as high value as 75% (w = 200nm, q = 0.75), which is about 10% higher than plasmonic slot waveguide, and 25% higher than Si slot waveguides [25]. Additionally, the adjustable performances of the DSHP waveguide (propagation loss and sensitivity) provide solutions for different qualities of EO polymers. For example, if the EO polymer has large nonlinear coefficient (r 33), a relative compact DSHP waveguide can be designed in order to increase the eficiency, reduce the power consumption and the device size. Vice versa, one can also get enough phase modulation by prolonging the DSHP waveguide with acceptable propagation loss, when low nonlinear coefficient (r 33) EO polymers are used. 5. Conclusion In this paper, we have theoretically and experimentally evaluated the performances of the DSHP waveguide in the application to homogeneous sensing. First, we have done numerical simulation and shown that the present DSHP waveguide has better sensitivity than SOI waveguide with the same width of Si ridge. The optical confinement factor for the region with # Received 8 Jul 2015; revised 24 Aug 2015; accepted 16 Sep 2015; published 22 Sep 2015 (C) 2015 OSA 5 Oct 2015 Vol. 23, No. 20 DOI: /OE OPTICS EXPRESS

196 the covering material (proportional to waveguide sensitivity), IPA, increases with narrower w slot. The factor IPA can reach as high as 90%, when w slot = 20nm and w Si = 100nm, however, in the expense of large propagation loss (0.1 db/ m). Further optimizations have been made by tuning the Si ridge ratio, q = w Si/w, from 0 to 1, as shown in Fig. 3 (d)-3(h). Results show that the DSHP waveguide has lower propagation loss as well as higher optical confinement factor IPA than a pure plasmonic slot waveguide, when the waveguide width is larger than 200nm, where hybrid photonic-plasmonic modes can be supported. We have shown that high sensitivity waveguide with acceptable propagation loss can be obtained by careful design. Generally, within the width ranges from 200nm to 700nm, the propagation loss can be as low as 0.001dB/ m (w = 700nm, q = 0.65), while the optical confinement factor of covering material can reach as high value as 85% (w = 200nm, q = 0.5), depending on the requirements of the device size and sensitivity. After the theoretical evaluation of the DSHP waveguide, we have designed and fabricated an MZI architecture employing a DSHP waveguide as an active sensing arm. The geometrical parameters of the DSHP waveguide are: w Si = 165nm and w slot = 150nm ( IPA 78% and Loss 0.01dB/ m according to simulation results). Grating couplers are used to couple light from optical fiber to the device and back to fiber, which have a coupling efficiency around 50%. Experimental results show that the sensitivity increases dramatically with the length of the DSHP waveguide: as for MZI with 40 m DSHP waveguide, the sensitivity can reach as high value as 1061nm/RIU. Further discussions on optical modulators, especially on EO modulator, have been done, where we discussed the advantages of the DSHP waveguide in the applications for optical modulator: (1) large sensitivity to slot materials (large slot); (2) adjustable waveguide performance for different quality of nonlinear polymer; (3) good interaction between RF mode and optical mode of EO modulators (plasmonic material pads can be used for electrodes). Acknowledgments This work was supported by the Swedish Research Council (VR) through its Linnæus Center of Excellence ADOPT. Xu Sun acknowledges China Scholarship Council (CSC) for the financial support. # Received 8 Jul 2015; revised 24 Aug 2015; accepted 16 Sep 2015; published 22 Sep 2015 (C) 2015 OSA 5 Oct 2015 Vol. 23, No. 20 DOI: /OE OPTICS EXPRESS

197 Photonics 2015, 2, ; doi: /photonics Article OPEN ACCESS photonics ISSN Double-Slot Hybrid Plasmonic Ring Resonator Used for Optical Sensors and Modulators Xu Sun 1,2, *, Daoxin Dai 2,3, Lars Thylén 1,2,4,5 and Lech Wosinski 1,2 1 School of Information and Communication Technology, KTH Royal Institute of Technology, , Kista, Sweden; s: lthylen@kth.se (L.T.); lech@kth.se (L.W.) 2 JORCEP, Joint Research Center of Photonics of the Royal Institute of Technology (Sweden) and Zhejiang University (China), Hangzhou, , China; dxdai@zju.edu.cn 3 Centre for Optical and Electromagnetic research, State Key Laboratory for Modern Optical Instrumentation, Zhejiang University, Zijingang Campus, Hangzhou, , China 4 Department of Theoretical Chemistry and Biology, KTH Royal Institute of Technology, Stockholm, Sweden 5 Hewlett-Packard Laboratories, Palo Alto, CA 94304, USA * Author to whom correspondence should be addressed; xus@kth.se; Tel.: Received: 15 October 2015 / Accepted: 19 November 2015 / Published: 25 November 2015 Abstract: An ultra-high sensitivity double-slot hybrid plasmonic (DSHP) ring resonator, used for optical sensors and modulators, is developed. Due to high index contrast, as well as plasmonic enhancement, a considerable part of the optical energy is concentrated in the narrow slots between Si and plasmonic materials (silver is used in this paper), which leads to high sensitivity to the infiltrating materials. By partial opening of the outer plasmonic circular sheet of the DSHP ring, a conventional side-coupled silicon on insulator (SOI) bus waveguide can be used. Experimental results demonstrate ultra-high sensitivity (687.5 nm/riu) of the developed DSHP ring resonator, which is about five-times higher than for the conventional Si ring with the same geometry. Further discussions show that a very low detection limit ( RIU) can be achieved after loaded Q factor modifications. In addition, the plasmonic metal structures offer also the way to process optical and electronic signals along the same hybrid plasmonic circuits with small capacitance (~0.275 ff) and large electric field, which leads to possible applications in compact high-efficiency electro-optic modulators, where no extra electrodes for electronic signals are required. 194

198 Photonics 2015, Keywords: integrated optics; waveguides; plasmonic 1. Introduction The possibilities of miniaturization, mass production, low power consumption and wide bandwidth cause photonic integrated circuits (PICs) [1] to play an increasingly important role in various applications. In particular, for electro-optic (EO) polymer-based optical modulators and refractive index (homogenous) sensors, the waveguide sensitivity to refractive index changes is one of the vital parameters. Many waveguide structures, including dielectric waveguides [2 12], subwavelength grating waveguides [13], hollow core waveguides [14], dielectric slot waveguides [15 19] and plasmonic slot waveguides [20], have been designed and optimized to increase the optical confinement factor of covering or infiltrating materials and, hence, to increase sensitivity. In contrast to dielectric- and subwavelength grating waveguide-based sensors (evanescent optical sensing), slot waveguides or hollow core waveguides can confine optical power in the narrow slots or hollow cores, which leads to large optical sensitivity to materials infiltrating the waveguides. In the following, we have limited our investigations to slot waveguides. The principles of slot-guiding waveguides are different from ordinary index guiding: for a dielectric slot waveguide, the optical confinement is provided by the special high-low-high indices structures, where the large index-contrast makes the optical power propagate in the low index slot; for the plasmonic slot waveguide, confinement is achieved by plasmonic optical enhancement, where optical energy is excited and propagated at the surface of metal layers. Generally speaking, plasmonic slot waveguides have better optical confinement than dielectric slot waveguides, due to the ultra-compact size, however, at the expense of larger propagation loss. To combine the advantages of both dielectric and plasmonic slot waveguides, a double-slot hybrid plasmonic (DSHP) waveguide, a novel high optical confinement, low propagation loss waveguide, has been developed [21,22]. The DSHP waveguide structure shows the advantages of low propagation loss, high optical confinement and a fabrication process compatible with conventional silicon on insulator (SOI) technologies. In [22], a DSHP Mach-Zehnder Interferometer (MZI) resonant sensor is experimentally demonstrated. In this paper, we continue our work on the investigation of the DSHP waveguides using here ring resonator structures. In comparison to MZI resonant cavities, the ring resonator has a better quality factor, which will give a smaller detection limit for optical sensor applications and can also decrease the power consumption for electro-optic (EO) modulators. In this paper, based on detailed simulation investigations, a Si bus waveguide side-coupled DSHP ring is designed, fabricated and characterized, showing the potential of applications in highly-efficient optical homogenous sensors and in EO polymer-based modulators. 2. Double-Slot Hybrid Plasmonic Ring 2.1. Schematic and Simulation Method As shown in Figure 1a, the DSHP ring resonator consists of a Si ring located between Ag (or other plasmonic material) circular sheets. When the slots between the Ag sheets and Si ring are narrow enough 195

199 Photonics 2015, (less than 500 nm), the quasi-transverse electric (TE) hybrid photonics (Si-slot materials) and plasmonic (slot material-ag) guided mode can be supported. In the ring structure, it is propagating as the known whispering-gallery mode. Figure 1. (a) Schematic of a double-slot hybrid plasmonic ring resonator; (b) x-z plane cross-section view; (c) power distribution of the x-z plane cross-section simulated by the axisymmetric finite element method. IPA, 2-isopropanol. The x-z cross-section view is shown in Figure 1b. SiO2 is used as the buffer layer, and liquids to be tested (or electro-optic polymer) are filling the slots and covering the device (infiltrating the device). The radius of the DSHP ring r is equal to the middle radius of the Si ring, as shown in Figure 1b. The width of the Si ring is denoted by wsi; the heights of the Si and metal layers are identical and denoted by hwg; the widths of the slots are wslot, and w is the total width (w = wsi + 2wslot). The power distribution of the simulated DSHP ring is shown in Figure 1c using the axisymmetric finite element method (FEM) [23], where the commercial simulation software, COMSOL Multriphysics, is used to solve the partial differential equation in cylindrical coordinates. The geometrical parameters are: hwg = 250 nm, wsi = 300 nm and wslot = 150 nm. The refractive indices of Si and SiO2 are 3.45 and 1.45, respectively, for the operation wavelength of 1550 nm. The infiltrating material is pure 2-isopropanol (IPA), whose refractive index is [24] at 1550 nm. The properties of Ag are calculated by the Drude model [25]: where 3.1, 2.2. Model Investigation 14 p rad/s and 2 p 2 j rad/s. The model investigations start from the generalized analysis of the quality factors (Q factors) of the DSHP ring with various widths of the slots, as shown in Figure 2a. The geometrical parameters of the DSHP ring are: wsi = 350 nm and hwg = 250 nm. In the simulation process, the resonant wavelength is fixed around 1550 nm, and the azimuthal numbers (m) are changed from 15 to 55 with a step of five. The radii of the DSHP ring are adjusted according to the resonant condition of whispering-gallery mode: 2 r m / neff (2) (1) 196

200 Photonics 2015, The Q factor is calculated by: f (real) (3) eig Q 2 f eig (imag) where feig(real) and feig(imag) are the real and imaginary parts of the eigenvalue of the m-th order whispering-gallery mode, which can be directly readout from the simulation software. Without considering the coupling loss, the Q factor of the DSHP ring is influenced by absorption and radiation losses [26], which can be written as: (4) Q Q Q abs Here, Qabs and Qrad are the absorption and radiation quality factors of the ring, respectively. As shown in the figure, the Q factor increases with the radius due to lower radiation loss; when the radius is large enough (larger than 6 μm), the radiation loss can be ignored, while the initial properties of the DSHP waveguide (absorption loss) play a more significant role in the Q factor, which tends to a constant value for specific geometrical parameters. In addition, the Q factor of the DSHP ring with wider slots is larger, which means that the absorption loss of the DSHP waveguide with wider slots is smaller due to lower plasmonic material influence. Summarizing the information given above, the absorption loss (or Qabs factor) is the major property of a DSHP ring with a large enough radius. In order to study the Qabs factor of the DSHP ring, one can fix the radius of the DSHP ring at 6 μm (radiation loss can be ignored) and change the geometry of the DSHP waveguide. In this way, the normal FEM simulation method can be used to study the properties of a DSHP waveguide per se. Since the hybrid propagation mode is a mixture between photonic and Surface Plasmon Polariton (SPP) modes, a q-parameter (q = wsi/w), representing the occupancy of a photonic mode, is used to study and optimize the performance of the DSHP ring resonator. Figure 2b shows the Qabs factor versus the q-parameter, when the total width of the DSHP ring is changed from 500 nm to 1000 nm. The Qabs factor is estimated by: Q n c rad g abs (5) where ng is the group index of the confined whispering-gallery mode, which is expressed by: dneff ( real) ng neff( real) (6) d neff(real) is the real part of effective refractive index. The dispersion of neff, dneff ( real)/ d, is computed by re-simulating the DSHP waveguide with a wavelength of, and the neff at can be obtained, which is denoted as n ( ). eff 197

201 Photonics 2015, Figure 2. (a) Q factor versus the radius of the double-slot hybrid plasmonic (DSHP) ring resonator with various widths of the slots (150 nm, 250 nm and 350 nm); the other geometrical parameters are: wsi = 350 nm and hwg = 250 nm; (b,c,d) the Qabs factor, effective refractive index and sensitivity changes with the q-parameter for waveguides with a total width w of 500 nm, 600 nm, 700 nm, 800 nm, 900 nm and 1000 nm. Then, the dispersion can be estimated by: dneff ( real) neff ( ) neff ( ) d α in Equation (5) is the absorption coefficient, which can be written as: 4 neff ( imag) (8) where neff(imag) is the imaginary part of effective refractive index. After simulating the DSHP waveguide, the Qabs factors versus the q-parameter are calculated according to Equation (5), as shown in Figure 2b, where the total widths of the DSHP waveguide are changed from 500 nm to 1000 nm with a step of 100 nm. One can observe that the Qabs factor of the DSHP ring decreases with a smaller width due to the larger influence of the plasmonic layers in the narrower DSHP waveguide. For the DSHP rings with the same total width, there are optimal values of (7) 198

202 Photonics 2015, the q-parameter giving the maximum Qabs factor, which expresses the hybrid propagation modes of the DSHP ring, where the propagation loss is much lower than that of a pure plasmonic slot waveguide (when q is equal to either zero or one). Values of neff versus the q-parameter for different total widths are shown in Figure 2c. The neff increases with the occupancy of the slot by the Si ring (increase of q), which needs to be explained from two aspects: (1) the high refractive index of Si has greater influence and causes higher neff of the DSHP waveguide; and (2) with the higher q-parameter, wslot of the DSHP ring is small, and so, the optical confinement is larger. The former explanation concerns the photonic mode, and the latter one concerns the plasmonic optical enhancement. The interaction between photonic and plasmonic modes leads to the nonlinear behavior of neff. In addition to the basic studies of the DSHP ring, we also analyze its sensitivity to infiltrating materials. The sensitivity is given by: where n res eff S / n n n cover res is the resonant wavelength shift and ncover ncover g cover (9) is the refractive index change of infiltrating materials ( is set to be in the simulation); Δneff is the change of effective indices of the DSHP waveguide infiltrated with different materials. As shown in Figure 2d, the sensitivity of the narrower waveguide is higher due to the better optical confinement. In addition, optimal q-parameters are also observed for the sensitivities of the DSHP ring, which means that the sensitivity is also enhanced by the hybrid modes compared to pure plasmonic modes (q = 0 or 1). The maximum sensitivity can reach a value as high as 700 nm/riu when w = 500 nm and q = 0.35, which can be further increased by decreasing the total width, however, at the expense of a lower Qabs factor. The trade-off between the Qabs factor and sensitivity is similar to the one between propagation loss and optical confinement, which is a general behavior in hybrid plasmonic and plasmonic waveguides [21,27]. Based on the different behaviors of the Qabs factor and the sensitivity of the DSHP ring, one needs to carefully design the geometry of the DSHP ring to satisfy the requirements for particular applications. 3. Experimental Realization 3.1. Si Side-Coupled DSHP Ring Resonator Design In a conventional SOI technology, a side-coupled Si bus waveguide is commonly used to characterize the performance of ring resonators. However, in our case, due to the presence of the outer Ag ring, almost no optical energy from the bus waveguide would be coupled into the DSHP ring. To solve this problem, one can reconfigure the DSHP ring with a partly open area, as shown in the sub-figure of the coupling area in Figure 3, where a part of the outer Ag ring is taken away. The gap between the Si bus waveguide and the DSHP waveguide is designed to be 100 nm to 200 nm, to find the experimental critical coupling condition. The geometrical parameters of the DSHP ring are: wslot1 = 250 nm, wslot2 = 350 nm, wsi = 350 nm and hwg = 250 nm. Special attention needs to be paid here to the different widths of slots, which is in accordance with the conformal mapping theory of a ring resonator [28]: the power of the outer slot of the whispering-gallery mode is larger than the inner slot, which results in the unbalance 199

203 Photonics 2015, between the two slots of the DSHP ring. The unbalance will cause larger propagation loss (or lower Q factor) due to a large part of the light confined at the slot material-ag interface compared to the DSHP waveguide without bending. In order to compensate such unbalance, the outer slot can be designed to be slightly wider than the inner one. Besides, the wider outer slot will also decrease the neff mismatch between the modes propagating in the open and closed areas of the DSHP ring, hence reducing the propagation loss of the designed, partly open DSHP ring resonator. Grating couplers are applied at each end of the device for the coupling between an optical fiber to on-chip devices. Figure 3. Schematic of the Si bus waveguide side-coupled double-slot hybrid plasmonic ring sensor. The sub-figures are the detailed structures of the coupling area and the DSHP ring. The measurement setup is also illustrated. OSA, optical spectrum analyzer Fabrication and Measurement Setup The fabrication starts from a commercial SOI wafer with 250-nm crystalline Si on top of a 3 μm-thick SiO2 buffer layer. E-beam lithography (EBL) is used to pattern the Si structure. Then, inductively-coupled plasma (ICP) dry etching with 10% over etch is performed, followed by a second EBL and ICP dry etching processes to fabricate the highly-efficient non-uniform grating couplers [29]. Finally, the pattern of the silver pads is introduced by the third E-beam exposure. After patterning, 20-nm Ge and 230-nm Ag layers are evaporated by a metal evaporation tool, where the Ge layer is used to increase the adhesive strength between silver and substrate material (SiO2). Then, a metal lift-off process is used to open the silver structures. The optical characterization is carried out by the grating coupler setup, as shown in Figure 3: the input/output optical fibers are placed above the grating couplers at each end of the tested device. The tunable continuous wave (CW) laser and polarization controller are connected to the input fiber, while 200

204 Photonics 2015, the optical spectrum analyzer (OSA) is connected to the output fiber. The test liquids (100% and 80% concentrations of IPA in water) are directly dropped onto the surface of the tested sample. The transmission response of the tested device is then obtained after adjusting the positions of input and output optical fibers Characterization Results The scanning electron microscope (SEM) view of the fabricated DSHP resonator is shown in Figure 4. The radius of the fabricated DSHP ring is about 6 μm, and the width of the Si ring and bus waveguide is 350 nm. The outer and inner slots have widths around 350 nm and 250 nm, respectively. Figure 4. Scanning electron microscope picture of the fabricated double-slot hybrid plasmonic ring sensor. Figure 5 shows the transmission responses of the DSHP ring (black curves) and pure Si ring resonator (red curves) infiltrated with 100% IPA (solid curve) and 80% IPA (dashed curve). The green reference level is the transmission response of a straight Si waveguide with input/output gratings. For the DSHP ring resonator, the insertion loss, excluding grating coupler loss, is around 4 db. The extinction ratio is larger than 25 db, and the free-spectral-range (FSR) is about 14 nm. The wavelength shift of the DSHP ring is 3.3 nm, which is about 5-times higher than that of the Si ring (0.63 nm). The refractive index of 80% IPA at a 1550-nm wavelength can be estimated by the reference Si ring transmission responses: according to the simulation results, the Si ring with a 350-nm width has a sensitivity of nm/riu. Calculated from the resonance peak shift (0.63 nm), the refractive index change of the infiltrating material is , which gives the refractive index of 80% IPA in water of Based on the data measured with a wavelength of 589 nm in [30], this value is reasonable. The corresponding sensitivity of the fabricated DSHP ring is nm/riu, slightly higher than the simulation result (~600 nm/riu), which is caused by: (1) the coupling area providing additional sensitivity to the final results; and (2) the 201

205 Photonics 2015, fabrication roughness of the Si and Ag elements inducing larger radiation losses compared to the theoretical situation and the radiated optical energy increasing the optical energy located in the infiltrating analytes, hence increasing the sensitivity. Figure 5. Characterization results of the double-slot hybrid plasmonic ring sensor (black curves) and a silicon ring resonator with the same radius (red curves) infiltrated with 100% and 80% 2-isopropanol. The reference level is the transmission response of the straight waveguide with input/output grating couplers. Besides, compared to the theoretical Qabs factor (larger than 10,000), the measured loaded Q factor is much lower (~300). Neglecting the radiation losses from waveguide bends, the coupling loss from the Si bus waveguide to the DSHP ring and fabrication-induced roughness, the phase mismatch between the open and closed areas of the DSHP ring resonator is the major reason that leads to the small loaded Q factor. It can be modified by decreasing the difference of neff between the two propagating modes, which will be shown in the following section. 4. Loaded Q Factor Modification From the characterization results of the fabricated DSHP ring resonator, the loaded Q factor is much lower compared to the initial Qabs factor shown in Figure 2b, which is mainly due to the phase mismatch between the different propagation modes (open and closed areas of the DSHP ring), in other words, the mismatch of neff. In order to compensate for such a mismatch, the difference between the neff of these two areas needs to be reduced. Since the neff of the closed DSHP ring is higher than that of the partly 202

206 Photonics 2015, open area with the same wsi due to better optical confinement, one can broaden the Si waveguide in the coupling area to get a higher Q factor, as shown in Figure 6a. Figure 6. (a) Schematic of the modified double-slot hybrid plasmonic ring sensor. (b) Finite difference time domain (FDTD) simulation results of the modified DSHP ring sensor with different wsi(modified). The sub-figure shows the loaded Q factor as a function of wsi(modified). In the coupling area, the widths of the Si bus waveguide and the partly open DSHP ring are modified, denoted by wsi(modified). One needs to notice that the widths of the Si bus waveguide and the Si ridge of the open area of the DSHP ring have to be identical to achieve the phase match condition. The size and other parameters of the modified DSHP ring are similar to the fabricated one (wsi = 350 nm, wslot1 = 250 nm and wslot2 = 350 nm). In order to decrease the coupling loss, Si tapers are used to connect the coupling area to the DSHP ring area. The simulation is done using the finite difference time domain (FDTD) method, where the geometry of the DSHP ring is fixed, and wsi(modified) increases from 350 nm to 550 nm. The transmission responses are shown in Figure 6b, where the different colors represent different wsi(modified). One can see that when wsi(modified) is around 500 nm, a maximum loaded Q factor is achieved (larger than 1000), which means that the neff of the DSHP ring and the coupling are nearly matched, and the coupling loss comes to the minimum value. 5. Discussion For optical homogenous sensing applications, to measure the refractive index of liquids, the DSHP ring resonator shows high sensitivity to the infiltrating materials, giving a value as high as nm/riu as obtained experimentally. To further evaluate the performance of the DSHP ring sensor, a figure of merit (FOM) [31], defined by: S S FOM Q (10) 203

207 Photonics 2015, expressing the number of linewidth shifts for an infiltrating material refractive index change of one unit, can be applied. From the experimental results, the FOM of the DSHP ring sensor is around 97.5, which can be increased to 466 after loaded Q factor modifications. The detection limit (DL), describing the smallest refractive index change that can be detected by the system, can be calculated by: f DL (11) FOM where f is a factor expressing the fraction of the resonance linewidth that can be resolved. The f factor is highly dependent on the performance of the detection system used. From [16], we can estimate this value as 1/400 to evaluate the property of the DSHP ring. The detection limit of the fabricated DSHP ring is around RIU ( RIU after loaded Q factor modification). Table 1 shows the comparisons between the fabricated DSHP ring sensor and other experimentally-demonstrated label-free ring sensors. Due to the high sensitivity of the DSHP ring, the DL after loaded Q factor modifications is low. Table 1. Comparison between different kinds of ring-type label-free sensors (* results after loaded Q factor modifications). Waveguide structure Width Height Radius Q Factor S (nm/riu) DL (RIU) Reference Si waveguide 500 nm 220 nm 5 m 20, [2] Si slot waveguide 640 nm 220 nm > 5 m [16] SiN slot waveguide 1150 nm m 1, [15] DSHP waveguide 950 nm 250 nm 6 m 300 (1034) * ( ) * This paper Another promising application of the DSHP ring resonator is as electro-optic modulator. The high-sensitivity to material filling the slots will result in the high efficiency of modulating optical devices. Moreover, the overlap between optical and electronic signals leads to a less complex fabrication process (no extra electrodes are required), where the electric field can be large due to the narrow gap between two plasmonic sheets. The performance of an EO polymer-based DSHP ring resonator modulator can be calculated by employing a typical high-quality EO polymer with properties as n = 1.5 and r33 = 300 pm/v [32], and assuming 80% of the resonant peak shift is provided by the slot material. Based on the given experimental results, the modulation voltage, 2 nwslot 2wslot V 3 3 nr FOMnr (12) for a 3-dB band shift is around 24 V. After loaded Q factor modification, it can decrease to as low a value as 5 V. The capacitance is estimated to be ff, which is calculated from: 2 r hwg C 0 EOP (13) w where 2 r hwg is the average area of the capacitance formed by inner and outer Ag rings and w is the total width of the DSHP ring (w = wsi + wslot1 + wslot2). By taking a reasonable resistance of electronic circuits (below 1500 Ω from [12]), the resistor-capacitor (RC) time constant is above 2 THz. For photon 204

208 Photonics 2015, lifetime limitation, estimated from the Q factor, the bandwidth can reach a value larger than 600 GHz. The power consumption, expressing the energy dissipation during the charge-discharge cycles, is given by: W CV f (14) According to the results given above, the power consumption is about 13.8 mw for 100-GHz modulation, which can decrease to 0.43 mw after loaded Q factor modification. The corresponding average power consumptions are 138 fj/bit and 4.3 fj/bit, respectively. 6. Conclusions In this paper, we have experimentally demonstrated a DSHP ring resonator with ultra-high sensitivity to infiltrating materials, which shows the potential to be applied in homogeneous sensors and electro-optic polymer-based modulators. Axisymmetric FEM simulations show that the Q factors of DSHP rings tend to their Qabs factors when the radius is large enough (larger than about 6 μm), where the waveguide absorption loss dominants the performance of the DSHP ring rather than radiation loss. Then, optimizations are made for Qabs factors by defining the q-parameter (q = wsi/w) as the occupancy of the photonics mode. Simulation results show that the Qabs factors for hybrid plasmonic-photonics mode (0 < q < 1) are much larger than that for a pure plasmonic slot waveguide (q = 0 or 1), as shown in Figure 2b, where the optimized Qabs factors can reach as high a value as 300,000 in theory (w = 1000 nm and q = 0.55). Due to the interactions of the hybrid photonic-plasmonic mode, optimal q-parameters for sensitivity are also observed, which can reach 700 nm/riu (w = 500 nm and q = 0.35), as shown in Figure 2d. Based on simulation results, a DSHP ring resonator with a Si access waveguide by opening a coupling area (partly without the outer Ag ring) is designed, whose fabrication process is compatible with conventional SOI technology. Experimental results show that the sensitivity to the refractive index change of infiltrating materials (100% and 80% aqueous solution of IPA) of the fabricated DSHP can reach as high a value as nm/riu. The sensitivity is about five-times larger than that of Si ring resonator without plasmonic materials ( nm/riu). The measured sensitivity is slightly higher than simulation results (~600 nm/riu), which is due to the sensitive coupling area and fabrication-induced roughness. Besides, the loaded Q factor of the DSHP ring is low (~300), which is mainly caused by the coupling loss between open and closed areas of the ring. In order to compensate for the coupling loss, as shown in Figure 6a, one can broaden the width of the Si ridge at the coupling area to decrease the difference of neff between open and closed areas of the DSHP ring. FDTD simulation results show that the modified Q factor can be over 1000, when phase matching is achieved, as shown in Figure 6b. Compared to other experimentally-demonstrated types of optical ring sensors (Table 1), the fabricated DSHP ring has higher sensitivity and quite a low detection limit, which can be applied in advanced optical homogeneous sensors. Moreover, the special structure of the DSHP ring resonator is also promising for high-speed electro-optic modulator applications. Two plasmonic sheets can be used as electrodes with very low capacitance (~0.245 ff), and the narrow slot (less than 1 μm) can provide quite a large electric field. Taking the reasonable parameters of the electro-optic polymer, the applied voltage 205

209 Photonics 2015, for a 3-dB band shift is about 5 V after loaded Q factor optimization, and the average energy consumption can reach as low value as 4.3 fj/bit. Acknowledgments This work was supported by the Swedish Research Council (VR) through its Linnæus Center of Excellence ADOPT. Xu Sun acknowledges China Scholarship Council (CSC) for the financial support. Author Contributions Xu Sun has done the design, performed the experiments and wrote the first manuscript; all the authors have discussed the problems and formulated the content. Conflicts of Interest The authors declare no conflict of interest. References 1. Soref, R.A. Silicon-based optoelectronics. Proc. IEEE 1993, 81, De Vos, K.; Bartolozzi, I.; Schacht, E.; Bienstman, P.; Baets, R. Silicon-on-insulator microring resonator for sensitive and label-free biosensing. Opt. Express 2007, 15, Densmore, A.; Xu, D.-X.; Waldron, P.; Janz, S.; Cheben, P.; Lapointe, J.; Delâge, A.; Lamontagne, B.; Schmid, J.; Post, E. A silicon-on-insulator photonic wire based evanescent field sensor. IEEE Photon. Technol. Lett. 2006, 18, Dong, P.; Liao, S.; Feng, D.; Liang, H.; Zheng, D.; Shafiiha, R.; Kung, C.-C.; Qian, W.; Li, G.; Zheng, X. Low Vpp, ultralow-energy, compact, high-speed silicon electro-optic modulator. Opt. Express 2009, 17, Wangüemert-Pérez, G.J.; Cheben, P.; Ortega-Moñux, A.; Alonso-Ramos, C.; Pérez-Galacho, D.; Halir, R.; Molina-Fernández, I.; Xu, D.-X.; Schmid, J.H. Evanescent field waveguide sensing with subwavelength grating structures in silicon-on-insulator. Opt. Lett. 2014, 39, Jin, L.; Li, M.; He, J.-J. Highly-sensitive silicon-on-insulator sensor based on two cascaded micro-ring resonators with vernier effect. Opt. Commun. 2011, 284, Li, G.; Zheng, X.; Yao, J.; Thacker, H.; Shubin, I.; Luo, Y.; Raj, K.; Cunningham, J.E.; Krishnamoorthy, A.V. 25 Gb/s 1V-driving CMOS ring modulator with integrated thermal tuning. Opt. Express 2011, 19, Li, H.; Fan, X. Characterization of sensing capability of optofluidic ring resonator biosensors. Appl. Phys. Lett. 2010, 97, doi: / Liu, A.; Jones, R.; Liao, L.; Samara-Rubio, D.; Rubin, D.; Cohen, O.; Nicolaescu, R.; Paniccia, M. A high-speed silicon optical modulator based on a metal oxide semiconductor capacitor. Nature 2004, 427, Wang, J.; Dai, D. Highly sensitive si nanowire-based optical sensor using a Mach Zehnder interferometer coupled microring. Opt. Lett. 2010, 35,

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212 This article has been accepted for publication in a future issue of this journal, but has not been fully edited. Content may change prior to final publication. Citation information: DOI /LPT , IEEE Photonics Technology Letters > REPLACE THIS LINE WITH YOUR PAPER IDENTIFICATION NUMBER (DOUBLE-CLICK HERE TO EDIT) < 1 Cascaded ring-resonators for multi-channel optical sensing with reduced temperaturesensitivity Mao Mao, Sitao Chen, and Daoxin Dai, Member, IEEE Abstract A configuration with cascaded ring-resonators is designed and demonstrated for realizing multi-channel optical sensing with reduced temperature-sensitivity. The present configuration integrates a microring-based 1 N wavelengthselective power splitter and N microring transducers. The 1 N wavelength- selective power splitter serves as a 1 N power splitter and N band-pass optical filters, which helps realize a compact chip with an optical sensor array. As an example, a sensor array with three microring transducers is demonstrated by using silicon-on-insulator nanowires. The present multi-channel optical sensor tolerates a temperature variation within ~10ºC. Index Terms microring, resonator, silicon-on-insulator(soi), sensor, array, temperature-insensitive. I. INTRODUCTION ptical sensors are widely used in many areas, such as O environmental monitoring, biochemical tests and chemical detections. Among various optical sensors, integrated-type optical sensors based on microring resonators (MRRs) [1] are very attractive because of their low costs, high sensitivity, compactness, and ease to realize a sensor array. When using optical microrings for sensing, a simple way is to measure the shift of the resonance wavelength [1], which is sensitive to any small environmental change. A very slight wavelength shift is detectable from the measured spectral response. As it is well known, the detection limit D for an MRR-based optical sensor is proportional to c /S [2], i.e., D c /S, where S is the sensitivity and c is the distinguishable wavelength shift. In order to obtain a good detection limit D for an optical sensor based on a high-q MRR, one apparent approach is to achieve a small c, which is mainly limited by the resolution of spectrum. Thus, one usually needs a measurement system with the combination of a high-precision tunable laser and a photodetector, or the combination of an optical spectrum analyzer (OSA) with a high resolution and a broadband light source. However, one should realize that both approaches are expensive and inconvenient for portable highly sensitive optical-sensing systems. This problem might be solved by utilizing a compact integrated-type OSA. However, an integrated OSA usually has a relatively low resolution [3] and This work was partially supported by the National Natural Science Foundation of China (No , , ), the Doctoral Fund of Ministry of Education of China (No ). The authors are with the Centre for Optical and Electromagnetic Research, State Key Laboratory for Modern Optical Instrumentation, Zhejiang University, Hangzhou , China ( dxdai@zju.edu.cn). thus it is difficult to achieve a high detection limit. Another approach for a good detection limit is to enhance the sensitivity according to D c /S. It has been demonstrated that the design with cascaded high-q MRRs provides an ultrahigh sensitivity due to the Vernier effect [4]-[8]. Therefore, it is helpful to make a low-resolution OSA available for achieving integrated optical sensor systems with a high detection limit [4]. On the other hand, it is desired to develop lab-on-chips enabling multiplexed detections by monolithically integrating multiple sensor elements, each of which interacts with a sample and can be applied to detect a specific analyte individually [9]. Traditionally, such a lab-on-chip is realized by using a 1 N power splitter cascaded by N elements based on a single microring add-drop filter [9]. The power splitter is usually based on cascaded directional couplers or multimode- interference couplers. This structure design is simple and easy to realize. However, this design makes the footprint of the lab-on-chip pretty large for the case of using the sensor element based on cascaded MRRs with the Vernier effect because the size for the cascaded MRRs is relatively large. Alternatively, a promising option is using a microring-based wavelength- selective power splitter proposed in [10] and demonstrated experimentally in [11], which serves as a 1 N power splitter and an N wavelength-selective filter cascaded simultaneously. Such a kind of wavelength-selective power splitter is helpful to realize a compact sensor array based on cascaded MRRs, which is attractive for the applications of lab-on-chips. In this paper, we propose and demonstrate a sensor array based on cascaded MRRs, which consists of a microring-based 1 N wavelength-selective power splitter and N microringbased transducer elements. The N microrings used for the transducer elements are with identical designs and their free spectral range (FSR) is slightly different from that of that MRR used for the wavelength-selective power splitter. When the ambient refractive index changes, the resonance peak of the transducer MRR shifts slightly, which introduces a significant shift for the major resonance wavelength of the cascaded-ring system due to the Vernier effect [4]. In this way, an ultra-high sensitivity (in the order of 10 5 nm/riu [4]-[5] ) is achieved for all the channels. Furthermore, as it is well known, the regular optical sensor based on MRRs is temperature-sensitive because the resonance wavelength shifts significantly as the environmental temperature varies. In order to solve this problem of temperature-sensitivity, one usually needs to develop a system (c) 2015 IEEE. Personal use is permitted, but republication/redistribution requires IEEE permission. See for more information.

213 This article has been accepted for publication in a future issue of this journal, but has not been fully edited. Content may change prior to final publication. Citation information: DOI /LPT , IEEE Photonics Technology Letters > REPLACE THIS LINE WITH YOUR PAPER IDENTIFICATION NUMBER (DOUBLE-CLICK HERE TO EDIT) < 2 with reference rings [12], thermo-electric coolers [13], etc. Very differently, the present multi-channel optical sensor is not temperature-sensitive because the shift of the major resonance peak is very slight compared to the distinguishable wavelength shift as the temperature varies. This temperature insensitivity makes the present multi-channel optical sensor very attractive in comparison with the regular microring-based optical sensors reported previously. In this paper, we present the design and some experimental results for our multi-channel MRR-based optical-sensing system. the transducer microring shifts slightly due to the slight change of the ambient refractive index, there is a significant wavelength shift for the major resonance wavelength peak of the cascaded-ring system due to the Vernier effect. In this case, the shift of the wavelength peak is equal to multiple FSRs of ring #0, i.e., peak =q FSR0 (q is an integer), as the refractive index changes. The present multi-channel optical sensor has the similar sensitivity as the single-channel cascaded-mrr optical sensor, and the sensitivity is given by [4] S= ( 0 /n g1 ) FSR0 /( FSR0 FSR1 ) S 0 M, (1) II. STRUCTURE AND DESIGN Fig. 1(a) shows the schematic configuration of the present multi-channel optical sensor based on cascaded MRRs. There are two parts integrated, i.e., a 1 N wavelength-selective power splitter based on a microring (ring #0), and N cascaded transducers based on microrings (i.e., rings #1, #2, #3). In this paper, we choose N=3 as an example. As shown in Fig.1 (b), the microring (ring #0) for the 1 3 power splitter includes four couplers (couplers #0, #1, #2, #3). For coupler #0, there is a critical coupling condition for achieving a high extinction ratio [10]. This critical coupling condition is corresponding to the destructive interference in the through waveguide for the resonant wavelength between the through-transmitted optical field and the optical field cross-coupled from the microring cavity. Uniform power splitting ratio can be achieved by choosing nearly identical coupling ratios for couplers #1, #2, and #3 according to the condition given in [10]. The coupling ratios are decided by the waveguide structure as well as the gaps widths between the microring and the access waveguide. It is convenient to obtain the relationship between the coupling ratio and the gap width through a three-dimensional finite-difference time-domain (3D-FDTD) simulation for the directional coupler consisting of a straight waveguide and a microring waveguide. Input Ring #1 Ring #3 Ring #0 (a) Ring #2 Output #6 #4 #2 Input (b) Coupler # Coupler #2 2 2 Ring # Coupler # Fig. 1(a) Schematic configuration of the present multi-channel optical sensor based on cascaded MRRs; (b) the wavelength-selective 1 3 power splitter. The cascaded microrings (rings #1, #2, and #3 shown in Fig. 1(a)) used as the transducer elements have the identical design and their bending radius R is slightly different from the bending radius R 0 of ring #0 (used for the wavelength-selective power splitter). Their FSRs can be calculated by using the formula FSR = 2 /(2 Rn g ), where n g is the group index. For an optical sensor based on cascaded MRRs, when the resonance peak of Coupler #1 where M FSR0 /( FSR0 FSR1 ), S 0 / n eff = 0 /n g1 (here S 0 is actually the sensitivity of a single ring), FSR0 and FSR1 are the FSRs of rings #0 and #1, respectively, n g1 is the group index of ring #1. One sees that the sensitivity of the present optical sensor is M times higher than that of a single microring sensor. It is well known that a regular optical sensor based on a single MRR is temperature-sensitive because the resonance wavelength shifts are compared with its distinguishable wavelength shift even when the environmental temperature varies slightly [12]-[13]. For the present cascaded-mrr optical sensor, the resonance wavelengths for both reference-ring (#0) and transducer-ring (#1) have some shifts ( T_0, T_1 ) as the temperature changes. As a result, the wavelength for the major resonance of the cascaded MRRs also has some temperature-dependent shift T_01. When the two rings are designed carefully, it is possible to make T_0 T_1. In this case, one has T_01 T_0 T_1. When using the cascaded-mrr sensor to measure the index n cl_j of the upper-cladding of the transducer-ring, the major-resonance wavelength peak_j will shift digitally with a step of FSR0 (i.e., peak_j = peak_0 + j FSR0 ) and one has a one-to-one relationship between the index n cl_j and the major-resonance wavelength peak_j. One can determine the index n cl_j of the upper-cladding according to the location of the major-resonance wavelength easily. When there is a temperature variation that introduces a wavelength-shift T_01, the major-resonance wavelength for the cascaded-mrr sensor becomes peak_j = peak_j + T_01. If T_01 < FSR0, it is still possible to determine that the index is n cl_j. Correspondingly, the temperature variation T should be less than T max, which is given by ( n eff1 / T) T max /n g1 = T_01 < FSR0, (2) i.e., T max < [n g1 /( n eff1 / T)] FSR0 /. (3) In contrast, for a single-mrr sensor, one has ( n eff1 / T) T max /n g1 = T_01 < c, (4) i.e., T max < [n g1 /( n eff1 / T)] c /, (5) where c is the distinguishable wavelength shift for the measurement system of the single-mrr sensor. Usually c is in the order of 0.1~0.01nm, which is 1~2 orders smaller than the FSR FSR0 (which is usually several nanometers). Therefore, the cascaded-mrr sensor can much more tolerant to the temperature variation. Since FSRi is usually in the order of several nanometers, a large tolerant temperature variation (10~10 2 ºC) is expected. As an example, in the present case we use a silicon-on-insulator (SOI) wafer with a 220nm-thick top silicon layer and the SOI nanowire is around 450nm wide to be (c) 2015 IEEE. Personal use is permitted, but republication/redistribution requires IEEE permission. See for more information.

214 This article has been accepted for publication in a future issue of this journal, but has not been fully edited. Content may change prior to final publication. Citation information: DOI /LPT , IEEE Photonics Technology Letters > REPLACE THIS LINE WITH YOUR PAPER IDENTIFICATION NUMBER (DOUBLE-CLICK HERE TO EDIT) < 3 singlemode. Here for the application of optical sensing, transverse-magnetic (TM) polarization is chosen for the sensor design because TM polarization has much stronger evanescent field than transverse-electric (TE) polarization. The bending radii of microring #0 and the transducer microrings (rings #1, #2, and #3) are chosen around 48.5 m and 51 m to have FSRs of about 2.102nm and 2.307nm, respectively. According to a 3D-FDTD simulation for the directional coupler consisting of a straight waveguide and a microring waveguide, the gap width of coupler #0 is chosen as 740nm to have a coupling ratio of ~0.043, while the gap widths of couplers #1, #2, and #3 are the same as 810nm to have a coupling ratio of ~0.03. III. FABRICATION AND CHARACTERIZATION The fabrication process of the present sensors was started from a 220nm-thick SOI wafer with a 3 m-thick SiO 2 insulator layer. An electron-beam lithography process with MA-N2403 photoresist was carried out for patterning the waveguides, and the silicon layer was etched through with an inductively coupled plasma (ICP) etching process. Grating couplers are then made with a shallow-etching process to achieve efficient coupling between the fibers and the chip. A thin film of PMMA photoresist is formed to cover the whole chip as the upper-cladding layer by using a spin-coating process. The PMMA upper-cladding layer on the top of the transducer microrings (#1, #2, and #3) was removed selectively to open the window for optical sensing. Sensing window input Input Ring #3 Ring #2 Ring #1 Ring #0 Fig. 2 Microscopic picture for the fabricated multi-channel optical sensor. Fig. 2 shows the optical microscope picture for the fabricated cascaded-mrrs-based optical sensor with three channels. The three transducer microrings (rings #1, #2, #3) are exposed in the sensing window so that the analyte to be tested can be contacted by the enhanced evanescent field in the microrings. For the characterization of the fabricated compact multi-channel cascaded-ring sensor, we use the setup with an OSA and a broadband ASE (amplified spontaneous emission) light source. A polarization controller is used to obtain TM-polarized light Output ports accordingly as the grating couplers were designed for TM polarization. The fiber-chip coupling loss is about 7dB per facet by using the focus grating couplers. Fig. 3(a) shows the measured spectral responses at the output ports of rings #1, #2, and #3 when the sensing window is covered by air. There are three major resonance wavelengths peak in the wavelength range from 1530nm to 1600nm, and the quasi-fsr is about ~20nm. The transmission responses at three ports have some differences in the major resonance wavelength, which is due to the fabrication deviation. When the concentration of the sample filled in the sensing window varies, the peak wavelength will shift digitally, which is very similar to the single-channel cascaded MRR optical sensors demonstrated in our previous paper [4]-[5]. One can monitor one of the major resonance wavelengths and detect the refractive index change of the sample filled in the sensing window by measuring the shift of the major resonance wavelength. For the present multi-channel optical sensor, it is possible to integrate microfludic channels for the three transducer microrings so that they can be used to measure three different samples or three parameters for the same sample simultaneously. Since the sensitivity of the present multi-channel optical sensor is very similar to that of a single-channel cascaded MRR optical sensors verified previously [5], in this paper we mainly focus on the characterization of the temperature-sensitivity of the present multi-channel optical sensing system. Fig. 4(a) shows the measured transmission at port #2 of another sample as the temperature varies from 28.5ºC to 62.8ºC. Power ( W) Power ( W) Power ( W) (a) Port # Wavelength (nm) 2.5 (b) Port # Wavelength (nm) 1.0 (c) Port # Wavelength (nm) Fig. 3. Measured transmission responses at the output ports of the three cascaded-ring sensors with air-cladding: (a) port #2 (ring #1); (b) port #4 (ring #2); (c) port #6 (ring #3). From Fig. 4(a), it can be seen that the major resonance peak locates around nm and when the temperature (c) 2015 IEEE. Personal use is permitted, but republication/redistribution requires IEEE permission. See for more information.

215 This article has been accepted for publication in a future issue of this journal, but has not been fully edited. Content may change prior to final publication. Citation information: DOI /LPT , IEEE Photonics Technology Letters > REPLACE THIS LINE WITH YOUR PAPER IDENTIFICATION NUMBER (DOUBLE-CLICK HERE TO EDIT) < 4 varies in the ranges of [28.5ºC, 34.9ºC] and [35.6ºC, 43.9ºC], respectively. As the temperature increases further to the ranges of [45ºC, 62.8ºC], the major resonance peak jumps to nm. Fig. 4(b) gives the peak wavelength peak of the major resonance at different temperatures. This kind of digital variation of the peak wavelength peak can be explained as follows. When there is a temperature increase T, the resonance wavelengths 0 of all the rings have red-shifts 0 ( n eff / T) T/n g, where n eff / T is the thermo-optical coefficient of the microring waveguide. The coefficients n/ T for PMMA, SiO 2, and Si are , , and ºC -1, respectively. The numerical simulation shows that the red-shifts / T for ring #0 and the transducer microring are estimated as 0.021nm/ºC, and 0.045nm/ºC. When the temperature increase is large enough, the major resonance peak wavelength will be digitally switched to a shorter one with a step of ~ FSR1, as shown in Fig. 4(b). Since ring #0 has a smaller FSR and smaller red-shift / T than the transducer ring, the major peak will jump to a short wavelength (see Fig. 4(b)) when the temperature increases. From Fig. 4(b), it can be seen that the multi-channel optical sensor is temperatureinsensitive and can tolerate a temperature variation within ~10ºC. It is possible to reduce the temperature-sensitivity further by optimizing the cascaded rings to have very similar temperature dependence of their resonance wavelengths. T (a.u.) T (a.u.) T (a.u.) ºC ºC ºC ºC ºC ºC ºC ºC ºC ºC ºC ºC ºC ºC ºC 37.1ºC ºC ºC ºC ºC ºC ºC ºC (a) peak (nm) (b) ºC ºC ºC ºC ºC ºC ºC ºC ºC ºC ºC ºC ºC ºC Wavelength (nm) ºC 45.0 ºC Temperature (ºC) Fig. 4 (a) Measured transmission powers T at output port of ring #1 as the temperature varies from 28.5ºC to 62.8ºC; (b) the peak wavelength peak of the major resonance as the temperature varies. IV. CONCLUSION In this paper, we have proposed a design for a multi-channel optical sensor by integrating a microring-based wavelengthselective optical power splitter and cascaded microrings. As an example, a three-channel optical sensor has been demonstrated with SOI nanowires experimentally. This wavelength-selective optical power splitter serves as a 1 N power splitter and microring-based optical filter simultaneously, which helps a lot to reduce the footprint of the sensor chip. Utilizing the Vernier effect of a cascaded-ring system makes the present multi-channel optical sensor have ultra-high sensitivity. Therefore, a very small refractive index change of the analyte introduces a significant wavelength shift, which makes it possible to detect the small index change by using a low-cost integrated-type optical spectrometer (whose resolution is usually low). It has also been shown that the present multi-channel optical sensor can tolerate a temperature variation of ~10ºC. The present multi-channel optical sensor integrated with multiple microfluidic channels so that multi-parameters sensing can be enabled in the future. REFERENCES [1]. J. T. Robinson, L. Chen, and M. Lipson, "On-chip gas detection in silicon optical microcavities," Opt. Express, vol. 16, no. 6, pp , Mar [2]. Chung-Yen Chao and L. Jay Guo, Design and Optimization of Microring Resonators in Biochemical Sensing Applications, J. Lightwave Technol. 24(3): , Mar [3]. P. Cheben, J. H. Schmid, A. Delâge, A. Densmore, S. Janz, B. Lamontagne, J. Lapointe, E. Post, P. Waldron, and D.-X. Xu, A high-resolution silicon-on-insulator arrayed waveguide grating microspectrometer with submicrometer aperture waveguides, Opt. Express, vol. 15, no. 5, pp , Mar [4]. D. Dai. "Highly sensitive optical sensor based on cascaded high-q ringresonators," Opt. Express, vol. 17, no. 26, pp , Dec [5]. J. Hu, and D. Dai, Cascaded-ring optical sensor with enhanced sensitivity by using suspended Si-nanowires, IEEE Photon. Technol. Lett., vol. 23, no. 13, pp , [6]. L. Jin, M. Y. Li and J. J. He, "Highly-sensitive silicon-on-insulator sensor based on two cascaded micro-ring resonators with Vernier effect," Opt. Commun., vol. 284, no. 1, pp , [7]. H. Yi, D. Citrin, Y. Chen, and Z. Zhou, "Dual-microring-resonator interference sensor," Appl. Phys. Lett., vol. 95, no. 19, pp , Nov [8]. T. Claes, W. Bogaerts, and P. Bienstman, "Experimental characterization of a silicon photonic biosensor consisting of two cascaded ring resonators based on the Vernier-effect and introduction of a curve fitting method for an improved detection limit," Opt. Express, vol. 18, no. 22, pp , Oct [9]. A. Densmore, M. Vachon, D.-X. Xu, S. Janz, R. Ma, Y.-H. Li, G. Lopinski, A. Delâge, J. Lapointe, C. C. Luebbert, Q. Y. Liu, P. Cheben, and J. H. Schmid, "Silicon photonic wire biosensor array for multiplexed real-time and label-free molecular detection," Opt. Lett., vol. 34, no. 23, pp , [10]. D. Dai and S. He, "Proposal of a coupled-microring-based wavelengthselective 1 N power splitter," IEEE Photon. Technol. Lett., vol. 21, no. 21, pp , [11]. D. Spencer, D. Dai, Y. Tang, M. Heck, and J. E. Bowers, Realization of a novel 1 N power splitter with uniformly excited ports, IEEE Photon. Technol. Lett., vol. 25(1), pp , [12]. A. Ramachandran, S. Wang, J. Clarke, S. J. Ja, D. Goad, L. Wald, E. M. Flood, E. Knobbe, J. V. Hryniewicz, S. T. Chu, D. Gill, W. Chen, O. King, and B. E. Little, A universal biosensing platform based on optical micro-ring resonators, Biosens. Bioelectron., vol. 23, no. 7, pp , [13]. H. Zhu, Ian M. White, J. D. Suter, M. Zourob and X. Fan, "Opto-fluidic micro-ring resonator for sensitive label-free viral detection," Analyst, vol. 133, pp , (c) 2015 IEEE. Personal use is permitted, but republication/redistribution requires IEEE permission. See for more information.

216 1580 IEEE PHOTONICS TECHNOLOGY LETTERS, VOL. 19, NO. 20, OCTOBER 15, 2007 Polarization-Insensitive Ultrasmall Microring Resonator Design Based on Optimized Si Sandwich Nanowires Zhechao Wang, Daoxin Dai, Member, IEEE, and Sailing He, Senior Member, IEEE Abstract Bent Si sandwich nanowires are used and optimized to obtain an ultrasmall polarization-insensitive microring resonator (MRR). The used Si sandwich nanowire has a low refractive index layer between two Si layers with high refractive indexes. By optimizing the refractive index and thickness of the sandwiched layer, the bent Si sandwich nanowire becomes nonbirefringent theoretically. The designed nonbirefringent nanowire has a relatively good fabrication tolerance. By using such a nonbirefringent bent Si sandwich nanowire, an ultrasmall polarization-insensitive MRR is designed. Index Terms Microring resonator (MRR), polarization insensitivity, sandwich waveguide, Si nanowire. I. INTRODUCTION SILICON dioxide (SiO ) buried waveguides are very popular for planar lightwave circuits (PLCs). However, they are not good for realizing a large-scale photonic integration in the future since a relative large bending radius is needed due to the weak confinement. Recently, Si nanowire waveguides [1], for which ultrasharp bending is possible due to the ultrahigh index contrast, are becoming more and more attractive in realizing ultracompact PLCs, such as arrayed waveguide gratings [2] and microring resonators (MRRs) [3]. As versatile elements in integrated optics, MRRs have been developed and can be used to realize many different functions such as wavelength filters, multiplexers, and modulators. Very high integration density (more than devices/cm ) can be realized when using Si nanowire waveguides with ultrasmall bending radii. However, due to the large index contrast, MRRs based on Si nanowire waveguides usually have a serious problem of polarization-sensitivity. Polarization-insensitivity is one of the most important requirements for lightwave devices. Great efforts have been done to obtain polarization-insensitive micrometric waveguides, such as choosing a specific ridge waveguide aspect ratio [4] and adjusting the cladding stress [5]. Recently, some special designs or approaches have been developed for polarization-insensitive devices based on Si Manuscript received January 25, 2007; revised May 12, This work was supported by the National Science Foundation of China ( and ) and by research grants from Zhejiang Province ( and 2006R10011). The authors are with the Centre for Optical and Electromagnetic Research, State Key Laboratory of Modern Optical Instrumentation, Zhejiang University, Zijingang, Hangzhou, China ( sailing@kth.se). Color versions of one or more of the figures in this letter are available at Digital Object Identifier /LPT Fig. 1. (a) Schematic configuration of an MRR. (b) Cross section of a sandwich waveguide. nanowires, such as an arrayed waveguide grating [6] and a multimode interferometer (MMI) coupler [7]. However, not much work has been done for ultrasmall polarization-insensitive MRRs. Recently, a so-called sandwich waveguide has been demonstrated [8] [10] and used for realizing polarization-insensitive ultrasmall optical devices, such as MMI couplers [11] and directional couplers [12]. In a sandwich waveguide, the guided light is strongly confined in a thin low index layer sandwiched by two Si layers with high refractive indexes. In this letter, we use such sandwich waveguides to realize an ultracompact polarization-insensitive MRR. The refractive index and thickness of the sandwiched layer are optimized to make the birefringence of the Si sandwich nanowire almost zero. II. ANALYSIS AND DESIGN Fig. 1(a) and (b) shows the configuration of the MRR and the cross section of the Si sandwich nanowire, respectively. The Si sandwich nanowire has a sandwich layer (with a low refractive index ) between two Si layers with high refractive indexes. The refractive index of the sandwich layer is optimized in the range from 2 to 3.48, which can be obtained by SiN [11]. First we study a bent (for an MRR with radius m) sandwich layer of SiN and choose the other parameters as follows:, the core width nm, and nm. By using a full-vectorial finite-differential method in a cylindrical coordinate [13], we calculate the effective refractive indexes (, ) of quasi-tm and quasi-te polarization modes in a Si sandwich nanowire. Fig. 2 shows the effective refractive indexes and and the birefringence (the difference between effective refractive indexes and ) as the thickness of the sandwich layer increases. One sees that the quasi-tm fundamental mode is more sensitive to the change of than the quasi-te fundamental mode and there /$ IEEE 213

217 WANG et al.: POLARIZATION-INSENSITIVE ULTRASMALL MRR DESIGN 1581 Fig. 2. Effective refractive indexes of quasi-tm and quasi-te modes for different values of h and the birefringence between them. The waveguide is bent with R =5 m. Fig. 4. Optimal value h as n varies for w = 390, 400, and 410 nm. The bending radius is fixed to R =5m. Fig. 5. Birefringence and optimal thickness as the bending radius R increases. Fig. 3. Electric field distributions of a bent sandwich waveguide for fundamental (a) quasi-te and (b) quasi-tm modes, when bending radius R =5m, h =220nm, n =3:48, h =50nm, and n =1:46. is a specific value corresponding to (i.e., a zero birefringence). In Fig. 2, one sees that birefringence changes as the thickness of the sandwich layer increases. When nm, the birefringence becomes zero. In contrast, when (i.e., a conventional Si nanowire waveguide), the bent waveguide has a large birefringence (about 0.1). From Fig. 2, we find that the fabrication tolerance for is about several nanometers. Since one can control the thickness precisely by using a slow deposition process, the designed nonbirefringent nanowire actually has a relative good fabrication tolerance. On the other hand, the variation of the core width has a great influence on the birefringence. For example, when the core width has a deviation of 10 nm from the designed value, the birefringence is about Therefore, it is a challenge to control the core width accurately in the etching process. Fig. 3(a) and (b) shows the electric field distributions of the fundamental modes of quasi-tm and quasi-te polarizations, respectively. Theoretically speaking, both polarization modes have very small bending losses due to the strong confinement even for a bend of several micrometers. Thus, the polarizationdependent loss should be small theoretically. For the quasi-te polarization, there are two peaks in the two Si regions with high refractive indexes and the power in the sandwich layer is relatively small, as shown in Fig. 3(a). However, for the quasi-tm polarization, the modal field is strongly confined in the sandwich layer with a low refractive index because of the continuity of the normal component of the electric displacement (i.e., ) at the interface [see Fig. 3(b)]. When the thickness increases from, more light is confined in the low index layer for quasi-tm mode while there is not much change for quasi-te mode. Therefore, decreases more rapidly than as increases (as shown in Fig. 2(a)). Since when, one can find an optimal value for a nonbirefringent Si sandwich nanowire for each specific bending radius [see Fig. 2(b)]. Fig. 4 shows the optimal value (a zero-birefringent design) as the refractive index ranges from 2.0 to 2.4 (the bending radius is fixed to m). From this figure, one sees that the optimal thickness of decreases when the refractive index decreases. When one chooses a material with for the sandwich layer (e.g., SiO ), it is still possible to find an optimal thickness for zero-birefringence. However, the value of is only about several nanometers. This makes it difficult to control the thickness and uniformity accurately. Therefore, in order to have larger optimal thickness, a larger is preferred. Here we choose a SiN sandwich layer. For a larger core width, one has a smaller thickness for a nonbirefringent sandwich waveguide. Since it is not easy to control the thickness and uniformity of an ultrathin layer (less than 10 nm), a smaller core width is preferred. However, a small core width will introduce large scattering loss. Therefore, there is a trade-off for the choice of the core width. Here we choose nm and the corresponding value of is 80 nm (for ). We also note that the birefringence is dependent on the bending radius. In all the above design, the Si sandwich wire is designed to be nonbirefringent when the bending radius is m. Fig. 5 shows the birefringence as the bending radius increases from while all the other parameters 214

218 1582 IEEE PHOTONICS TECHNOLOGY LETTERS, VOL. 19, NO. 20, OCTOBER 15, 2007 III. CONCLUSION In this letter, we have obtained the optimal thickness of the sandwich layer for nonbirefringent bent Si sandwich wire with different refractive index. An ultracompact polarization-insensitive MRR based on Si sandwich wires has been designed. The spectrum of the drop channel has been calculated and shown a very small polarization-dependent wavelength. The designed nonbirefringent nanowire has a relatively good fabrication tolerance (for a slow deposition process). The fabrication tolerance is improved by controlling the vertical thickness (rather than the horizontal width of the waveguide) with acceptable surface roughness. Fig. 6. Drop spectrums for the fundamental quasi-tm and quasi-te modes. are fixed to the designed values (see the solid line). From this figure, one sees that the absolute value of the birefringence converges to a constant, which corresponds to the birefringence of a straight wire. When is small, the difference in the birefringence between the straight and ultrasharp bend wires should be considered in the design of a polarization insensitive device. The optimal thickness decreases from 80 to 76.5 nm (for nonbirefringent straight wire) when the bending radius increases from 5 to 23 m (see the dashed curve in Fig. 5). To obtain the spectrum of the drop channel with affordable computer resources, we calculate the coupling coefficients between the MRR and straight waveguide by using the well-known finite-difference time-domain (FDTD) method. In our FDTD simulation, the computational window only includes the coupling region of the input straight waveguides and the microring (see the inset in Fig. 6). The grid sizes are nm, nm, and nm. Then the coupling coefficients obtained from the FDTD simulation are put into the formulas in [14] to calculate the spectrum. In the design of the polarization-insensitive MRR, we choose the gap nm (between the straight waveguide and the microring) and the following parameters for both the straight and bent Si sandwich wires: nm,, nm, and nm. In this case, the Si sandwich wire with m is almost nonbirefringent. The calculated coupling coefficients are slightly wavelength-dependent and the coupling coefficients at the center wavelength (i.e., 1550 nm) are and for quasi-te and quasi-tm modes, respectively. Fig. 6 shows the calculated spectrum of the drop channel. From this figure, one sees that the center wavelengths of both polarization modes are almost centered at 1550 nm, and the polarization-dependent wavelength PD is about 0.01 nm, which is induced by the small birefringence mentioned above. Since the quasi-te polarization has a smaller coupling coefficient than the quasi-tm polarization (i.e., ), the -factor of the quasi-te mode is larger than that of the quasi-tm mode. The present MRR is useful for some applications (e.g., optical filters) in which very small PD is critical and the -factor is not important. A polarization-insensitive -factor can be realized by using, e.g., a polarization-insensitive coupler [15]. REFERENCES [1] T. Tsuchizawa, K. Yamada, H. Fukuda, T. Watanabe, J. Takahashi, M. Takahashi, T. Shoji, E. Tamechika, S. Itabashi, and H. Morita, Microphotonics devices based on silicon micro fabrication technology, IEEE J. Sel. Topics Quantum Electron., vol. 11, no. 1, pp , Jan./Feb [2] D. Dai, L. Liu, L. Wosinski, and S. He, Design and fabrication of ultra-small overlapped AWG demultiplexer based on -Si nanowire waveguides, Electron. Lett., vol. 42, no. 7, pp , [3] P. Dumon, W. Bogaerts, V. Wiaux, J. Wouters, S. Beckx, J. V. Campenhout, D. Taillaert, B. 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219 704 JOURNAL OF LIGHTWAVE TECHNOLOGY, VOL. 26, NO. 6, MARCH 15, 2008 Ultrasmall Thermally Tunable Microring Resonator With a Submicrometer Heater on Si Nanowires Daoxin Dai, Member, IEEE, Liu Yang, and Sailing He, Senior Member, IEEE, Fellow, OSA Abstract An ultracompact widely tunable thermooptical (TO) microring resonator (MRR) filter based on Si nanowires is presented. The Si nanowire waveguide has a SiO 2 insulator, Si core, a SiO 2 up-cladding, and a thin metal film at the top. The metal circuit along the microring is used as a submicrometer heater which has the same width as the Si nanowire waveguide. The up-cladding is optimized to reduce the light absorption of the metal as well as to have a good heat-conduction from the heater to the Si core. Two pads used as the contact points for the probes connecting to the electrical power are perpendicularly connected to the microring by using optimized T-junctions (with a low excess loss of about 0.06 db per T-junction). With such a design, the present thermally tunable microring resonator (MRR) can be fabricated by using a standard fabrication process with a single lithography process, which is much simpler than the fabrication with double lithography processes used for the conventional TO components. Finally, the simulation results show that the designed MRR has a wide tuning range of about 20 nm with a low heating power of 5 mw. Index Terms Filter, microring, nanowire, resonator, Si, thermal, tunable. I. INTRODUCTION AS versatile elements for photonic integrated circuits (PICs), microring resonators (MRRs) have received much attention recently because of their compact size, easy realization of large-scale photonic integrations, etc. Various MRR-based functional components for optical communications have been developed, e.g., add-drop filters [1], optical modulators [2], and optical switches [3]. For a future flexible and scalable optical network, the development of optical components with wide-range tunability becomes very important [4]. One of the effective and simple methods to realize tunable components is to make use of the well-known thermo-optical (TO) effect. Published literature has already shown that both polymer and Si are good choices for TO components with low power consumption due to their large TO coefficients (about K ) [5], [6]. Recently, it has been an interesting topic to realize ultracompact PICs by using Si nanowire waveguides [7] [12], which have the ability of ultrasharp bending ( m [9]) Manuscript received March 14, 2007; revised November 16, This work was supported by the provincial government of Zhejiang Province of China under Grants and 2006R10011 and in part by the National Science Foundation of China under Grants and The authors are with the Center for Optical and Electromagnetic Research, State Key Laboratory for Modern Optical Instrumentation, Zhejiang University, Hangzhou , China, and also with the Joint Research Center of Photonics, KTH (Royal Institute of Technology), Stockholm SE , Sweden ( dxdai@zju.edu.cn). Color versions of one or more of the figures in this paper are available online at Digital Object Identifier /JLT due to the ultrahigh index contrast. For example, one realized ultrasmall MRRs with an area of no more than 10 m 10 m [12]. With such an ultrasmall MRR, it is possible to realize large-scale PICs and synthesize the desired spectral responses. Therefore, in this paper we focus on the improved design of thermally tunable MRR filters based on Si nanowires. In the previously published literatures, the fabrication of conventional TO components (including thermally tunable MRR filters) usually needs double lithography processes with two different photomasks. One is for optical waveguide circuits and the other is for the heater electrodes [5], [13]. In this conventional way, one has to align these two lithography masks carefully. Such a complex fabrication is not good for the cost reduction. In this paper, we propose an improved design for a thermally tunable MRR filter which is based on Si ridge nanowires including a SiO insulator, a Si core, a SiO up-cladding, and a thin metal film (all layers are stacked on a Si substrate). The SiO insulator and up-cladding are thick enough to reduce the leakage loss (to the Si substrate) and the absorption loss (due to the metal heater), respectively. In order to minimize the power consumption for the tunability, a heater of small width is preferred [14]. Here we use a submicrometer heater with the same width as the Si nanowire waveguide. The submicrometer heater on the microring is connected to two 100 m 100 m pads (i.e., the contact point for the probes connecting to the electrical power) by using two T-junctions. The excess loss due to the inserted T-junction is minimized by expanding the waveguide width at the junction (like those crosses used for suspended waveguides [15], [16]). For the present Si nanowire MRR, one only needs a standard fabrication process with only single lithography process, which defines the waveguide and the heater in the same time. In this way, the double-lithography process and the careful alignment used in the fabrication for a conventionally designed TO components are avoided. The details of the fabrication process and the improved design will be given in Sections II and III. We also present the numerical simulation of the temperature distribution at different power consumptions and the corresponding spectral responses from the through and drop channels. II. STRUCTURE AND FABRICATION PROCESS Fig. 1(a) and (b) shows the 3-D view of the schematic configuration and the designed mask (i.e., the top view) of the present ultrasmall MRR filter with four ports. Two 100 m 100 m pads are placed at the two sides of the microring as the contact points for the probes connecting to the electrical power and each pad is connected to the microring circuit with a T-junction. Fig. 1(b) shows the enlarged views of the microring and the used T-junctions. In order to avoid a large excess loss due to the /$ IEEE 216

220 DAI et al.: ULTRASMALL THERMALLY TUNABLE MICRORING RESONATOR 705 commercial SOI wafer, and then the SiO up-cladding layer can be formed by using a process of thermal-oxidation or PECVD. Then a thin metal film is formed on the up-cladding layer by using a sputtering machine. Now there are four layers of thin films on the Si substrate, i.e., a SiO insulator, a Si core, a SiO up-cladding, and the metal film. The followed process is the photoresist coating and then an E-beam (or deep-uv) lithography to form the photoresist pattern. The formed photoresist pattern is then transformed to the metal layer by using a process of wet-etching. Both the photoresist and metal layers are used as the mask for the followed ICP etching process and then a ridge nanowire waveguide is formed by etching through the layers of SiO up-cladding and Si core [see Fig. 1(a)]. Such an etching process may introduce some roughness at the sidewall, which depends on the quality of the fabrication process. After the ICP etching, the remained photoresist is removed and the metal layer left on the top of the microring is used as the submicrometer heater. For our designed structure, one only needs one photomask in the fabrication for the lithography process (instead of two photomasks needed for conventionally designed TO devices). On the other hand, since the metal on the bus waveguides is still left, some thermal crosstalk with adjacent devices may be introduced in some cases when the layout is not designed carefully (e.g., the microring and bus waveguides are not separated). Fortunately, in our current case the metal circuits on the microring and the bus waveguides are separated and thus no electrical current flows through the metal circuits on the bus waveguides. In this case, the thermal crosstalk could be avoided. Fig. 1. (a). 3-D view of schematic configuration of the present tunable MRR filter. (b) Designed mask and the details of the structure. (c) Cross section of the used Si nanowire waveguide. T-junctions, we choose a narrow connection circuit with a small width (e.g., 200 nm) as shown in Fig. 1(b). This excess loss can be minimized further by expanding the singlemode Si nanowire waveguide at the T-junctions with two inversed cosine tapers [see the enlarged view of T-junction shown in Fig. 1(b)]. In the expanded section, the field is confined very well in the Si core and will be influenced less by the crosses [15], [16]. Fig. 1(c) shows the cross section of the used Si nanowire, which consists of a SiO insulator (on a Si substrate), a Si core, a SiO up-cladding, and a thin metal film. The metal on the top (of the mask shape) will not be removed, and the metal on top of the microring is used as the submicrometer heater [see Fig. 1(a)]. In order to reduce the leakage to the Si substrate, the SiO insulator should be thick enough (usually about 1.0 m [8]). The thickness of the SiO up-cladding should also be thick enough to make the absorption due to the metal heater negligible. For the fabrication, one can deposit a thick SiO insulator layer, a thin amorphous-si core layer (e.g., 300 nm), and a thick SiO up-cladding layer on a Si substrate in sequence by using the PECVD technology [11]. Another better way for lower propagation loss is to use a III. RESULTS AND DISCUSSIONS First we consider a quasi-singlemode Si nanowire with a core of 500 nm 300 nm. The refractive indices for the core and cladding layers are and 1.46 at the wavelength of 1.55 m. Here we use a 100-nm-thick Cr-Au (20 nm/80 nm) metal heater [17]. In a large SOI rib waveguide, the SiO insulator/cladding layer is usually very thin (about 0.2 m) while it is very different for the Si nanowire. For example, the thickness of the insulator layer is usually larger than 1 m to prevent the leakage to the Si substrate [8]. For the present Si nanowire with a metal heater, a thick SiO up-cladding is also required to be thick enough to reduce the absorption of the metal heater. On the other hand, a thick up-cladding is not beneficial to obtain a fast thermal-conduction from the submicrometer heater to the Si core. From this consideration, the SiO cladding should be as thin as possible. Fig. 3(a) shows the absorption loss (due to the metal heater) for TE and TM polarizations for different thicknesses of the SiO cladding. From this figure, one sees that the absorption losses for both polarizations decrease exponentially as the thickness increases and the TM polarization has a larger loss than the TE polarization. Since the propagation loss of a Si nanowire (due to scatterings at the rough surfaces) is usually relatively large, e.g., 2.4 db/cm [8], it is negligible for an absorption loss as low as 0.1 db/cm. For the case of nm and nm, one should choose a minimal thickness of nm to make the absorption loss negligible for both polarizations [see Fig. 2(a)]. The minimal thickness of cladding can be reduced by increasing the core height ; however, it 217

221 706 JOURNAL OF LIGHTWAVE TECHNOLOGY, VOL. 26, NO. 6, MARCH 15, 2008 Fig. 2. Absorption loss due to the submicrometer metal heater as the cladding thickness h increases. (a) w =500nm, h = 300 nm. (b) w = 400 nm, h = 350 nm. Fig D-FDTD simulated light propagation in an optimally designed T-junction for (a) TE polarization and (b) TM polarization. may introduce undesirable multiple modes. In order to make a Si nanowire singlemode, here we increase the core height to 350 nm while reduce the core width to 400 nm. With this design, the minimal thickness of the up-cladding (for an acceptably low absorption loss of 0.1 db/cm) is reduced to 600 nm for both polarizations [see Fig. 2(b)], which is beneficial to have a fast thermal conduction. Therefore, for the Si nanowire used in this paper, we choose the following parameters: nm, nm, and nm. By using the Si nanowire designed above, we choose the parameters for the MRR filter as follows. A small bending radius of m is used to achieve a negligible bending loss and the gap between the microring and the straight waveguide is nm to have a good coupling. We choose a relatively narrow width nm at the intersection end of the T-junction (connecting the microring and the electrode pad) to avoid large excess loss [see Fig. 1(b)]. In order to avoid a large local resistor at the junction, the section with nm has a short length of 300 nm and is connected to a taper (which expands the T-junction width quickly as shown in Fig. 1(b). In order to minimize the excess loss further, we use two reversed cosine tapers to expand the waveguide width at junctions [as shown in Fig. 1(b)]. Theoretically speaking, a larger expanding width is desirable to have a lower diffraction angle of a wider mode and consequently to reduce the excess loss due to T-junctions. However, in this case a longer taper is required to make the mode expanding adiabatically, which will increase the cavity length and thus reduce the free spectral range (FSR) of the MRR filter. In this paper, we choose a moderate taper width m and a short taper with a length of m to ensure a compact MRR with a large FSR. With such a design, the excess losses (per T-junction) for TE and TM polarizations are about and db, respectively. When there is no taper for the T-junction, the calculated excess losses for TE and TM polarizations are about 0.26 and db per junction, respectively. From this comparison, one sees the excess loss has been reduced greatly by introducing tapers (especially for the TE polarization). We find that the excess loss can be reduced further by inserting a short straight section (with a width of and a length of ) between the two reversed cosine tapers. Here we choose this length m, which is slightly larger than the width at the intersection end of the T-junction. Fig. 5(a) and (b) shows the simulated light propagation in the designed T-junction for the TE and TM polarizations, respectively. Here a two-dimensional finite-difference time-domain (2D-FDTD) modeling based on an effective index method (EIM) is used to avoid a time-consumed 3D-FDTD simulation. In order to verify the accuracy of the EIM-based 2D-FDTD method used here, we also calculate the transmission in the optimized S-bend bridge given in [15]. The transmission calculated here is about 0.993, which is a little smaller than given in [15]. This comparison shows that the 2D-FDTD modeling used here can give a relatively accurate simulation result for the T-junction. In our case, the effective indices for the TE and TM polarizations are and (@1550 nm), respectively. From this figure, one sees the light propagates through the tapers without observable scatterings. Our 2D-FDTD simulation shows that the excess losses per T-junction for TE and TM polarizations are reduced to about and db, respectively. For an MRR with relatively low -factor (e.g., for a high bandwidth [18]), such a loss is low enough. However, for a high- MRR, it is necessary to reduce the excess loss further by using an optimize taper with larger width and length. For example, one obtains a very low excess loss of 0.026, and db when the width and length of the cosine taper increase to 0.8 m and 2 m, respectively. It is also possible to have a lower loss by choosing a smaller end width of the T-junction. 218

222 DAI et al.: ULTRASMALL THERMALLY TUNABLE MICRORING RESONATOR 707 Fig. 4. (a) Temperature distribution when the power P =5mW. (b) Effective index as the power increases. Fig. 5. Spectral responses of the TE polarization from the through and drop ports for different heating powers. (a) P =0mW. (b) P =1mW. (c) P = 2 mw. (d) P =3mW. (e) P =4mW. (f) P =5mW. However, the end width should be large enough to avoid some undesirable effects such as very high local temperature (which may burn the metal at the junction). In this paper, we focus our work on a high-bandwidth MRR filter which has a relative low -factor [18]. Therefore, we choose the following parameters of the T-junction to have an acceptably low loss and a compact size: nm, m, m, and m. It is well known that Si nanowires have serious polarization dependency due to the strong confinement and submicrometer cross section. Therefore, we only consider the TE polarization in Section IV. Fig. 4(a) shows the numerically simulated temperature distribution in the cross section the designed Si nanowire when a power of 5 mw is applied to the submicrometer heater. Here the temperature distribution is obtained by numerically solving the Laplacian equation with appropriate boundary conditions at the interfaces. From this simulation, one sees that the region close to the submicrometer heater has a high temperature of 350 C and the temperature at the region far way from the heater decreases gradually. The temperature at the waveguide core ranges from 152 C to 155 C. From this calculated temperature distribution, one can obtain the corresponding refractive index distribution after heating according to the formula [19] and then obtain the effective refractive index of the heated Si nanowire by using a full-vectorial finite-different method (FDM) [9]. Fig. 4(b) shows that the calculated effective refractive index increases almost linearly with the heating power. The slope is about mw-1 for both polarizations and the effective index increases by about under the condition of mw. The corresponding wavelength shift is about 20 nm estimated by the formula of. Such an increase of temperature will also influence the coupling coefficient between the bus waveguide and the microring. Fortunately, this influence is very small. In this paper, we concentrate our analysis on the thermo-optical effect in the microring, which introduces a tunable resonant wavelength. For the present designed microring, the total loss includes the bending loss, the absorption loss due to the metal submicrometer heater, the scattering loss due to the surface roughness, and the excess loss due to the two T-junctions. In our case, the absorption loss are small enough db/cm to be neglected in comparison with the relative large scattering loss in a Si nanowire, e.g., 2.4 db/cm [8]. The bending loss for bending radius m is also small enough to neglect (e.g., in [20], the authors shown a measured bending loss of db for bending radius m). Since the perimeter of the microring is very small (about 30 m), the scattering loss is only about db. The excess loss due to the two T-junctions is about 0.12 db and thus becomes the dominant part of the total loss. Since an FDTD simulation for the whole MRR is time-consuming due to the large computational domain, we use the analytical formula given in [21] to calculate the spectral response from the through and drop channels. Fig. 5 shows the calculated spectral response of the TE polarization from the through and drop ports at different heating powers. The TM polarization has similar results while the resonant wavelengths, the FSR and the -factor are different. The calculated FSR of the MRR filter is about 33 nm. When the heating power increases, the shape of the spectral response does not change much except the resonator wavelength. When the heating power increases from 0 to 5 mw, the resonator wavelength is tuned from to nm. One sees that a largely tunable MRR filter with low power consumption is obtained. In our calculation, the excess losses due to the two T-junctions are included. Due to the T-junction loss, the peak of the drop channel is about db and the extinction ratio is more than 20 db. The 3-dB bandwidth of the dropped spectrum is about 1.6 nm and the corresponding 219

223 708 JOURNAL OF LIGHTWAVE TECHNOLOGY, VOL. 26, NO. 6, MARCH 15, factor is about This -factor is not high due to the large coupling coefficient in our considered case. One can achieve a much higher -factor by reducing the coupling between the input/drop waveguides and the microring. For example, when using a weak coupling by increasing the gap to 250 nm, one obtains a smaller 3-dB bandwidth of nm and a higher -factor of more than One also should note that when a MRR filter with an ultrahigh -factor is desirable, the excess loss of T-junctions is required to be very low, which could be realized by optimizing the T-junction further. IV. CONCLUSION In this paper, we have proposed an improved design for an ultrasmall thermally tunable MRR filter based on Si ridge nanowires (which has a SiO insulator layer, a Si core, a SiO up-cladding, and a thin metal film at the top). The metal circuit along the microring is used as the submicrometer heater to reduce the power consumption for tunability. Two 100 m 100 m (as the contact points for the probes connecting to the electrical power) are placed on the two sides of the microring and perpendicularly connected to the submicrometer heater on the microring by using T-junctions. Our simulation results have shown that a low excess loss of about 0.06 db per T-junction has been obtained by expanding the waveguide width at the T-junction with two inversed cosine tapers. With the present design, one can use a standard fabrication process with only a one-time lithography process (unlike the double lithography processes required in the fabrication of conventional TO components). Finally, the spectral responses at different heating power are calculated and the resonator wavelength has a wide tuning range of about 20 nm when the heating power varies from 0 to 5 mw. We note that the present process is not suitable for any kind of photonic circuits, e.g., Mach Zehnder interferometers (MZI) with Y-branches (because the heaters on the two arms cannot be isolated). In this case, one has to design the layout carefully to avoid any undesirable electrical coupling and thermal coupling. For example, for an MZI, it is possible to replace Y-branches by using direction couplers so that the two arms could be isolated well. REFERENCES [1] Y. Kokubun, Y. Hatakeyama, M. Ogata, and S. S. Zaizen, Fabrication technologies for vertically coupled microring resonator with multilevel crossing busline and ultracompact-ring radius, IEEE J. Sel. Topics Quantum Electron., vol. 11, no. 1, pp. 4 10, Jan./Feb [2] Q. F. Xu, B. Schmidt, S. Pradhan, and M. Lipson, Micrometre-scale silicon electro-optic modulator, Nature, vol. 435, no. 7040, pp , May [3] Y. Goebuchi, T. Kato, and Y. Kokubun, Fast and stable wavelengthselective switch using double-series coupled dielectric microring resonator, IEEE Photon. Technol. Lett., vol. 18, no. 1, pp , Jan. Feb [4] S. Yamagata, Y. Yanagase, and Y. Kokubuny, Wide-range tunable microring resonator filter by thermo-optic effect in polymer waveguide, Jpn. J. Appl. Phys., vol. 43, no. 8B, pp , [5] T. Tsuchizawa, K. Yamada, H. Fukuda, T. Watanabe, S. Uchiyama, and S. Itabashi, Low-loss Si wire waveguides and their application to thermooptic switches, Jpn. J. Appl. Phys. Part 1, vol. 45, no. 8B, pp , Aug [6] G. Sekiguchi, S. Yamagata, and Y. Kokubun, Polarization-independent tuning of widely tunable vertically coupled microring resonator using thermo-optic effect, Jpn. J. Appl. Phys., vol. 44, no. 4A, pp , [7] T. Tsuchizawa, K. Yamada, H. Fukuda, T. Watanabe, J. Takahashi, M. Takahashi, T. Shoji, E. Tamechika, S. Itabashi, and H. Morita, Microphotonics devices based on silicon microfabrication technology, IEEE J. Sel. 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Cheben, J. H. Schmid, and B. Lamontagne, High bandwidth SOI photonic wire ring resonators using MMI couplers, Opt. Express, vol. 15, no. 6, pp , [19] G. Cocorullo, F. G. D. Corte, and I. Rendina, Temperature dependence of the thermo-optic coefficient in crystalline silicon between room temperature and 550 K at the wavelength of 1523 nm, Appl. Phys. Lett., vol. 74, no. 22, pp , May [20] Y. A. Vlasov and S. J. McNab, Losses in single-mode silicon-on-insulator strip waveguides and bends, Opt. Express, vol. 12, no. 8, pp , Apr [21] A. Yariv, Universal relations for coupling of optical power between microresonators and dielectric waveguides, Electron. Lett., vol. 36, pp , Daoxin Dai (M 07) received the B.Eng. and Ph.D. degrees from the Department of Optical Engineering, Zhejiang University, Hangzhou, China, in 2000 and 2005, respectively. His current research interests include silicon micro-/nano-photonics for optical communications, optical interconnections, and optical sensing. He has first-authored about 30 papers in refereed international journals. Liu Yang received the B.Eng. degree in the Department of Automation, Kunming University of Science and Technology, Kunming, China, in She is currently pursuing the Ph.D. degree in the Department of Optical Engineering, Zhejiang University, Hangzhou, China, and her research activities are in the design and fabrication of planar lightwave circuits. 220

224 DAI et al.: ULTRASMALL THERMALLY TUNABLE MICRORING RESONATOR 709 Sailing He (M 92 SM 98) received the Licentiate of Technology and Ph.D. degrees in electromagnetic theory from the Royal Institute of Technology, Stockholm, Sweden, in 1991 and 1992, respectively. After the Ph.D. degree, he has worked at the KTH (Royal Institute of Technology), Stockholm, Sweden, as an Assistant Professor, an Associate Professor, and a Full Professor. He has also been with Zhejiang University, Hangzhou, China, since 1999 when appointed as a Chang-Jiang project Professor by the Ministry of Education of China. He is a Chief Scientist for the Joint Research Center of Photonics, KTH, and Zhejiang University, and a Fellow of the Optical Society of America (OSA). He has first-authored one monograph (Oxford University Press) and authored/coauthored about 300 papers in refereed international journals. 221

225 254 IEEE PHOTONICS TECHNOLOGY LETTERS, VOL. 21, NO. 4, FEBRUARY 15, 2009 Compact Microracetrack Resonator Devices Based on Small SU-8 Polymer Strip Waveguides Daoxin Dai, Member, IEEE, Bo Yang, Liu Yang, Zhen Sheng, and Sailing He, Senior Member, IEEE Abstract Compact microracetrack resonator (MRR) devices are presented with small SU-8 polymer strip waveguides. The SU-8 strip waveguide has an SU-8 polymer core ( 1 573), a SiO 2 buffer ( 1 445), and an air cladding. The fabricated straight waveguide has a low propagation loss of about 0.1 db/mm. With such a high index-contrast optical waveguide, a compact MRR with a small bending radius ( 150 m) are designed and fabricated. The measured spectral responses of the through/drop ports show a -factor of Index Terms Bending, resonator, strip, SU-8, waveguide. I. INTRODUCTION AS A versatile element for photonic integrated circuits (PICs), microresonators (including microrings, microracetracks, microdisks) have received much attention due to their outstanding advantages, e.g., the compact size and easy realization of large-scale PICs, etc. With microresonators, people have developed various functional components for optical communications, such as add drop filters [1] and optical modulators [2]. Because of the potential high -factor, it is also very attractive to use microresonators for highly sensitive optical sensing by measuring the resonant wavelength shift or the output power variation [3]. In the past years, various optical waveguides with different materials and structures have been developed for microresonators [1] [3]. Usually a small bending radius is desirable for compact microresonators. Therefore, an optical waveguide with a high index contrast (i.e., the difference of the refractive index between the core and the cladding in an optical waveguide) is preferred [4], [5]. For example, the recently developed Si nanowire waveguide has an ultrahigh and consequently could realize ultrasmall microresonators ( 10 m ) [2]. However, for such a Si nanowire, the very small cross section (e.g., 500 nm 250 nm) makes the fabrication expensive and difficult (e.g., expensive E-beam or deep-ultraviolet (UV) lithography process is necessary [4]). Furthermore, since Si material is not transparent for visible light, Si nanowires are only available in the infrared range ( 1200 nm), which is good for optical communication but not good for optical sensing in the visible light range. Manuscript received September 29, 2008; revised November 20, First published January 06, 2009; current version published February 04, This project was supported by the National Science Foundation of China ( and ). The authors are with the Centre for Optical and Electromagnetic Research, State Key Laboratory of Modern Optical Instrumentation, Zhejiang University, Zijingang, Hangzhou, China ( dxdai@zju.edu.cn). Color versions of one or more of the figures in this letter are available online at Digital Object Identifier /LPT Recently, polymer has become a good candidate for PICs due to its low cost, and easy fabrication [6] [8]. Furthermore, the rich surface functionalities of polymer make it also very attractive for potential applications of biosensing [3]. Various kinds of polymer materials (e.g., benzocyclobuten (BCB) [6], SU-8 [7], polycarbonate [8], etc.) have been developed and used for photonic integrated devices (including microresonators) [3], [7]. In the work reported previously, one usually used polymer buried optical waveguides, which is very similar to SiO -on-si buried waveguides and consequently a large bending radius is required (several millimeters) due to the relatively low refractive index [6]. Recently, some theoretical and experimental results on polycarbonate-based strip waveguides with an air cladding were demonstrated [8]. Such an air cladding introduces a high, which is consequently helpful to achieve a small bending radius. On the other hand, because of the high, one has to choose a very narrow gap ( hundreds of nanometer) in the coupling region for a microring resonator to have a good coupling. Therefore, in order to achieve such a narrow gap, one usually needs some special techniques, e.g., the nanoimprint technique used in [8] and [9]. An alternative way to enhance the coupling is to use microracetrack (with a long coupling region). In this letter, we focus on the use of SU-8 polymer material for realizing a small strip waveguide with a high and compact microracetrack resonators (MRRs) with small bending radii. Considering the resolution limitation of a regular UV-lithography process, the gap in the coupling region in our design is no less than 1.0 m. In this way, the fabrication becomes very simple (only a regular UV-lithography process is needed). In order to enhance the coupling, we reduce the widths of the optical waveguides in the coupling region. Meanwhile, wide optical waveguides are used for the bending sections to reduce the bending loss. A single-side taper is then used to connect these two sections with different widths so that the gap width is kept as small as 1.0 whole region. m in the II. STRUCTURAL DESIGN The waveguide used here has a SiO buffer layer, an air cladding, and a core of SU-8 polymer (see Fig. 1). In this letter, the used polymer material is SU negative tone photoresist (from MicroChem Corporation), which has a refractive index of (at 1550 nm). The SiO buffer should be thick enough to guarantee a low leakage loss. Fig. 2 shows the leakage loss calculated by using a finite-difference method mode-solver [5]. According to the single-mode condition of a SU-8 strip waveguide [5], we consider three cases with different core heights and core widths (see Fig. 2). From this figure, one sees that a smaller core width or core height causes larger leakage loss. When m, the leakage loss is negligible ( 0.1 db/cm) for the present three cases. In our /$ IEEE Authorized licensed use limited to: Zhejiang University. Downloaded on February 222 9, 2009 at 00:35 from IEEE Xplore. Restrictions apply.

226 DAI et al.: COMPACT MICRORACETRACK RESONATOR DEVICES BASED ON SMALL SU-8 POLYMER STRIP WAVEGUIDES 255 Fig. 1. Cross section of the present small SU-8 polymer strip waveguide. Fig. 4. Schematic configuration of the present MRR. Fig. 2. Leakage loss L as the buffer thickness h increases. Fig. 5. Coupling length L of two parallel straight waveguides as the core width w increases. Fig. 3. Calculated bending loss as the bending radius R increases. (a) The pure bending loss L (db/90 ); (b) the transition loss L (db). fabrication, we choose m for a large tolerance to guarantee a low leakage loss even when the thickness of the SU-8 is thinner than the designed value (due to the fabrication errors). Fig. 3 shows the bending loss (including the pure bending loss and the transition loss ) for a 90 -bending as the bending radius decreases. The transition loss is due to the mode mismatch between the straight and bending sections [5]. Here the straight and bending sections have the same core widths. From this figure, one sees that the bending radius can be reduced greatly by increasing the core height and core width. In order to achieve a compact microresonator, we choose a wide core width to have a small bending radius. For example, here we choose m and m so that the total bending loss is very low even when m. For the microresonators, the design of the coupling region is also very important. In order to have a good coupling, usually one should reduce the gap between the two coupling optical waveguides as much as possible. However, for the fabrication of a submicron gap, highly precise deep-uv lithography or nanoimprint technologies are usually needed. Considering the resolution limitation of the UV-lithography process, in our case the gap in the coupling region of the microresonator is chosen to be as larger as 1 m so that an easy fabrication can be realized with a regular UV lithography process. In order to have a good coupling, we use an MRR which has relatively long coupling region (including two parallel straight waveguides). Fig. 4 shows the schematic configuration of the present MRR. In order to enhance the coupling, we reduce the core width of the optical waveguide in the coupling region (see Fig. 4). Fig. 5 shows the calculated coupling length of two parallel straight waveguides (with m) as the core width decreases. The coupling length corresponds to the length of transferring the power from one waveguide to the other one completely. From this figure, one sees that the coupling length is reduced greatly when the core width decreases. However, we note that the leakage loss increases when the core width is reduced. For example, when m, the fundamental mode is hardly supported and the leakage loss becomes very large. Therefore, in this letter, we choose m for the straight waveguide in the coupling region in order to enhance the coupling as well as guarantee a low leakage loss. On the other hand, when the core width decreases, the bending loss will increase and a larger bending radius is needed (as shown in Fig. 3). Therefore, we should choose a large core width for the bending section. Here we choose m and the corresponding bending radius m. In this case, tapers are needed between the narrow waveguide in the coupling region and the wide bending sections. Here we introduce adiabatic single-side tapers so that the two parallel waveguide in the coupling region has a constant gap width (e.g., m) as shown in Fig. 4. The length of the single-side taper is m and the coupling length is m. In summary, for the MRR we choose Authorized licensed use limited to: Zhejiang University. Downloaded on February 223 9, 2009 at 00:35 from IEEE Xplore. Restrictions apply.

227 256 IEEE PHOTONICS TECHNOLOGY LETTERS, VOL. 21, NO. 4, FEBRUARY 15, 2009 responses. Fig. 6(b) shows the measured spectral responses of the through port and drop port for the design with m. This spectral response is normalized by the spectrum of the straight waveguide with the same length. Because the gap in the coupling region is not fabricated well [see the inset in Fig. 6(a)], some excess losses are introduced. Consequently, the -factor of the measured spectral response is not very high. In our future work, it is possible to achieve a higher -factor by reducing the loss in the coupling region with an improved fabrication process. With a higher -factor, this MRR will become very attractive for optical sensing (like the high- -factor obtained in [9]). Fig. 6. (a) SEM picture for the fabricated MRR. (b) Measured spectral responses for the fabricated MRR with R =150m and L =85m. m, m, m, m, m, m, and m. III. FABRICATION AND MEASUREMENT In our fabrication, first a 6- m-thick SiO buffer layer was deposited on a Si substrate by plasma-enhanced chemical vapor deposition system and the measured refractive index is about (at 1550 nm). Before spin-coating SU-8 polymer on the SiO buffer layer, we diluted the SU-8 material with cyclopentanone to achieve SU-8 films as thin as 1 2 m. Otherwise the spin-coated SU-8 film will be thicker than 5 m, which is too thick for our case. This diluted SU-8 material was then used to form a 1.7- m-thick SU-8 thin film by using the technique of spin-coating at the speed of 800 r/s. Then we proceeded with a prebaking process with two steps (including 1-h baking at 65 C and 2-h baking at 95 C). After this two-step prebaking process, the UV lithography process was followed. One should adjust the exposure time for a good patter-transfer from the photomask to the SU-8 thin film. The followed processes include a two-step postbaking and the development. Finally, the process of thermal-flow (i.e., a further baking at 120 C) was carried out to reduce the surface roughness. Fig. 6(a) shows the scanning electron microscope (SEM) photograph for the fabricated compact MRR. The insert in this figure shows the enlarged view of the coupling region with single-side tapers. The SEM photograph for the cross section of the fabricated SU-8 polymer strip waveguide is also shown in the inset at the right-top corner of this figure. One sees that the waveguide profile is deformed due to the thermal-flow process [9]. Not only are the waveguide corners rounded off but also the width becomes larger to some degree. By using the cut-back method, the measured propagation loss is as low as 0.1 db/mm. For the characterization of the fabricated MRR, a broadband amplified spontaneous emission laser was used as the light source. In order to improve the coupling efficiency, the light was butt-coupled into the input waveguide through a tapered lens fiber, which has a focus spot size of about 2.5 m. In our measurement, the butt-coupling loss is about 3.5 db per facet. At the output end, we use another tapered lens fiber to receive the power from the output (through/drop) ports and an optical spectrum analyzer was used to measure the spectral IV. CONCLUSION In summary, we have demonstrated the design and fabrication of compact MRRs based on small SU-8 polymer strip waveguides. The gap width in the coupling region of MRR is as large as 1 m considering the limitation of resolution of the regular UV lithography process. In order to enhance the coupling between the microracetrack and the coupled straight waveguides, the waveguides in the coupling region have narrow core widths. On the other hand, a wide bending section is used to minimize the bending radius. In order to connect these two sections with different widths, we have used single-side tapers so that one has a constant gap width in the coupling region. With the process of thermal-flow, the fabricated small SU-8 polymer strip waveguides has a low loss of about 0.1 db/mm. Our measurement results have shown that the fabricated compact MRR has a -factor of It is possible to achieve a higher -factor by improving the fabrication process. REFERENCES [1] Y. Kokubun, Y. Hatakeyama, M. Ogata, S. Suzuki, and N. Zaizen, Fabrication technologies for vertically coupled microring resonator with multilevel crossing busline and ultracompact-ring radius, IEEE J. Sel. Topics Quantum Electron., vol. 11, no. 1, pp. 4 10, Jan./Feb [2] Q. F. Xu, B. Schmidt, S. Pradhan, and M. Lipson, Micrometre-scale silicon electro-optic modulator, Nature, vol. 435, no. 7040, pp , May [3] C.-Y. Chao and L. J. Guo, Biochemical sensors based on polymer microrings with sharp asymmetrical resonance, Appl. Phys. Lett., vol. 83, no. 8, pp , Aug [4] P. Dumon, W. Bogaerts, V. Wiaux, J. Wouters, S. Beckx, J. V. Campenhout, D. Taillaert, B. Luyssaert, P. Bienstman, D. V. Thourhout, and R. Baets, Low-loss SOI photonic wires and ring resonators fabricated with deep UV lithography, IEEE Photon. Technol. Lett., vol. 16, no. 5, pp , May [5] D. Dai, R. Hu, and S. He, A minimized SiO waveguide using an antiresonant reflecting structure for large-scale optical integrations, IEEE Photon. Technol. Lett., vol. 19, no. 10, pp , May 15, [6] S. Y. Cheng, K. S. Chiang, and H. P. Chan, Birefringence in benzocyclobutene strip optical waveguides, IEEE Photon. Technol. Lett., vol. 15, no. 5, pp , May [7] P. Rabiei and W. H. Steier, Tunable polymer double micro-ring filters, IEEE Photon. Technol. Lett., vol. 15, no. 9, pp , Sep [8] C. Y. Chao and L. J. Guo, Polymer microring resonators fabricated by nanoimprint technique, J. Vacuum Sci. Technol. B, vol. 20, no. 6, pp , Nov./Dec [9] C.-Y. Chao, W. Fung, and L. J. Guo, Polymer microring resonators for biochemical sensing applications, IEEE J. Sel. Topics Quantum Electron., vol. 12, no. 1, pp , Jan./Feb Authorized licensed use limited to: Zhejiang University. Downloaded on February 224 9, 2009 at 00:35 from IEEE Xplore. Restrictions apply.

228 4878 JOURNAL OF LIGHTWAVE TECHNOLOGY, VOL. 27, NO. 21, NOVEMBER 1, 2009 Compact Microring Resonator With 2 2 Tapered Multimode Interference Couplers Daoxin Dai, Member, IEEE, Member, OSA, Liu Yang, Zhen Sheng, Bo Yang, and Sailing He, Senior Member, IEEE Abstract Compact microring resonator devices are realized by using a small SU-8 polymer strip waveguide that has an SU-8 polymer core ( 1.573), an SiO 2 buffer ( 1.445) and an air cladding. Due to the high index contrast of the optical waveguide, a small bending radius ( 150 m) is used for the MRR. To enhance the coupling between the access optical waveguides and the microring, 2 2 multimode interference couplers are used. The measured spectral response of the through port shows a high extinction ratio of over 15 db and a 3-dB bandwidth of about 0.38 nm (corresponding to a moderate -value of 4500). Index Terms Microring, multimode interference (MMI), SU-8. I. INTRODUCTION AS a versatile element for photonic ICs (PICs), microring resonators (MRRs) have received much attention due to their compact size, and easy realization of large-scale PICs. With MRRs, various functional components have been realized for optical communications, such as add--drop filters [1], optical modulators [2], and optical switches [3]. The potential high -factor also makes an MRR very attractive to realize highly sensitive optical sensors by measuring the resonant wavelength shift or the output power variation [4]. In the past years, people have developed various optical waveguides with different materials and structures for realizing MRRs [1] [4]. In order to obtain compact MRRs, a small bending radius is desirable. The simplest way is to use an optical waveguide with high index contrast (i.e., the difference between the core and the cladding, ) [5], [6]. For example, by using the recently developed silicon-on-insulator (SOI) nanowire waveguide, which has the ability of ultrasharp bending due to its ultrahigh 2.0, one could realize ultrasmall microresonators ( m ) [2]. However, for the fabrication of SOI nanowires, one usually has to use the expensive E-beam or deep-uv lithography process [6] due to the submicron cross section (e.g., 500 nm 250 nm). Furthermore, SOI nanowire is unavailable for the applications (e.g., some optical sensing) in visible range where Si material is not transparent. Recently, polymer has become an attractive candidate for photonic ICs (PICs) due to its large transparent window, low Manuscript received May 13, 2009; revised July 04, 2009, August 05, First published August 18, 2009; current version published September 10, This work was supported in part by Zhejiang Provincial Natural Science Foundation (no. J ). D. Dai, L. Yang, Z. Sheng, B. Yang, and S. He are with Centre for Optical and Electromagnetic Research, State Key Laboratory of Modern Optical Instrumentation, Zhejiang University, Hangzhou, China ( dxdai@zju. edu.cn). Digital Object Identifier /JLT cost, and easy fabrication [7] [10]. Many photonic integrated devices have been demonstrated for biosensors [4], tunable filters [9], thermo-optical switches [3], etc., by using various kinds of polymer materials (such as d-pfma [7], BCB [8], SU-8 [9], polycarbonate (PC) [10]). Usually, polymer-buried optical waveguides were used. However, in this case, a large bending radius is required (several millimeters) due to the relatively low refractive index [7], which is very similar to SiO -on-si buried waveguides. To enhance the index contrast, polymer strip waveguides with an air cladding are preferred [10]. On the other hand, because of the high, one has to choose a very narrow gap ( hundreds of nanometers) in the coupling region for an MRR so that a good coupling is obtained. In this case, the fabrication of such a narrow gap needs some special techniques of e.g., nanoimprint technique [10]. In our case, a regular UV-lithography process is used to make the fabrication simpler and easier. Considering the resolution limitation of a regular UV-lithography process, the gap in the coupling region should be no less than 1.0 m. When using a directional coupler for the MRR, such a large gap will result in a relatively long coupling region. A good alternative is to use a multimode interference (MMI) coupler for the coupling [11] because the fabrication is relatively easy, especially when a large bandwidth MRR filter is desirable. In this paper, we use tapered MMI couplers (instead of standard straight MMI couplers used in [11]) for the MRR filter so that the size of the MRR is reduced. Furthermore, the access waveguides for a tapered MMI coupler are usually connected to the MMI section with a tilted angle [13]. In this way, the access waveguides for the MMI section are separated quickly, which is helpful to minimize the coupling between the access waveguides even when choosing a small separation between them to have reduced MMI section width. II. STRUCTURE AND DESIGN Fig. 1 shows the cross section of the small SU-8 polymer strip waveguide used in this paper. This waveguide has an SiO buffer layer, an air cladding, and a core of SU-8 polymer. In this paper, the used polymer material is NANO SU negative tone photoresist (from MicroChem Corporation). The refractive index is about (at 1550 nm), which is measured by using a Metricon 2010 prism coupler system. The SiO buffer is about 6 m thick to guarantee a low leakage loss [12]. Fig. 2 shows the cutoff boundaries of the fundamental and the first-order eigenmodes for TE and TM polarizations at the wavelength of 1550 nm. In order to determine the boundary, we scan the core width and height step by step and use a finite-difference method mode solver to check whether it is single /$ IEEE Authorized licensed use limited to: Univ of Calif Santa Barbara. Downloaded on September 22511, 2009 at 01:48 from IEEE Xplore. Restrictions apply.

229 DAI et al.: COMPACT MICRORING RESONATOR WITH 2 2TAPERED MULTIMODE INTERFERENCE COUPLERS 4879 Fig. 1. Cross section of the present small SU-8 polymer strip waveguide. Fig. 3. Calculated fundamental-mode profile when w = 2:0 m and h = 1:7 m. Fig. 2. Single mode of the present small SU-8 polymer strip waveguide. mode. Here, the first-order eigenmode is the mode with two peaks horizontally and one peak vertically when the core width is larger than the core height. When the core width is smaller than the core height, the first-order eigenmode is the mode with one peak horizontally and two peaks vertically. These two cutoff boundaries define the single-mode condition for the present air-cladded SU-8 ridge waveguide. Due to the geometrical asymmetry, the SU-8 ridge waveguide is a little birefringent, which makes the single-mode condition slightly polarization-dependent. According to the single-mode condition, we choose the width and height of the core as m and m in our design and fabrication. The calculated fundamental-mode profile is shown in Fig. 3. For the present small SU-8 ridge optical waveguide, because of the small cross section and high index contrast, the discontinuity of normal electrical field at the air--su-8 interfaces is relatively significant. Therefore, smooth sidewall is very important to ensure a low scattering loss. For the bending section of the microring, the bending radius should be large enough to have a small bending loss. Here, we use a finite-difference method mode solver and calculate the pure bending loss and the transition loss of the present small SU-8 strip waveguides, as shown by the squares in Fig. 4(a) and (b), respectively. In Fig. 4(a) and (b), we also show the calculated bending loss for the other two types of SU-8 optical waveguides to give a comparison. The first one is air-cladded SU-8 optical waveguide, which has an air buffer layer and an air upper cladding [see the circles in Fig. 4(a) and (b)]. This type of waveguide is similar to the pedestal structure in [10]. The second one is an SiO -cladded SU-8 waveguide, which has an SiO buffer Fig. 4. Calculated bending loss as the bending radius varies. (a) Pure bending loss L. (b) Transition loss L. layer and an SiO upper cladding [see the diamonds in Fig. 4(a) and (b)]. From the pure bending loss shown in Fig. 4(a), one sees the air-cladded type has the ability of ultra-sharp bending. This is because of its ultrahigh index contrast between the core (SU-8) and the cladding (air). In contrast, for the SiO -caldded type, the minimal bending radius is much larger due to its relatively weak confinement. For our present optical waveguide, the air upper cladding is helpful to have a strong optical confinement. On the other hand, the relatively low index contrast between the SU-8 core and the SiO buffer layer limits the reduction of the bending radius. We note that the transition loss (due to the mode mismatch between the fundamental modes of the straight and bending Authorized licensed use limited to: Univ of Calif Santa Barbara. Downloaded on September 22611, 2009 at 01:48 from IEEE Xplore. Restrictions apply.

230 4880 JOURNAL OF LIGHTWAVE TECHNOLOGY, VOL. 27, NO. 21, NOVEMBER 1, 2009 sections) is a significant source for the total bending loss. From Fig. 4(b), one sees that the transition losses for the air-cladded one and the present one are similar. In contrast, the SiO -cladded optical waveguide has a much higher transition loss. From this comparison, one sees the bending radius could be reduced greatly by introducing the air cladding/buffer. However, we should note that the fabrication is not easy to have an air buffer layer by introducing a suspended structure or pedestal structure. In this paper, in order to have a simple fabrication and solid waveguides, we use the structure of SU-8 optical waveguide with air upper cladding on an SiO buffer. For the present waveguide, the minimal bending radius could be as small as 75 m for the requirement of the total bending loss db (where ). In our design and fabrication later, we choose m, for which the theoretical bending loss is much smaller than 0.1 db/90. For MRRs, the design of the coupling region is very important. Here, we use tapered MMI couplers for MRRs [as shown in Fig. 5(a)], which gives a coupling ratio of about 54.5%:43.4%. By tapering the MMI section, the MMI length is reduced greatly [13], [14]. The access waveguides are connected to the MMI section with a tilted angle to match the phase front [13]. In this way, the access waveguides for the MMI section are separated quickly, which is helpful to reduce the coupling between the access waveguides. This is useful to have a smaller MMI width. Fig. 5(b) shows the schematic configuration of the used parabolically tapered MMI coupler, which is defined by where and are the widths at the entrance and the waist, respectively, and is the length of the MMI section. For a general interference (GI) type 2 2 MMI coupler [see Fig. 5(b)], one usually has, where is the gap width and is the core width of the access waveguide. Considering the resolution limitation of the UV lithography process, we choose a relatively large gap width m) between the two access waveguides of the tapered MMI coupler. This makes it possible to realize by using a regular UV lithography process. According to the procedure given in [13], the tapered MMI coupler is designed with the following parameters: m, m, and m. By using a 3-D beam propagation method (BPM) simulation, the estimated theoretical excess loss in the tapered MMI section is small ( 0.1 db), which is due to the nonperfect self-imaging in the MMI section. In the fabrication, a 6- m-thick SiO buffer layer was deposited on a Si substrate by plasma-enhanced chemical vapor deposition (PECVD) system. The SiO buffer has a refractive index of about (at 1550 nm). Then, a 1.7- m-thick SU-8 thin film is formed by using the technique of spin coating at the speed of 800 r/s. After the pre-baking process with two steps (including 1-h baking at 65 C and 2-h baking at 95 C), a regular UV lithography process is followed to form the patters on the SU-8 thin film. For the UV lithography process, the exposure time was optimized to have a good quality of pattern transfer. The followed processes is a 2-h postbaking (i.e., 1 h at 65 C and 1 h at 95 C), which is necessary to make the Fig. 5. (a) Schematic configuration of the present MRR with tapered MMI couplers. (b) Structure of tapered MMI coupler. exposed SU-8 cross-linked sufficiently. Then, a development process follows. Finally, with the process of thermal flow [10] (i.e., a further baking at 120 C), the surface roughness was reduced so that low-loss SU-8 strip waveguides are obtained. The propagation loss measured by using the cutback method is as low as 0.1 db/mm. Due to the long postbaking, the corners on the top of the fabricated waveguide were rounded (see Fig. 1). Such a corner rounding will make the eigenmode s effective indexes deviated from the design values slightly. The influence is similar to that due to the variation of the core width. In this case, the central wavelength will shift for the waveguide devices, e.g., the MRRs considered here. The wavelength deviation could be calibrated during the design and fabrication, or compensated with the temperature tenability. It is also possible to have square waveguides by optimizing the fabrication process further, e.g., using a shorter baking time [15]. In addition, the corner rounding does not introduce significant influences on the mode profile, which has been checked by using a charge-coupled device (CCD) camera. Fig. 6 shows the SEM photo for the fabricated compact MRR with tapered MMI couplers. For the characterization of the fabricated MRR, a broadband amplified spontaneous emission (ASE) laser was used as the light source. The input light was polarized by using an in-line polarizer and was then butt-coupled to the input waveguide through a standard polarization maintaining fiber (PMF), which introduces an estimated coupling loss of about 6.7 db. At the output side, a tapered lens fiber with a focus spot size of about 2.5 m was used at the output side to improve the coupling efficiency from the chip Authorized licensed use limited to: Univ of Calif Santa Barbara. Downloaded on September 22711, 2009 at 01:48 from IEEE Xplore. Restrictions apply.

231 DAI et al.: COMPACT MICRORING RESONATOR WITH 2 2TAPERED MULTIMODE INTERFERENCE COUPLERS 4881 Fig. 8. Measured spectral responses for TE and TM polarizations. Fig. 6. SEM picture for the fabricated MRR filter. Fig. 7. Measured spectral responses of the fabricated MRR filter for TE polarization. to the output fiber and the corresponding butt-coupling loss is about 3.5 db in our measurement. Fig. 7 shows the measured spectral responses of the through port and drop port for TE polarization (see the circles ). The spectral responses are normalized by the spectrum of the straight waveguide with the same length. The solid curves show the theoretical fitting. The measured extinction ratio of the drop port is close to 20 db. From the fitting, the coupling ratio is about 46.5%:45.1% and the estimated loss of the tapered MMI coupler is 0.38 db. The loss of 0.38 db is caused by the fabrication errors of MMI section, e.g., the deviation of the MMI width due to the lithography process. Due to deviation of the MMI width, the self-imaging position shifts, and consequently, the excess loss is introduced. It is possible to estimate the excess loss due to the deviation of the MMI width by using 3-D BPM simulation. For example, the excess loss of the MMI section is about 0.4 db when the deviation of the MMI width is 0.2 m. The spectral response shows a free spectral range (FSR) of 1.49 nm, which is consistent with theoretical estimation. The measured spectral response shows that the 3 db bandwidth is about 0.38 nm, which corresponds to a moderate -value In order to have better performances (e.g., a high extinction ratio, a low loss for the drop channel), the fabrication process should be improved (especially to reduce the loss in the coupling region). In Fig. 8, the measured spectral responses of the through port for TE and TM polarizations are shown by the solid and dashed Fig. 9. (a) Spectral response at the through port as the temperature increases. (b) Resonant wavelength as the temperature increases. curves, respectively. In our experiment, the TE- or TM-polarized lights were obtained by rotating the PMF. Due to the birefringence of the SU-8 strip optical waveguides, there is a polarization-dependent wavelength (PD ). From this figure, one sees that the PD is about 0.37 nm. Furthermore, the TM polarization has a larger loss. This is because the tapered MMI coupler (which was designed for TE polarization) has larger excess loss for TM polarization [14]. This also makes the spectral response of the TM polarization expanded a little (i.e., a lower -value). In order to achieve a polarization-independent MRR filter, one should have a nonbirefringent microring waveguide Authorized licensed use limited to: Univ of Calif Santa Barbara. Downloaded on September 22811, 2009 at 01:48 from IEEE Xplore. Restrictions apply.

232 4882 JOURNAL OF LIGHTWAVE TECHNOLOGY, VOL. 27, NO. 21, NOVEMBER 1, 2009 by appropriately choosing the cross section of the bending section [5] and optimize the tapered MMI couplers for polarization independence [16]. It is well known that polymer usually has a large negative thermooptical coefficient. When the temperature decreases, the resonant wavelength of the SU-8 MRR filter will, therefore, shift to the short wavelength. In our experiments, the chip is heated by using a thermoresistor. A large voltage introduced higher temperature. Here, we measured the spectral response of the fabricated MRR when the temperature increases. Fig. 9(a) shows measured the spectral responses of the through port for the TE polarization when the temperatures are 26.9, 27.3, 28.1, 29.4, and 31.5 C, respectively. From this measurement result, one sees that the resonant wavelength shifts to the shorter wavelength when the temperature increases, which is expected due to the negative thermooptical coefficient of SU-8 polymer. Fig. 9(b) shows the resonant wavelength as the temperature increases. One sees the slope is about nm/ C. The estimated thermooptical coefficient is about. A temperature change of 80 C will introduce a wavelength shift of more than 10 nm. This makes it possible to realize a thermally tunable MRR filter with a large tenability range. III. CONCLUSION In summary, we have demonstrated the design and fabrication of compact MMRs by using the small SU-8 polymer strip waveguide with an air cladding. In order to enhance the coupling between the microring and the access waveguides, tapered MMI couplers have been used. In this way, no submicron gap is introduced, and thus, the regular UV lithography process is sufficient for the fabrication. Our measurement results have shown that the fabricated compact microracetrack resonator has a 3 db bandwidth of about 0.38 nm (corresponding to a moderate -value of 4500) and a high extinction ratio of about 20 db. By improving the fabrication process, a higher -factor and better extinction ratio are expected. The thermal tunability of the fabricated MRR filter has also been characterized. It has been shown that the SU-8 MRR filter can give a large tenability range because of the large TO coefficient. REFERENCES [1] Y. Kokubun, Y. Hatakeyama, M. Ogata, S. Suzuki, and N. Zaizen, Fabrication technologies for vertically coupled microring resonator with multilevel crossing busline and ultracompact-ring radius, IEEE J. Sel. Top. Quantum Electron., vol. 11, no. 1, pp. 4 11, Jan./Feb [2] Q. F. Xu, B. Schmidt, S. Pradhan, and M. Lipson, Micrometre-scale silicon electro-optic modulator, Nature, vol. 435, pp , [3] S. Yamagata, T. Kato, and Y. Kokubun, Non-blocking wavelength channel switch using TO effect of double series coupled microring resonator, Electron. Lett., vol. 41, no. 10, pp , May [4] C.-Y. Chao and L. J. Guoa, Biochemical sensors based on polymer microrings with sharp asymmetrical resonance, Appl. Phys. Lett., vol. 83, pp , [5] R. Hu, D. Dai, and S. He, A small polymeric ridge waveguide with a high index contrast, J. Lightw. Technol., vol. 26, no. 13, pp , Jul [6] P. Dumon, W. Bogaerts, V. Wiaux, J. Wouter, S. Beckx, J. V. Campenhout, D. Taillaert, B. Luyssaert, P. Bienstman, D. V. Thourhout, and R. Baets, Low-loss SOI photonic wires and ring resonators fabricated with deep UV lithography, IEEE Photon. Technol. Lett., vol. 16, no. 5, pp , May [7] R. Yoshimura, Low-loss polymeric optical waveguides fabricated with deuterated polyfluoromethacrylate, J. Lightw. Technol., vol. 16, no. 6, pp , Jun [8] S. Y. Cheng, K. S. Chiang, and H. P. Chan, Birefringence in benzocyclobutene strip optical waveguides, IEEE Photon. Technol. Lett., vol. 15, no. 5, pp , May [9] P. Rabiei and W. H. Steier, Tunable polymer double micro-ring filters, IEEE Photon. Technol. Lett., vol. 15, no. 9, pp , Sep [10] C. Y. Chao and L. J. Guo, Polymer microring resonators fabricated by nanoimprint technique, J. Vac. Sci. Technol. B, vol. 20, pp , [11] D.-X. Xu, A. Densmore, P. Waldron, J. Lapointe, E. Post, A. Delâge, S. Janz, P. Cheben, J. H. Schmid, and B. Lamontagne, High bandwidth SOI photonic wire ring resonators using MMI couplers, Opt. Exp., vol. 15, pp , [12] D. Dai, B. Yang, L. Yang, Z. Sheng, and S. He, Compact microracetrack resonator devices based on small SU-8 polymer strip waveguides, IEEE Photon. Technol. Lett., vol. 21, no. 4, pp , Feb [13] D. Dai and S. He, Design of an ultrashort Si-nanowaveguide-based multimode interference coupler of arbitrary shape, Appl. Opt., vol. 47, pp , [14] L. Yang, B. Yang, Z. Sheng, J. Wang, D. Dai, and S. He, Compact tapered multimode interference couplers based on SU-8 polymer rectangular waveguides, Appl. Phys. Lett., vol. 93, pp , [15] M. Nordström, D. A. Zauner, A. Boisen, and J. Hübner, Single-mode waveguides with SU-8 polymer core and cladding for MOEMS applications, J. Lightw.Technol., vol. 25, no. 5, pp , May [16] D. Dai and S. He, Proposal for diminishment of the polarization-dependency in a Si-nanowire multimode interference (MMI) coupler by tapering the MMI section, IEEE Photon. Technol. Lett., vol. 20, no. 8, pp , Apr Daoxin Dai (M 07) received the B.Eng. degree from the Department of Optical Engineering, Zhejiang University, Hangzhou, China, and the Ph.D. degree from the Royal Institute of Technology (KTH), Stockholm, Sweden, in 2000 and 2005, respectively. He joined Zhejiang University, Hangzhou, China, as an Assistant Professor, where he became an Associate Professor in His current research interests include silicon micro/nanophotonic integrated devices. He has authored or coauthored more than 50 refereed international journals papers. Dr. Dai is a member the Optical Society of America and the International Society for Optical Engineers. Liu Yang received the B.Eng. degree from Kunming University of Science and Technology, Kunming, China, in She is currently working toward the Ph.D. degree in the Department of Optical Engineering, Zhejiang University, Hangzhou, China. His current research interests include the design and fabrication of planar lightwave circuits. Zhen Sheng was born in Shandong, China, in He received the B.Eng. degree in 2005 from the Department of Optical Engineering, Zhejiang University, Hangzhou, China, where he is currently working toward the Ph.D. degree. His current research interests include the design and fabrication of planar lightwave circuits. Authorized licensed use limited to: Univ of Calif Santa Barbara. Downloaded on September 22911, 2009 at 01:48 from IEEE Xplore. Restrictions apply.

233 DAI et al.: COMPACT MICRORING RESONATOR WITH 2 2TAPERED MULTIMODE INTERFERENCE COUPLERS 4883 Bo Yang was born in Hunan, China, in She received the B.E. degree in 2007 from Zhejiang University, Hangzhou, China, where she is currently working toward the Master s degree. Sailing He (M 92 SM 98) received the Licentiate of Technology and Ph.D. degrees in electromagnetic theory from the Royal Institute of Technology, Stockholm, Sweden, in 1991 and 1992, respectively. Since 1992, he has been a member of the faculty of the Royal Institute of Technology. Since 1999, he has also been with the Centre for Optical and Electromagnetic Research, Zhejiang University, Hangzhou, China, as a Special Changjiang Professor appointed by the Ministry of Education of China. He is also a Chief Scientist for the Joint Research Center of Photonics of the Royal Institute of Technology and Zhejiang University. He has first-authored one monograph (Oxford Univ. Press), and authored or coauthored more than 300 papers in refereed international journals. He is the holder of a dozen of patents in optical communications. Authorized licensed use limited to: Univ of Calif Santa Barbara. Downloaded on September 23011, 2009 at 01:48 from IEEE Xplore. Restrictions apply.

234 Electrically-pumped compact hybrid silicon microring lasers for optical interconnects Di Liang, 1 * Marco Fiorentino, 2 Tadashi Okumura, 1 Hsu-Hao Chang, 1 Daryl T. Spencer, 1 Ying-Hao Kuo, 1 Alexander W. Fang, 1 Daoxin Dai, 1 Raymond G. Beausoleil, 2 and John E. Bowers 1 1 Department of Electrical and Computer Engineering, University of California, Santa Barbara, CA 93106, USA 2 Information and Quantum Systems Lab, Hewlett Packard Laboratories, Palo Alto, CA 94304, USA *dliang@ece.ucsb.edu Abstract: We demonstrate an electrically-pumped hybrid silicon microring laser fabricated by a self-aligned process. The compact structure (D = 50 m) and small electrical and optical losses result in lasing threshold as low as 5.4 ma and up to 65 C operation temperature in continuous-wave (cw) mode. The spectrum is single mode with large extinction ratio and small linewidth observed. Application as on-chip optical interconnects is discussed from a system perspective Optical Society of America OCIS codes: ( ) Semiconductor lasers; ( ) Microcavity devices. References and links 1. A. S.-H. Liao, and S. Wang, Semiconductor injection lasers with a circular resonator, Appl. Phys. Lett. 36(10), (1980). 2. A. M. Prabhu, A. Tsay, H. Zhanghua, and V. Vien, Ultracompact SOI Microring Add/Drop Filter With Wide Bandwidth and Wide FSR, IEEE Photon. Technol. Lett. 21(10), (2009). 3. A. W. Poon, X. S. Luo, F. Xu, and H. Chen, Cascaded Microresonator-Based Matrix Switch for Silicon On- Chip Optical Interconnection, Proc. IEEE 97(7), (2009). 4. S. Wang, A. Ramachandran, and S.-J. Ja, Integrated microring resonator biosensors for monitoring cell growth and detectionr of toxic chemicals in water, Biosens. Bioelectron. 24(10), (2009). 5. Q. Xu, B. Schmidt, S. Pradhan, and M. Lipson, Micrometre-scale silicon electro-optic modulator, Nature 435(7040), (2005). 6. F. Xia, L. Sekaric, and Y. Vlasov, Ultracompact optical buffers on a silicon chip, Nat. Photonics 1(1), (2007). 7. H. Park, A. W. Fang, S. Kodama, and J. E. Bowers, Hybrid silicon evanescent laser fabricated with a silicon waveguide and III-V offset quantum wells, Opt. Express 13(23), (2005). 8. A. W. Fang, H. Park, O. Cohen, R. Jones, M. J. Paniccia, and J. E. Bowers, Electrically pumped hybrid AlGaInAs-silicon evanescent laser, Opt. Express 14(20), (2006). 9. A. W. Fang, R. Jones, H. Park, O. Cohen, O. Raday, M. J. Paniccia, and J. E. Bowers, Integrated AlGaInAssilicon evanescent race track laser and photodetector, Opt. Express 15(5), (2007). 10. A. W. Fang, E. Lively, Y.-H. Kuo, D. Liang, and J. E. Bowers, A distributed feedback silicon evanescent laser, Opt. Express 16(7), (2008). 11. J. Van Campenhout, P. Rojo Romeo, P. Regreny, C. Seassal, D. Van Thourhout, S. Verstuyft, L. Di Cioccio, J. M. Fedeli, C. Lagahe, and R. Baets, Electrically pumped InP-based microdisk lasers integrated with a nanophotonic silicon-on-insulator waveguide circuit, Opt. Express 15(11), (2007). 12. D. Liang, M. Fiorentino, A. W. Fang, D. Dai, Y.-H. Kuo, R. G. Beausoleil, and J. E. Bowers, An Optically- Pumped Silicon Evanescent Microring Resonator Laser, in The 6th IEEE international conference on Group IV Photonics, 2009), paper FA K. K. Lee, D. R. Lim, H.-C. Luan, A. Agarwal, J. Foresi, and L. C. Kimerling, Effect of size and roughness on light transmission in a Si/SiO2 waveguide: experiments and model, Appl. Phys. Lett. 77(11), (2000). 14. H. Park, A. W. Fang, R. Jones, O. Cohen, O. Raday, M. N. Sysak, M. J. Paniccia, and J. E. Bowers, A hybrid AlGaInAs-silicon evanescent waveguide photodetector, Opt. Express 15(10), (2007). 15. D. Liang, and J. E. Bowers, Highly Efficient Vertical Outgassing Channels for Low-Temperature InP-to-Silicon Direct Wafer Bonding on the Silicon-On-Insulator (SOI) Substrate, J. Vac. Sci. Technol. B 26(4), (2008). 16. Q. Xu, D. Fattal, and R. G. Beausoleil, Silicon microring resonators with 1.5-microm radius, Opt. Express 16(6), (2008). 17. G. Mezosi, M. J. Strain, S. Furst, Z. Wang, S. Yu, and M. Sorel, Unidirectional Bistability in AlGaInAs Microring and Microdisk Semiconductor Lasers, IEEE Photon. Technol. Lett. 21(2), (2009). (C) 2009 OSA 26 October 2009 / Vol. 17, No. 22 / OPTICS EXPRESS

235 18. G. Franz, Damage in III/V semiconductors caused by hard- and soft-etching plasmas, J. Vac. Sci. Technol. A 19(3), (2001). 19. S. Bull, A. V. Andrianov, I. Harrison, and E. C. Larkins, The study of strain and defects in high power laser diodes by spectroscopically resolved photoluminescence microscopy, Eur. Phys. J. Appl. Phys. 27(1-3), (2004). 20. A. Boudjani, B. Sieber, F. Cleton, and A. Rudra, Cl and EBIC analysis of a p+-ingaas/n-ingaas/n-inp/n+-inp heterostructure, Mater. Sci. Eng. B 42(1-3), (1996). 21. J.-T. Lim, J.-G. Choi, S. K. Noh, K.-C. Je, S.-Y. Yim, and S.-H. Park, Nondestructive Photoacoustic Measurement of Doping Densities in Bulk GaAs, Jpn. J. Appl. Phys. 46(12), (2007). 22. U. Schade, S. Kollakowski, E. H. Böttcher, and D. Bimberg, Improved performance of large-area InP/InGaAs metal-semiconductor-metal photodetectors by sulfur passivation, Appl. Phys. Lett. 64(11), (1994). 23. L. A. Coldren, and S. W. Corzine, Diode Lasers and Photonic Integrated Circuits (Wiley-Interscience, New York, USA, 1995). 24. M. Sorel, P. J. R. Laybourn, G. Giuliani, and S. Donati, Unidirectional bistability in semiconductor waveguide ring lasers, Appl. Phys. Lett. 80(17), (2002). 25. A. W. Fang, B. R. Koch, R. Jones, E. Lively, Di Liang, Ying-Hao Kuo, and J. E. Bowers, A Distributed Bragg Reflector Silicon Evanescent Laser, IEEE Photon. Technol. Lett. 20(20), (2008) D. M. Taylor, C. R. Bennett, T. J. Shepherd, L. F. Michaille, M. D. Nielsen, and H. R. Simonsen, Demonstration of multi-core photonic crystal fibre in an optical interconnect, Electron. Lett. 42(6), (2006). 28. D. Taillaert, W. Bogaerts, P. Bienstman, T. F. Krauss, P. Van Daele, I. Moerman, S. Verstuyft, K. De Mesel, and R. Baets, An out-of-plane grating coupler for efficient butt-coupling between compact planar waveguides and single-mode fibers, IEEE J. Quantum Electron. 38(7), (2002). 29. J. Song, Q. Fang, S. H. Tao, M. B. Yu, G. Q. Lo, and D. L. Kwong, Passive ring-assisted Mach-Zehnder interleaver on silicon-on-insulator, Opt. Express 16(12), (2008). 30. D. M. Taylor, and T. J. Shepherd, (personal communication, 2008). 1. Introduction Diode lasers with ring or disk resonator geometries are one of the most attractive on-chip light sources for photonic integrated circuits (PICs) since their inherent traveling wave operation nature requires no gratings or Fabry-Perot (FP) facets for optical feedback [1]. As a type of multi-functional component, compact passive microring resonators have been used extensively on Si substrates for wavelength division multiplexing (WDM) add-drop filters/routers [2], switches [3], sensors [4], modulator [5] and buffers [6]. A microring-based Si transmitter is possible for on-chip optical interconnect application if a laser can be integrated as well. Practical use requires power efficient, continuous-wave (cw) operation, high-speed direct modulation and operation at evaluated temperature, which are analyzed here. The hybrid silicon platform (HSP) [7, 8] is a promising approach to enable robust active components on a complementary metal-oxide semiconductor (CMOS)-compatible Si platform. The first on-chip light source fabricated on HSP employs a racetrack ring resonator geometry [9] but retains the same cross-sectional structure as that of straight Fabry-Perot (FP) ones [8]. It consisted of a 1-2 m wide SOI waveguide covered by a wider III-V mesa, which leads to a hybrid mode that spans both III-V and Si. The poor lateral optical confinement for the hybrid optical mode requires the bend radius 100 m such that resulting excess bending loss is smaller than available gain. The long cavity length of ~2.6 mm and modal mismatch at the straight and bent waveguide sections cause relatively high threshold current of ~175 ma [9]. More recently distributed feedback (DFB) hybrid silicon lasers achieved up to 7 threshold decrease with 340 m long grating region [10]. Further reduction in threshold and device footprint was demonstrated by a 7.5 m-diameter disk laser integrated on SOI substrate with polymer-based wafer bonding technique [11], thus showing the potential to realize on-chip Si light sources with low power consumption and high-speed direct modulation using a compact micro-ring/disk structure. Recently, we developed opticallypumped hybrid silicon microring lasers with small diameters of 15 and 25 m [12]. In these lasers we measured a threshold carrier density of ~ cm 3 indicating low optical and electrical losses. In this paper we demonstrate the electrically-driven version of this compact microring laser and discuss their potential application for optical interconnects from a system perspective. (C) 2009 OSA 26 October 2009 / Vol. 17, No. 22 / OPTICS EXPRESS

236 2. Device design and fabrication Figure 1(a) shows the schematic of the hybrid silicon microring laser. The laser comprises an III-V ring resonator on top of a silicon disk with the same diameter. The fundamental whisper-gallery mode shifts towards the resonator edge as shown by a Beam Propagation Method (BPM) simulated mode profile in the inset of Fig. 1(a). The III-V epitaxial structure includes five periods of InAlGaAs-based, quantum wells ( g =1.51 m) plus a p-doped 50 nmthick InAlGaAs separate confinement heterostructure (SCH) layer are sandwiched by a 110 nm-thick n-doped InP contact layer and a p-doped 1.5 m-thick InP cladding layer. This structure is bonded on top of a SOI wafer with a 350 nm-thick silicon device layer, resulting in confinement factors of 15.2% and 51.7% in active region and silicon, respectively. A SOI bus waveguide w WG =0.6, 0.8 and 1 m-wide, 25 m-long is s= nm away from the resonator, as shown in Fig. 1. The SOI waveguide is then tapered up to 1.5 m through two 105 m long tapers to minimize the sidewall-induced scattering loss [13], resulting a 235 mlong bus waveguide to guide coupled light to two integrated photodetectors. The taper-shaped photodetectors with a total length of 180 m are employed to adiabatically transform the mode from the passive SOI waveguide to hybrid waveguide detectors with low coupling loss and small reflection [14]. Fig. 1. (a) Schematic of compact hybrid silicon ring resonator laser with BPM mode profile and integrated, tapered photodetectors. Variables of coupling gap s and bus waveguide width w WG are labeled. (b) The microscopic image of a finished device with critical dimension labeled. (c) SEM cross-sectional image of the evanescent point coupler. Figure 2 schematically highlights the critical processing steps in the device fabrication. The fabrication starts by patterning 1.5 m-wide bus waveguides on the SOI substrate where tapered photodetectors will sit. Vertical outgassing channels are formed in the same step to allow the transfer of a high-quality III-V epitaxial layer onto silicon through a lowtemperature O 2 plasma-assisted wafer bonding process [15]. After bonding the InP carrier substrate is selectively removed and the p-type contact metal (W/Pd/Ti/Pd) is deposited on the p-ingaas contact layer by E-beam evaporation (Pd/Ti/Pd) and sputtering (W). The metal is coated with a SiO 2 hardmask using plasma-enhanced chemical vapor deposition (PECVD). The narrow bus waveguide with tapered sections and the 50 m diameter disk resonator are patterned in a resist layer using E-beam lithography (Fig. 2(a)). Successive inductively coupled plasma (ICP) reactive ion etching steps are used to transfer the pattern to the SiO 2 hardmask, p-metal, and the ~2 m-thick III-V all the way through top silicon layer. This process is highly anisotropic and gives smooth sidewall profile (Fig. 2(b)) for tight dimension control and low scattering loss. We measured an etch angle of ~86 in the scanning electron microscope in Fig. 1(c). This is, therefore, a self-aligned process to avoid misalignment (C) 2009 OSA 26 October 2009 / Vol. 17, No. 22 / OPTICS EXPRESS

237 between III-V ring and Si disk resonators. After passivating the etch-exposed III-V sidewall with PECVD SiO 2, a 45 m diameter open circular area inside the disk is defined by conventional projection lithography (Fig. 2(c)). We then apply dry-etch steps to remove PECVD SiO 2, metal, and InP to reach the active region which is selectively removed by H 2 SO 4 -based solution, resulting in the exposure of the n-type InP contact layer (Fig. 2(d)). The III-V material, with the exception of a thin n-inp layer on top of Si bus waveguide, is removed in this step. These steps form a III-V ring resonator with a 2.5 m waveguide width. In contrast to the typical silicon hybrid device structure, this deep-etched interface allows much stronger lateral optical confinement ( n 2). After depositing another layer of PECVD SiO 2 to passivate the inner sidewall of the ring, the n-metal (Ni/Ge/Au/Ni/Au) is then formed onto the n-contact InP layer inside the ring and near the photodetector mesa through photolithography and lift-off (Fig. 2(e)). After metallization and final dielectric passivation, the thick probe metal pads are deposited (Fig. 2(f)). Fig. 2. Schematic of critical fabrication steps (not to scale). 3. Experimental results Figure 3 shows the typical cw, temperature-dependent light-current (LI) characteristic of devices with (a) 150 nm and (b) 250 nm coupling gaps and w WG =0.6 m bus waveguide. Devices with III-V junction side up sit on a copper stage whose temperature (labeled next to each LI curve) is actively controlled. For coupling gap s=150 and 250 nm, the minimum threshold currents are 8.37 and 5.97 ma at 10 C, respectively. They correspond to the respective threshold current densities of 2.02 and 1.43 ka/cm 2, assuming uniform carrier distribution in the w ring_wg =2.8 m active region. There numbers are similar to that of previously demonstrated FP (2 ka/cm 2 ) [8], racetrack (1.7 ka/cm 2 ) [9] and DFB (1.4 ka/cm 2 ) [10] lasers. Threshold voltages measured at room temperature (RT=20 C) are 1.39 V (I th =9.56 ma) and 1.33 V (I th =7.61 ma) for devices in Figs. 5(a) and 5(b), respectively, which lead to laser turn-on powers of mw and mw. The average series resistance of 24 devices is at RT. Devices of s=150 and 250 nm lase up to a stage temperatures of 40 and 65 C, respectively. The cw LI measurement stops at 25 ma typically in order to avoid excessive device heating. Figure 3(c) summarizes the threshold currents for different bus waveguide widths as a function of coupling gap at RT. As the coupling gap increases from 50 to 250 nm, outcoupling coefficient equivalent to mirror loss for straight devices decreases exponentially from 0.03 to based on 2-dimentional (2D) finite-difference time-domain (FDTD) simulation. However, the threshold follows a linear or weak exponential decay, resulting in (C) 2009 OSA 26 October 2009 / Vol. 17, No. 22 / OPTICS EXPRESS

238 only ~2.4 reduction to s=250 nm. It indicates internal cavity loss comparable or even larger than the distributed outcoupling loss at s=50 nm, and dominating the total round-trip loss for weak coupling (s=50 nm). Lower threshold for large s is likely to be from the slightly lower internal cavity loss since narrow trench (i.e., small s) results in dry etch lag and poor PECVD SiO 2 sidewall coverage, introducing higher modal loss at evanescent point coupling region. We detect lasing in devices with s=500 nm by monitoring the infrared image since the photodetectors are unable to capture the lasing signal due to negligible outcoupling from the microrings and large waveguide loss. No lasing at RT is observed for devices with w WG =800 and 1000 nm when s=50 nm. We measure higher thresholds are for devices with s=150 nm and bus waveguide widths w WG =800 and 1000 nm. FDTD simulation shows higher outcoupling coefficient for wider bus waveguides, however, the cavity Q-factor also decreases dramatically if bus waveguide is wider than modal width in the microring cavity due to phase mismatch between ring and bus waveguide [16]. We attribute the absence of lasing for s=50 nm and higher threshold for s=150 nm for bus waveguide widths of 800 and 1000 nm to higher outcoupling and higher internal cavity losses. Fig. 3. LI characteristic of microring lasers with coupling gap (a) s=150 nm and (b) s=250 nm at various stage temperatures. (c) Threshold currents of different bus waveguide widths as a function of coupling gap width. The output power in Fig. 3 is the sum of the photocurrent measured at both photodetectors. The photodetector responsivity is assumed to be 1 A/W therefore the laser power values are conservatively estimated [14]. As mentioned in the fabrication section, we failed to remove III-V epitaxial layers on the Si bus waveguide, resulting in a 235 m long saturable absorber region. In addition to this substantial power loss from band-to-band absorption, free carrier absorption (FCA) and scattering loss also contribute to reduce the measured photocurrent. A column of devices with asymmetric photodetector position (i.e., with the right photodetectors 300 m away from the laser) is used to estimate the total bus waveguide loss. We dice off the right photodetectors leaving the lossy 235 m long bus waveguide intact and measure the amplified spontaneous emission (ASE) output from the left photodetector which is forward biased at V. We then compare this output with the ASE from a photodetector at the same bias, which doesn t go through the bus waveguide region. The coupling gap s is 500 nm in this measurement to avoid the coupling to the microring. From these measurements, we conservatively estimate the power loss to be 7 db, corresponding to a 70 cm 1 waveguide loss, with assumption that both photodetectors have the same ASE efficiency and suffer identical coupling losses. Diode currents of both photodetectors are similar for identical biases, indicating similar ASE efficiency. Theoretical models give losses of ~3.37 cm 1 and ~5.77 cm 1 for free carrier absorption and scattering loss, respectively. These results were obtained assuming a 45% confinement factor in III-V and RMS sidewall roughness of 60 nm. Based on these estimates we believe that the output power would be at least 5 higher if the active region and InP cladding were removed. We attribute the kinks in the LI curves to a combination effect of bidirectional instability, and saturable absorption in the bus waveguide because they tend to appear at the similar power levels for different stage temperatures. When outcoupling is small and output is low (e.g., Fig. 3(b)), a small back reflection either from the bus waveguide/photodetector junctions or from the evanescent point coupler cannot be negligible. This leads to the coupling of (C) 2009 OSA 26 October 2009 / Vol. 17, No. 22 / OPTICS EXPRESS

239 transverse modes as well as of clock-wise (CW) and counter-clock-wise CCW) lasing modes [17], and subsequently extra kinks in LI curves. In contrast to previously demonstrated devices on HSP where the current channel is defined by proton implantation [8], the deeply-etched structure in this work poses a concern of the dry etch-exposed active region sidewall at the outer circumference of the microring. For a typical ridge waveguide lasers, the mesa etch stops above the active region to avoid exposing the active region. In the situations where active region needs to be exposed (e.g., vertical cavity surface-emitting lasers(vcsel)), wet etch is preferable because dry etch causes more severe lattice damage, consequently generating more non-radiative recombination centers at the interface [18]. This creates a current leakage path at the interfaces of the active region with exposed surfaces thus increasing the threshold current, reducing the differential quantum efficiency, and inducing early device degradation. This effect is even more detrimental for narrow stripe geometry (i.e., this work) since the ratio of exposed surface-to-active region volume is high. Instead of employing conventional methods (e.g., time-resolved PL [19], electron beam induced current [20], or photoacoustic measurements [21]) to locate the defects and determine the non-radiative recombination velocity at the deep-etched III-V interface on the Si substrate, we studied the leakage current of photodetectors and lasers in reverse bias condition. Since only is the laser active region at outer circumference exposed by dry etch while active region at inner circumference and on photodetectors is exposed by wet etch, comparison of reverse bias dark current density for lasers and photodetectors allows qualitative and straightforward estimation of the leakage induced by dry-etching. Owing to the difference in the area of active regions for lasers and photodetectors, we define a one-dimensional (1D) dark current density J as I J (1) L where I and L are dark current and the length of exposed active region, respectively. Here we assume that reserve bias saturation current in the diode region far from sidewall is negligibly small, i.e., only leakage current at the sidewall contributes to measured dark current. Therefore, we can write dark current for lasers I l and photodetectors I p as: Il JlLl JoLo JiLi (2) I J L (3) p p p where J o (J i ) and L o (L i ) are dark current densities and exposed active region length at the ring outer (inner) sidewalls, respectively. Same definition applies to parameters for photodetectors with subscript p. It is valid to assume that J i = J p since active region at inner ring and photodetector mesa are exposed simultaneously with same wet etch. Plugging (3) into (2), we then obtain the ratio between the leakage current densities for dry etch and wet etch surfaces: J IL o l p LI i p (4) J L I i o p (C) 2009 OSA 26 October 2009 / Vol. 17, No. 22 / OPTICS EXPRESS

240 Fig. 4. Typical IV characteristics of a microring laser and one of its on-chip photodetectors. The length of exposed active region for laser and photodetector are shown in the inset. Blue and black present wet and dry etch defined interface. Figure 4 shows typical current-voltage (IV) curves for a microring laser and a photodetector. Similar performance in both forward and reverse bias region exhibits comparable leakage current. The length of exposed active region for laser and photodetector are shown in the inset of Fig. 7, where blue and black lines represent wet and dry etch interfaces, respectively. If we take the angle of the dry etch surface into consideration, the inner and outer diameters of the microring are 44.7 and 50.3 m, respectively. The measured dark current average values (its standard deviation) for 20 lasers and 24 photodetectors are 13.5 (10.3) and 7.6 (2.8) na. Both lasers and photodetectors have dark currents in na range. Plugging the average dark current values into Eq. (4), we obtain J o /J i =3.22, meaning that the leakage current at a dry-etch interface is 3.22 larger, per unit length, than a wet etch surface. The larger dark current standard deviation for lasers also indicates performance variation caused by the dry etched interface. However, this qualitative study shows that surface recombination at the dry etch-exposed active region does not significantly compromise device operation. The typical 2D dark current densities at 3 V for lasers and photodetectors are and pa/ m 2, respectively. These values are comparable to the values obtained from devices with special surface treatment [22]. Low intrinsic surface recombination velocity for InP-based semiconductors, well-controlled ICP dry etch, and good PECVD dielectric passivation all contribute to good interface condition for our deep-etched, narrow mesa structure. Fig. 5. (a) Spectrum measured at cw injection current of 16 ma (1.15 I th) compared with photoluminescence result. (b) Spectra of primary lasing peak 16 to 30 ma cw current. Inset: LI curve measured from the photodetector on the left hand side. The color dots in the LI curve highlights the corresponding spectrum taken at the same current but with different laser emission direction. Figure 5 shows the spectrum of a laser, the spectrum was measured by fiber coupling the output of a cleaved waveguide. The broadband spectrum in Fig. 5(a) shows that multiple (C) 2009 OSA 26 October 2009 / Vol. 17, No. 22 / OPTICS EXPRESS

241 longitudinal cavity modes lase when device is driven at 16 ma (1.15 I th ) at RT. The blue trace shows the photoluminescence (PL) spectrum measured by exciting a device without top InGaAs contact layer with a 0.5 mw 980 nm source at RT. Notice that the primary lasing peak is aligned with the PL maximum at nm. The free spectral range (FSR) is 4.2± 0.05 nm ((0.1 nm resolution for broadand sweep). Theoretical FSR value can be calculated from FSR= 0 2 /(n g D) [23] where 0, n g are laser vacuum wavelength and group index, respectively, and D is round-trip modal length. According to the FDTD simulation for the fundamental mode n g =3.462 and D=49.77 m and the FSR is 4.32 nm which agrees with the experimental data very well. A unique characteristic of disk/ring resonator lasers, unidirectional bistability [24], is also noticeable by comparing the peak intensity change in Fig. 5(b) and inset LI curve in it. The LI curve records the CW laser emission while the peak intensity change represents the output power variation of CCW lasing. It is clearly seen that for currents around 20 ma the primary lasing direction switches from CW to CCW. While characterization of the dynamic properties of our devices is under development, Fig. 6 shows the calculated 3 db bandwidth for injection current 10, 20 and 30 ma as a function of device diameter (cavity length). Previously FP and racetrack ring devices have shown ~50% injection efficiency, 1500 cm 1 material gain and 15 cm 1 modal loss. The racetrack devices, however have lower surface recombination and scattering losses and better carrier/optical mode overlap compared with the devices under study here. We therefore used a conservative estimate of the parameters including 30% injection efficiency, 1200 cm 1 material gain, 30 cm 1 modal loss and 3% outcoupling coefficient. These estimates result in ~5 ma threshold current for a 50 m microring laser. No thermal effect is taken into account in this calculation. In order to achieve 3 db bandwidth of 10 GHz, 50 m diameter device needs to be driven with 20 ma bias current, i.e., 4 I th. Devices in Fig. 4 demonstrate the capacity to operate at 4 I th without serious thermal roll-over. Devices with smaller dimension have smaller threshold and require less injection current to reach 10 GHz 3 db bandwidth. As a reference, a DBR laser with 600 m-long gain region fabricated on the same HSP has shown experimentally a ~2.5 GHz 3 db bandwidth for a 105-mA (1.6 I th ) bias current (black dot in Fig. 6). These same devices have shown 4 Gbit/sec data transmission for a bias of ~2 I th [25]. Clearly, employing short cavity devices (e.g., microring lasers) is an efficient approach to further increase the direct modulation bandwidth without sacrificing low power dissipation. Increased thermal impedance poses a major obstacle for all compact devices. Fig. 6. Calculated 3 db bandwidth as a function of microring laser diameter (cavity length) for 10, 20 and 30 ma injection current. Black dot represents experimental 3 db bandwidth of 2.5 GHz measured on a hybrid Si DBR laser without about 1.6 I th bias current [25]. 4. Applications In the past years a number of companies have announced and started selling active optical cables products [26]. These products are mostly targeted as replacement to existing Infiniband (C) 2009 OSA 26 October 2009 / Vol. 17, No. 22 / OPTICS EXPRESS

242 cables. The main premise of these products is that they can fit into existing infrastructure while providing additional functionality (extended span without repeaters and, possibly lower power consumption) and reducing the system s total cost of ownership. Their appeal mostly resides in the fact that the optical protocol is completely transparent to the user, thus eliminating the need for on-site optical installation. Most active optical cables use directly modulated VCSELs as the optical engines. VCSELs are likely the most expensive component in the optical module and they present numerous coupling problems. Other companies use CMOS photonics to build modulators and use flip-chip DFB/DBR lasers as optical engine. Once again the lasers and the flip-chip process add cost and potential failure points for these products. Because they need to conform to existing Infiniband protocols, these cables are mostly limited to 10-Gbit/sec (single data rate, or SDR), 20-Gbit/sec (dual data rate, DDR), and 40-Gbit/sec (quad data rate, QDR). Cable lengths are typically of the order of 100 m (300 m for products that use more expensive single longitudinal mode DFB lasers and single-mode fibers). Future generations of active optical cables will need to meet the increasing bandwidth requirements of peta- and exa-scale computers (i.e. computer systems with to flops) and data centers while keeping costs and complexity low. We believe that the hybrid silicon platform and the microring lasers presented in this paper provide the technology to meet these needs. A schematic of a possible cable configuration is shown in Fig. 7. The optical engines consist of bundles of microring lasers that are coupled on a single waveguide. The hybrid silicon lasers are designed to emit light at different wavelengths (with a spacing of ~5 nm) and can be directly modulated to create a 10 Gbit/sec on-off keying (OOK) signal. The modulated light from the lasers is coupled into one of the cores of a multicore photonic crystal fiber (PCF) [27]. PCFs together with vertical grating couplers [28] allow high-density connections while reducing the cost of pigtailing the photonic circuit. At the other end of the cable light is coupled onto a second photonic integrated circuit and send to an interleaverbased demultiplexer [29] that separates the various wavelength components and send them to hybrid detectors that recover the data sent. Each fiber core can therefore carry multiple (typically 4-5 for current active medium gain spectrum) 10 Gbit/sec channels in one direction. The fiber consists of up to 19 cores [30] that can be configured (at the hardware level) for upload or download depending on the traffic needs. This combination of technologies can therefore provide a bandwidth increase of at least one order of magnitude over existing active cables while at the same time reducing complexity and, possibly, cost. Fig. 7. Schematic view of a CWDM optical cable based on the hybrid silicon platform 5. Conclusion We have demonstrated electrically-pumped compact microring resonator lasers with integrated photodetectors on a hybrid silicon platform. A new deep-etch, self-aligned fabrication process was developed to enable 50 m diameter, 2.5 m wide III-V ring (C) 2009 OSA 26 October 2009 / Vol. 17, No. 22 / OPTICS EXPRESS

243 resonator on a self-aligned Si disk resonator with same dimension. Threshold current as low as 5.4 ma was measured at stage temperature of 10 C and lasing was observed for temperatures up to 65 C. Typical threshold power consumption is mw at RT (20 C). Multiple longitudinal mode lasing is observed with major lasing peak at nm aligned with the gain peak which is measured from RT PL. Experimental FSR of 4.2 nm agrees with theoretical calculation for fundamental transverse mode. More than 40 db extinction ratio and nm linewidth (limited by instrument resolution) are measured. A simple IV study reveals that dry etch-exposed active region interface experiences comparable leakage current as wet etch-exposed interface, indicating low surface recombination. Simulated 3 db bandwidth is 10 GHz for 50 mm diameter microring laser with 4 I th bias current. The overall device performance meets the basic requirements of small footprint, low power consumption with promising capacity for high-speed modulation. Future devices with smaller diameters and improved processing are expected to result in lower thresholds, higher power and higher temperature operation for optical interconnects. Acknowledgments The authors gratefully thank Hui-Wen Chen, Matthew Sysak, Martijn Heck and Mike Haney for valuable discussion and fabrication assistance. We acknowledge the support from HP Innovation Research Program (SBY572738), DARPA Phaser (HR ), NSF NNIN REU internship program and NSF funded NNIN fabrication facility at the University of California, Santa Barbara. (C) 2009 OSA 26 October 2009 / Vol. 17, No. 22 / OPTICS EXPRESS

244 1630 IEEE PHOTONICS TECHNOLOGY LETTERS, VOL. 21, NO. 21, NOVEMBER 1, 2009 Proposal of a Coupled-Microring-Based Wavelength-Selective 1 N Power Splitter Daoxin Dai, Member, IEEE, and Sailing He, Senior Member, IEEE Abstract A novel wavelength-selective 1 power splitter, which consists of a microring and +1couplers, is presented. One coupler is for coupling the light signal from the input port into the microring and the other couplers are for coupling the signal light from the microring to the output ports. The channels with the resonant wavelength of the microring are dropped and split into output ports. The critical coupling condition to achieve a high extinction ratio is also given. By appropriately choosing the coupling coefficients for the input/output couplers, it is flexible to have a uniform or nonuniform power splitting as desired. Index Terms Microring, power splitter, wavelength selective. I. INTRODUCTION ASONE of the most promising broadband access network solutions, passive optical networks (PONs) [1] for a broadband access have attracted much attention recently because of their long service coverage, high reliability, and low maintenance expenditure. Various PONs have been developed [1], e.g., time-division-multiplexed (TDM)-PON [2], and wavelength-division-multiplexed (WDM)-PON [3]. Among them, the TDM-PON has a low per-subscriber cost by sharing a single wavelength channel with a number of optical network units (ONUs) [2]. However, the bandwidth available for per-subscriber is limited. In contrast, the WDM-PON connects an optical line termination and ONUs with pluralities of multiplexed channels with different carrier wavelengths and consequently the capacity is expanded greatly [2]. However, because of relatively expensive WDM components, the WDM-PON is considered as a next-generation solution following TDM-PONs [2], [4]. A hybrid PON combining TDM and WDM techniques is, therefore, becoming one of the most attractive solutions [4], [5]. The hybrid PON takes the advantages of the power splitting in the TDM-PON and the wavelength-routing in the WDM- PON. Thus, at the remote node of a hybrid TDM/WDM-PON, the combination of wavelength-selective filters (for wavelength routing) and power splitters (for power-splitting) is needed [5]. Manuscript received July 07, 2009; revised August 09, First published September 09, 2009; current version published October 14, This project was supported in part by the Zhejiang Provincial Natural Science Foundation (J ), and in part by the National Science Foundation of China ( ). The authors are with the Centre for Optical and Electromagnetic Research, State Key Laboratory of Modern Optical Instrumentation, Zhejiang University, Zijingang, Hangzhou, China ( dxdai@zju.edu.cn). Color versions of one or more of the figures in this letter are available online at Digital Object Identifier /LPT Fig. 1. Schematic configuration of the proposed wavelength-selective 1 2 N power splitter. Usually people use an arrayed waveguide grating (AWG) cascaded with power splitters [4], [5]. This is suitable for demultiplexing many channels simultaneously. For some cases when it is desirable to select only one or a few channels from the multiplexed channels and split them to different terminals, an AWG demultiplexer may be not a good choice. A simple solution is using a conventional microring add drop filter cascaded with a power splitter as microring add drop filters have been very attractive due to the compactness and flexibility. The power splitter could be realized by using a multimode interference (MMI) coupler, or a directional coupler. In order to have an arbitrary splitter ratio, usually one could use, e.g., cascaded directional couplers or MMI couplers. This cascaded structure may introduce a relatively large size. Here we propose a compact microcavity-based wavelength-selective power splitter which serves as a wavelength-selective filter as well as a power splitter. With the proposal structure, it is easy to realize a very compact wavelength-selective power splitting with an arbitrary ratio. II. STRUCTURE AND THEORY Fig. 1 shows the schematic configuration of our proposed wavelength-selective power splitter, which includes a microcavity, and couplers (i.e., ). Among these couplers, the zeroth one is for coupling the light signal from the input port into the microcavity and coupling the signal light from the microcavity to the through port. The other couplers (coupler ) are used for coupling out the light signal with a specific wavelength from the microcavity to the output ports. Here the specific wavelength is actually the resonant wavelength of the microcavity (which will be shown below). Theoretically speaking, the microcavity in Fig. 1 could be in any form, e.g., microrings [6], microdisks [7], etc. In this /$ IEEE Authorized licensed use limited to: Univ of California-Santa Barbara. Downloaded on October , 2009 at 18:53 from IEEE Xplore. Restrictions apply.

245 DAI AND HE: PROPOSAL OF A COUPLED-MICRORING-BASEDWAVELENGTH-SELECTIVE POWER SPLITTER 1631 letter, we use a microring resonator, which is a very popular block element. The microring resonator will drop the channel at the resonant wavelength (which is similar to the conventional add drop filters [6], [8]) and split the power into the output waveguides. For a microring, when light is launched from the input port (i.e., port #1 of the zeroth coupler), the relationships between the electrical fields at the other ports of the zeroth coupler are given by where is the electric field at port of the zeroth coupler, is the cross coupling coefficient from port to port of the zeroth coupler, is the through transmission coefficient from port to port of the zeroth coupler. And the electric fields at port #1 and port #2 are related by, where is the transmission coefficient from port #2 to port #1 through the long path in the counter-clockwise direction. One has where and are the total propagation loss and total phase from port #2 to #1 of the zeroth coupler along the light propagation direction. From (1) and (2), one obtains the following formula for the electric fields: The output from port #2 of the th coupler is then given by where and are the propagation loss and the phase delay from port #2 of the zeroth coupler to port #1 of the th coupler. For an all-pass filter [i.e., there is only one coupler (e.g., #0)], it is well known that there is a critical coupling condition for achieving a high extinction ratio. This condition is corresponding to the destructive interference for a specific wavelength (i.e., the resonant wavelength) in the through waveguide between the through transmitted optical field and the optical field coupled from the microring cavity [8]. On the other hand, at the drop port, the successive tap coupled optical fields (from the microcavity) due to any drop coupler have a constructive interference, which makes a maximal output at the resonant wavelength. Similarly, the critical coupling condition for the present structure is given by (1) (2) (3) (4) (5) When, it corresponds to the cases of all-pass filters, and add drop filters, respectively. From (4), the ratio between two adjacent outputs (e.g., the output from the th and the couplers) is given by In order to have a uniform power splitting ratio, one should make Usually a low-loss optical waveguide is used, i.e.,, and thus. For a high- microring, the through transmission coefficient is very close to 1. In this case, the condition to have a uniform power splitter is very simple, i.e., This indicates that one could use uniform couplers for all the output waveguide, which consequently makes the design very simple. On the other hand, when a low- microring is used or the microring has high-loss, in order to have a uniform splitting ratio one should choose different coupling coefficients for the couplers individually according to (7). By choosing the coupling coefficient according to (6), one could realize arbitrary splitting ratio, which may be desired for some applications. III. DESIGN AND ANALYSIS Here we consider the case of using a silicon-on-insulator (SOI) nanowire waveguide, which has drawn much attention in recent years [6] [9]. SOI nanowire has an ultrahigh index contrast and consequently has the ability of ultrasharp bending, which is very attractive to have an ultrasmall microring resonator. Here we choose an SOI nanowire with a dimension of nm for a single-mode operation at the wavelength of 1550 nm. The refractive indexes for silicon and silica are and (for the buffer and cladding). TE polarization (for which the electrical field is horizontal) is considered here. The through transmission coefficients for the output couplers should satisfy (5) to have a high extinction ratio. For the present example, we consider a 1 3 uniform power splitter and consequently the coupling ratio for the th coupler should satisfy. In order to obtain the required different coefficients for the input coupler and the output coupler, a simple way is to choose appropriate gap widths for them. Fig. 2(a) shows the calculated coefficients and as the gap width varies. The microring has a bending radius of m. Here the through transmission coefficient and the cross coupling ratio are calculated by using a threedimensional finite-difference time-domain (3D-FDTD) method for which the grid sizes are nm, nm, and nm. From Fig. 2, for example, if we choose nm for the input coupler, the corresponding through transmission coefficient is. According to (5), the coefficient for the output coupler should be, which is obtained by choosing nm according to the results shown in Fig. 2(a). We also check the fabrication tolerance for the designed input/output couplers. When there is a fabrication (6) (7) (8) Authorized licensed use limited to: Univ of California-Santa Barbara. Downloaded on October , 2009 at 18:53 from IEEE Xplore. Restrictions apply.

246 1632 IEEE PHOTONICS TECHNOLOGY LETTERS, VOL. 21, NO. 21, NOVEMBER 1, 2009 Fig. 2. Coefficients t and k for the case of R = 5 m and w = 0:45 m: (a) as the gap width w varies; (b) as the deviation 1w varies (w = 110 nm, and 150 nm for the zeroth and nth couplers, respectively). Fig. 3. Calculated spectral responses of (a) the through port; (b) output port #1; (c) output port #2; and (d) output port #3. error of (i.e., the deviation of the waveguide width from its design value), one has, and. Fig. 2(b) shows the coupling ratio of and as the deviation varies. When the core width varies, the coupling ratio changes significantly. In Fig. 2(b), the value of is also shown as the deviation varies (see the red circles). From this figure, one sees that and almost satisfy the relationship when the deviation are the same for the couplers. In a practical case, the core-width deviation for all the waveguides may be nonuniform. This nonuniformity will degrade the extinction ratio and make the splitting ratio deviated from the designed value. Therefore, a careful control is needed for the fabrication. Fortunately, the difference of the deviation should be small in a small area usually. Thus, it is possible to have a high extinction ratio of the spectral response at the through port when the variation of the core width is smaller than 40 nm. By using (3) and (4), we calculate the spectral responses at the through port and the output ports ( ), as shown in Fig. 3(a) (d). We also use a 3D-FDTD method and give a simulation for the present design (see the circles in Fig. 3). From the comparison in Fig. 3, one sees that the analytical result is close to that from the FDTD simulation. From Fig. 3, one also sees that the wavelength is dropped and the splitting ratio is uniform (i.e., 33 : 33 : 33). For the present design, the 3 db-bandwidth is about 0.3 nm. When a larger bandwidth is desirable, one could achieve a flat-top spectral response by cascading two or more microrings [9], which also extends the free spectral range (FSR) of the wavelength-selective power splitter. We also design a 1 3 wavelength-selective power splitter with an arbitrary splitting ratio by choosing the coupling coefficients for coupler #0 #4 as , , , and , respectively. And the corresponding gap widths are 0.1, 0.14, 0.14, and 0.16 m. With such a design, the power splitter ratio is 42% : 40% : 18%. One sees that it is possible to design any given splitter ratio by choosing the coupling ratio appropriately. IV. CONCLUSION In summary, we have presented a novel wavelength-selective power splitter, which consists of a microcavity and couplers. One coupler is for coupling the light signal from the input port into the microcavity and the other couplers (coupler ) are used for coupling the signal light of a specific wavelength from the microcavity to the output ports. With the microcavity, the channels with the resonant wavelengths are selectively dropped and split into the output ports. We have derived the critical coupling condition for determining the coupling coefficients of the input/output couplers to achieve a high extinction ratio. By appropriately choosing the coupling coefficients for the input/output couplers, it is flexible to have a uniform or nonuniform power splitting as desired. Our proposed structure is equivalent to a conventional add drop filter combined with a power splitter. If a flat-top spectral response with a larger 3-dB bandwidth is desirable, a simple and effective way is to cascade two or more microrings, which also extends the FSR of the wavelength-selective power splitter. REFERENCES [1] C. H. Lee, W. V. Sorin, and B. Y. Kim, Fiber to the home using a PON infrastructure, J. Lightw. Technol., vol. 24, no. 12, pp , Dec [2] L. G. Kazovsky, W.-T. Shaw, D. Gutierrez, N. Cheng, and S.-W. 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247 Silicon hybrid plasmonic submicron-donut resonator with pure dielectric access waveguides Daoxin Dai, 1,2,* Yaocheng Shi, 1,2 Sailing He, 1,2 Lech Wosinski, 2,3 and Lars Thylen 2,3,4 1 Centre for Optical and Electromagnetic Research, State Key Laboratory for Modern Optical Instrumentation, Zhejiang Provincial Key Laboratory for Sensing Technologies, Zhejiang University, East Building No.5, Zijingang Campus, Hangzhou , China 2 JORCEP [Joint Research Center of Photonics of the Royal Institute of Technology (KTH) and Zhejiang University], Zhejiang University, Hangzhou , China 3 Laboratory of Photonics and Microwave Engineering, Royal Institute of Technology (KTH), Kista, Sweden. 4 Hewlett-Packard Laboratories, Palo Alto, California USA *dxdai@zju.edu.cn Abstract: Characteristic analyses are given for a bent silicon hybrid plasmonic waveguide, which has the ability of submicron bending (e.g., R = 500nm) even when operating at the infrared wavelength range (1.2 m~2 m). A silicon hybrid plasmonic submicron-donut resonator is then presented by utilizing the sharp-bending ability of the hybrid plasmonic waveguide. In order to enable long-distance optical interconnects, a pure dielectric access waveguide is introduced for the present hybrid plasmonic submicron-donut resonator by utilizing the evanescent coupling between this pure dielectric waveguide and the submicron hybrid plasmonic resonator. Since the hybrid plasmonic waveguide has a relatively low intrinsic loss, the theoretical intrinsic Q-value is up to 2000 even when the bending radius is reduced to 800nm. By using a three-dimensional finitedifference time-domain (FDTD) method, the spectral response of hybrid plasmonic submicron-donut resonators with a bending radius of 800nm is simulated. The critical coupling of the resonance at around 1423nm is achieved by choosing a 80nm-wide gap between the access waveguide and the resonator. The corresponding loaded Q-value of the submicron-donut resonator is about Optical Society of America OCIS codes: ( ) Surface plasmons; ( ) Photonic integrated circuits; ( ) Guided waves. References and links 1. K. Tanaka and M. Tanaka, Simulations of nanometric optical circuits based on surface plasmon polariton gap waveguide, Appl. Phys. Lett. 82(8), (2003). 2. K. Tanaka, M. Tanaka, and T. Sugiyama, Simulation of practical nanometric optical circuits based on surface plasmon polariton gap waveguides, Opt. Express 13(1), (2005). 3. F. Kusunoki, T. Yotsuya, J. Takahara, and T. Kobayashi, Propagation properties of guided waves in indexguided two-dimensional optical waveguides, Appl. Phys. Lett. 86(21), (2005). 4. D. F. P. Pile and D. K. Gramotnev, Plasmonic subwavelength waveguides: next to zero losses at sharp bends, Opt. Lett. 30(10), (2005). 5. L. Liu, Z. H. Han, and S. L. He, Novel surface plasmon waveguide for high integration, Opt. Express 13(17), (2005). 6. S. Xiao, L. Liu, and M. Qiu, Resonator channel drop filters in a plasmon-polaritons metal, Opt. Express 14(7), (2006). 7. G. Veronis and S. H. Fan, Bends and splitters in metal-dielectric-metal subwavelength plasmonic waveguides, Appl. Phys. Lett. 87(13), (2005). 8. D. F. P. Pile and D. K. Gramotnev, Channel plasmon-polariton in a triangular groove on a metal surface, Opt. Lett. 29(10), (2004). 9. S. I. Bozhevolnyi, V. S. Volkov, E. Devaux, J. Y. Laluet, and T. W. Ebbesen, Channel plasmon subwavelength waveguide components including interferometers and ring resonators, Nature 440(7083), (2006). 10. R. F. Oulton, V. J. Sorger, D. A. Genov, D. F. P. Pile, and X. Zhang, A hybrid plasmonic waveguide for subwavelength confinement and long-range propagation, Nat. Photonics 2(8), (2008). # $15.00 USD Received 19 Aug 2011; revised 10 Oct 2011; accepted 10 Oct 2011; published 7 Nov 2011 (C) 2011 OSA 21 November 2011 / Vol. 19, No. 24 / OPTICS EXPRESS

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Gong, High quality factor, small mode volume, ring-type plasmonic microresonator on a silver chip, J. Phys. At. Mol. Opt. Phys. 43(3), (2010). 41. are P. R. Villeneuve, J. S. Foresi, J. Ferrera, E. R. Thoen, G. Steinmeyer, S. Fan, J. D. Joannopoulos, L. C. Kimerling, H. I. Smith, and E. P. Ippen, Photonic-bandgap microcavities in optical waveguides, Nature 390(6656), (1997). # $15.00 USD Received 19 Aug 2011; revised 10 Oct 2011; accepted 10 Oct 2011; published 7 Nov 2011 (C) 2011 OSA 21 November 2011 / Vol. 19, No. 24 / OPTICS EXPRESS

249 42. X. Wang, C.-Y. Lin, S. Chakravarty, J. Luo, A. K.-Y. Jen, and R. T. Chen, Effective in-device r 33 of 735 pm/v on electro-optic polymer infiltrated silicon photonic crystal slot waveguides, Opt. Lett. 36(6), (2011). 1. Introduction It is well known that a surface plasmon (SP) waveguides can break the diffraction limit and thus enable nano-scale optical waveguiding and light confinement. Therefore, surface plasmon (SP) waveguides have attracted a lot of attention to achieve photonic integrated circuits (PICs) with an ultrahigh integration density. Furthermore, plasmonics offers a way in order to transfer and process both photonic and electronic signals along the same plasmonic circuit, which is desired to combine photonics and electronics for high-speed signal processing and to easily realize some easy realization of active components. In the past decades, many types of three-dimensional plasmonic waveguides have been proposed to support highly localized fields, e.g., narrow gaps between two metal interfaces [1 7] and V- grooves in metals [8, 9]. The problem is that the propagation distance is usually limited to the order of several micrometers due to the huge intrinsic loss. Recently hybrid plasmonic waveguides have been proposed and attracted a lot of attention as a good option to realize nano-scale light confinement as well as relatively long propagation distance [10 26]. This makes it interesting to realize elements of various functionality by using hybrid plasmonic waveguides. As a versatile element for photonic integrated circuits, optical cavities have been used in many applications, e.g., light sources [27], optical filters [28], optical modulators/switches [29], optical sensing [30], nonlinear optics [31], etc. People have developed various optical cavities based on different materials/structures (especially pure dielectric platforms), e.g., photonic crystal cavities, silicon microring/microdisk, etc. However, there is not much work on optical cavities based on hybrid plasmonic waveguides. It is well known that for many applications one usually desires to have an optical cavity with a high-q factor and low volume. Therefore, it is very important to use an optical waveguide, which allows an ultrasharp bending. In Ref [24], an analysis is given for a semiconductor-insulator-metal strip waveguide (which is a kind of hybrid plasmonic waveguide). In this paper, we focus on the bent hybrid plasmonic waveguide with a metal cap, which has not been characterized well. Our results show that the present hybrid plasmonic waveguide enables a submicron bending radius. Consequently this makes it available for realization of submicron resonators. In Ref [26], a subwavelength hybrid plasmonic nanodisk without access waveguides is investigated theoretically and shows that it is possible to simultaneously achieve a relatively high Q-factor and Purcell factor. Even though a hybrid plasmonic waveguide has a relatively low loss and enables a relatively long propagation distance (~10 2 m), it is still not a good option for long-distance (e.g., 10 3 ~10 4 m) optical interconnects if there is no assistance from gain mediums [32].Therefore, in this paper, we propose a silicon hybrid plasmonic submicron-donut resonator with pure dielectric access waveguides by utilizing the evanescent coupling between the pure dielectric waveguide and the submicron hybrid plasmonic resonator. This way, the pure dielectric waveguide enables a long-distance optical interconnect because of its low intrinsic low loss. Meanwhile, no additional mode converter is needed to combine the hybrid plasmonic circuits and the pure dielectric waveguides. A microdonut resonator is essentially a microdisk with an inner hole perforated at the center, and a single mode operation can be made by adjusting the radius of the inner hole. In comparison with a microring resonator, a microdonut resonator is expected to have a higher quality factor because the fundamental mode only interacts with the outer sidewall of the resonator by adjusting the radius of the inner hole [33]. In this paper, the submicron-donut resonator operating at the near-infrared wavelength range (1200nm~2000nm) is realized by using Si hybrid plasmonic waveguides with the ability of sharp-bending. Furthermore, particularly the hybrid plasmonic waveguide used for the submicron-donut resonator has a large contact area between the metal layer and the low-index layer, which helps to maintain a good adherence of the metal layer and makes the fabrication easy and robust. # $15.00 USD Received 19 Aug 2011; revised 10 Oct 2011; accepted 10 Oct 2011; published 7 Nov 2011 (C) 2011 OSA 21 November 2011 / Vol. 19, No. 24 / OPTICS EXPRESS

250 2. Structure and theory Figure 1(a) shows the schematic configuration of the present hybrid plasmonic submicrondonut resonator. The hybrid plasmonic waveguide consists of a Si substrate, buffer layer, a high-index dielectric rib, a low-index cladding, a low-index nano-slot and a metal cap. A lowindex nano-slot region is inserted between the high-index region and the metal region. For the TM fundamental mode, there is a significant field enhancement in the low-index nano-slot region due to the boundary condition of the perpendicular electrical field. Usually the lowindex material could be SiO 2, Al 2 O 3, SiN, or polymer while the high-index material could be silicon [14], or III-V semiconductor [25]. In present hybrid plasmonic submicron-donut resonator, one can achieve a single-mode operation since the fundamental mode of the resonator is mostly confined around the outer perimeter of the microdonut while the higherorder modes are pushed into the leaky zone. This is the difference between microdonut resonators and microdisk resonators. Furthermore, in a microdonut resonator, the fundamental mode only interacts with the outer sidewall of the resonator (which will be seen in Fig. 6 below) by adjusting the radius of the inner hole. In contrast, in a microring resonator, the mode interacts with two sidewalls in microring resonators. Consequently, a higher quality factor for the fundamental mode is expected when using microdonut resonator. Since the hybrid plasmonic waveguide used for submicron-donut resonators is wide, there is a large contact area between the metal layer and the low-index layer, which helps to achieve a good adherence of the metal layer and consequently makes an easy and robust fabrication. Fig. 1. (a) The submicron-donut resonators; (b) the cross section. Since silicon photonics has become very attractive because of its fabrication compatibility to the standard CMOS microelectronics technology, here we choose silicon-on-insulator (SOI) wafers for the present hybrid plasmonic structure as an example. The wavelength-dependent refractive indices of the materials involved are given by the following formulas Metal [34] The frequency-dependent complex refractive index ( ) of any metal can be appropriately given by the Drude formula as follows. 2 p ( ) 1, (1) ( i c ) where c is the collision frequency and p is the plasma frequency. The temperature dependence of the plasma frequency owing to its volumetric effects is written as / 1 ( T T ), (2) p p0 e 0 where e is the expansion coefficient of the metal and T 0 is the reference temperature (e.g., room temperature). The collision frequency c is given by # $15.00 USD Received 19 Aug 2011; revised 10 Oct 2011; accepted 10 Oct 2011; published 7 Nov 2011 (C) 2011 OSA 21 November 2011 / Vol. 19, No. 24 / OPTICS EXPRESS

251 (3) c cp ce, where cp and ce are corresponding to contributions from the phonon electron scattering and electron electron scattering, respectively. The phonon-electron scattering frequency cp is given by [35] 4 TD / T 5 cp( T) 0[2/5 4( T / TD) ] d z, 0 z where T D is the Debye temperature. The electron-electron scattering frequency ce is given by [36] B hef z (4) e 1 1 ce ( T) {( k T) [ h /(4 )] }, (5) 6 where E F is the Fermi energy, k B is Boltzmann constant, h is Plank constant. is a constant giving the average over the Fermi surface of the scattering probability and is the fractional umklapp scattering. All the parameters involved for Ag are given in Table SiO 2 and Si Table 1. The Parameters of Silver [34] Plasma frequency at room temperature p rad/s Thermal expansion coefficient e K 1 Debye temperature T D 215 K Fermi energy E F 5.48 ev rad/s Boltzmann constant k B m 2 kg s 2 K 1 H m 2 kg / s The refractive index of a dielectric is usually given by the Sellmeier formula. For SiO 2, one has [34] n SiO2 Q ( ) 1 Bq /( q), q 1 (6) where is the wavelength given in micron ( m), B 1 = , B 2 = , B 3 = , 2 1 = m 2, 2 2 = m 2, 2 3 = m 2. For Si, one has [37] A1 A2 2 4 dn nsi ( ) n 0 A A4 ( T T0 ), 1 ( 1) (7) dt where n 0 = , A 1 = , A 2 = , A 3 = , A 4 = , 1 =0.028 (for undoped silicon), T 0 is the ambient temperature (T 0 = 300K), dn/dt is the temperature coefficient, and T 0 =293K, dn/dt = /K. 3. Results and discussions By using Eqs. (1), (6) and (7), we obtain the dependences of the refractive indices of SiO 2 Si, and Ag on the wavelength, as shown in Fig. 2(a) and 2(b). The experimental data from Ref [38]. for the silver s refractive index n Ag is also shown here. From this figure, it can be seen that the Drude formula gives a good estimation for the refractive index of silver in the wavelength range from 1.2 m to 2.0 m. # $15.00 USD Received 19 Aug 2011; revised 10 Oct 2011; accepted 10 Oct 2011; published 7 Nov 2011 (C) 2011 OSA 21 November 2011 / Vol. 19, No. 24 / OPTICS EXPRESS

252 Fig. 2. (a) The refractive indices of Si and SiO 2; (b) the real part (n Ag_re) and the imaginary part (n Ag_im) of the calculated refractive index n Ag of silver. The experimental data from Ref. [38]. for n Ag is also shown here Ultrasharply bent hybrid plasmonic waveguides Fig. 3. The real part (n eff_re) of the effective index n eff of the TM fundamental mode for bent hybrid plasmonic waveguides with different core widths (@1550nm); (a) h slot=10nm; (b) h slot=20nm; (c) h slot=50nm. In order to give a characteristic analysis for the bent hybrid plasmonic waveguide, first we consider the case of =1550nm, which is one of the most concerned window. The corresponding parameters in this example are: the high index n H = (Si), n L =1.444 (SiO 2 ), n metal = i (Ag), the index of the buffer layer n buf =1.444 (SiO 2 ). The silicon # $15.00 USD Received 19 Aug 2011; revised 10 Oct 2011; accepted 10 Oct 2011; published 7 Nov 2011 (C) 2011 OSA 21 November 2011 / Vol. 19, No. 24 / OPTICS EXPRESS

253 height H=300nm, and the metal height h m =200nm. In order to have a sharp bending, we choose a deep etching, i.e., h rib =H=300nm. For the calculation of the complex propagation constants of the eigenmodes of bent hybrid plasmonic waveguides, we use a full-vectorial finite-difference method (FV-FDM) mode-solver in a cylindrical coordinate system. The complex effective index n eff is then given by n eff = /k 0, where k 0 is the wavenumber in vacuum. Figure 3(a) 3(c) show the real part of the calculated effective index n eff for the TM fundamental mode of the bent hybrid plasmonic waveguides as the bending radius R decreases from 2 m to 0.5 m. Here we consider the cases with h slot = 10, 20, and 50nm. The waveguide widths are set at w = R, 400, 300, and 200nm, respectively. The radius R is for the outer sidewall of the bent waveguide, as shown in Fig. 1. Note that the submicron-donut becomes a submicro-disk when choosing w = R. From Fig. 3(a) 3(c), it can be seen that one has a larger effective index when choosing a larger waveguide width, especially when the bending radius is larger (e.g., R = 1~2 m). This is because more power is confined in the core region. As the bending radius decreases, the peak of the mode profile shifts outward and consequently the inner surface influence the mode profile less. Therefore, the effective index of the bent waveguide becomes less sensitive to the waveguide width. Fig. 4. The imaginary part n eff_im of the effective index of the TM fundamental mode for bent hybrid plasmonic waveguides with different core widths (@1550nm); (a) h slot = 10nm; (b) h slot = 20nm; (c) h slot = 50nm. Figure 4(a) 4(c) show the imaginary part n eff_im of the effective index for bent hybrid plasmonic waveguides as the bending radius decreases. There are two sources contributing to the imaginary part (i.e, the loss). One is from the intrinsic loss due to the metal absorption. This intrinsic loss per unit length is not sensitive to the bending radius. The other one is from the leakage due to the bending, which increases exponentially as the bending radius decreases. Therefore, from Fig. 4(a) 4(c), one sees that the imaginary part n eff_im is not sensitive to the # $15.00 USD Received 19 Aug 2011; revised 10 Oct 2011; accepted 10 Oct 2011; published 7 Nov 2011 (C) 2011 OSA 21 November 2011 / Vol. 19, No. 24 / OPTICS EXPRESS

254 bending radius when the bending radius is relatively large. When one reduces the bending radius further to a certain value (R 0 ), a significant increase is observed. The low-index slot height h slot also plays an important role for the loss in a bent hybrid plasmonic waveguide. According to our previous analysis, a straight hybrid plasmonic waveguide with a smaller slot height h slot has a higher loss because more power sees the metal [14, 32]. Since a bent waveguide with a relatively large bending radius is similar to a straight waveguide, one has a larger imaginary part (loss) when choosing a smaller h slot. However, on the other hand, a hybrid plasmonic waveguide with a smaller slot height has a stronger confinement (see the effective index shown in Fig. 3(a) 3(c)), and consequently lower bending loss can be achieved and a smaller bending radius is allowed. For example, when h slot = 50nm, a significant imaginary part is observed when R <R 0 (where R 0 = 1.2 m). In contrast, when h slot = 10nm, the radius R 0 is as small as 0.75 m. Figure 4(a) 4(c) also show that the imaginary part (loss) becomes lower by choosing a wider waveguide. This is because there is less power confined in the metal region for a hybrid plasmonic waveguide with a larger core width. Fig. 5. (a) The bending loss for bent hybrid plasmonic waveguides with different core widths (@1550nm); (a) h slot = 10nm; (b) h slot = 20nm; (c) h slot = 50nm. We also calculate the loss for a 90 -bending hybrid plasmonic waveguide with the imaginary part n eff_im of the effective index, i.e., L = 20log 10 [exp( n eff_im k 0 R /2)], wehre k 0 is the wavenumber in vacuum. The calculated results for the cases of h SiO2 = 10, 20, and 50nm are shown in Fig. 5(a) 5(c), respectively. From these figures, it can be seen that there is an optimal bending radius, which gives a minimal total loss for a 90 -bending. This is due to the joint contributions from the bending leakage (which increases exponentially as the bending radius decreases) and the intrinsic loss due to the metal absorption. This intrinsic loss per 90 bending is proportional to the bending radius. Therefore, one has a minimal total loss at an optimal bending radius R opt. When R>R opt, the intrinsic loss due to the metal absorption is dominant and the loss decreases linearly almost as the bending radius decreases. Otherwise, # $15.00 USD Received 19 Aug 2011; revised 10 Oct 2011; accepted 10 Oct 2011; published 7 Nov 2011 (C) 2011 OSA 21 November 2011 / Vol. 19, No. 24 / OPTICS EXPRESS

255 the bending loss becomes dominant and the total loss increases exponentially as the bending radius decreases. The low-index slot height h slot also plays an important role for the loss in a bent hybrid plasmonic waveguide. From Fig. 5(a) 5(c), one sees that the optimal bending radius R opt for a minimal loss is sensitive to the slot height h slot. When choosing a smaller slot height h slot, one has a smaller optimal bending radius R opt. For example, one has R opt = 600nm, 800nm, and 1.1 m when choosing h slot = 10, 20, and 50nm, respectively. The reason is that the smaller slot height provides a stronger ability of light confinement, as discussed in Ref [14,32]. For the case with a small slot height (e.g., h slot = 10nm), the bending loss is observed until the bending radius becomes very small. In contrast, when there is a large slot height (e.g., h slot = 50nm), the hybrid plasmonic effect becomes weaker and one has a smaller intrinsic loss [32]. In this case, however, the behavior of the hybrid plasmonic waveguide is like a dielectric waveguide and the bending loss becomes huge when the bending radius is smaller than 1 m. Figure 5(a) 5(c) also show that the loss becomes lower by choosing a wider waveguide. This is because there is a stronger confinement for a hybrid plasmonic waveguide with a larger core width Submicron-donut resonator For the design of submicron-donut resonators, we consider the case of h slot = 20nm and w co = 400nm as an example. Figure 6(a) 6(d) show the electrical field distribution E y (x, y) of the TM fundamental mode for the cases of R = 2 m, 1 m, 800nm, and 500nm, respectively. From these figures, it can be seen that there is a field enhancement in the low-index slot region. We note that the light is still well confined in the slot region even when the bending radius is as small as 500nm (about 1/3 of the operation wavelength). When the radius decreases, one sees that the peak of the electrical field shifts outward as expected. Consequently the TM fundamental mode less interacts with the inner sidewall, which helps to achieve low scattering loss. For example, when the bending radius is reduced to 800nm, the field hardly interacts with the inner sidewall at tall. Figure 7(a) shows the calculated real part of the effective index and the loss of a bent hybrid plasmonic waveguide when the wavelength varies from 1.2 m to 2 m. From this figure, it can be seen that the effective index decreases as the wavelength increases, which is similar to a pure dielectric waveguide. Such a negative dispersion comes from the material dispersion and the waveguide dispersion. The dispersion coefficient D = ( n eff / ) is about 0.8~ 0.4 m 1. As the wavelength increases, the loss of the bent hybrid plasmonic waveguide becomes higher. There are two reasons. The first reason is related with the metal absorption loss. For the hybrid plasmonic waveguide, the power confined in the silicon region at the short wavelength is more than that at long wavelength. It indicates that less light see the metal and consequently less metal absorption at the shorter wavelength in the range from 1.2 m to 2 m. The other reason is that the confinement ability becomes weaker at longer wavelength and consequently the loss due to the bending leakage increases. When the wavelength varies from 1200nm to 2000nm, the loss is roughly doubled. Figure 7(b) shows the group index N g of the bent hybrid plasmonic waveguide. The group index N g is given by N g = n eff D, where D is the dispersion coefficient. The intrinsic Q-value of the submicron-donut resonators based on the bent hybrid plasmonic waveguide is also shown in Fig. 7(b). The intrinsic Q-value is calculated by the following formula: Q = N g 2 /( 0 ) [39], where is the attenuation coefficient, 0 is the wavelength in vacuum. Since = 2n eff_im k 0, one has Q = N g /(2n eff_im ), where n eff_im is the imaginary part of the effective index. From this figure, it can be seen that the intrinsic Q-value decreases as the wavelength increases, which is due to the higher loss at longer wavelength. Because of the relatively low loss of the hybrid plasmonic waveguide, the intrinsic Q-value is expected to be as high as 10 2 ~10 3 even when choosing a very small bending radius, R = 800nm. This Q-value for the present submicron-donut resonator is comparable to that for a plasmonic microring resonator with R = 5 m calculated in Ref [40]. Meanwhile, the small volume of the submicron-donut resonator helps to achieve a high Purcell factor F P given by F P = 3(4 2 ) 1 ( 0 /n) 3 (Q/V eff ) [26], where V eff is the effective mode volume, V eff = P(r)d 3 r/p max [41], where P(r) is the # $15.00 USD Received 19 Aug 2011; revised 10 Oct 2011; accepted 10 Oct 2011; published 7 Nov 2011 (C) 2011 OSA 21 November 2011 / Vol. 19, No. 24 / OPTICS EXPRESS

256 electromagnetic energy density of the mode, and P max is the peak value of P(r). With this definition, one has an effective modal volume V eff 0.01 m 3 for the present case (R = 800nm and h slot = 20nm) and the corresponding Purcell factor F P is about Fig. 6. The electrical field distribution E y(x, y) for the cases of (a) R = 2 m, (b) R = 1 m, (c) R = 800nm, (d) R = 500nm. The other parameters are: h Slot = 20nm, w co = 400nm. Fig. 7. For a bent hybrid plasmonic waveguide with h slot = 20nm and h rib = 300nm, the wavelength dependence of (a) the effective refractive index and the loss; (b) the group index and the intrinsic Q-value. In order to achieve the spectral responses of the hybrid plasmonic submicron-donut resonator, we use a three-dimensional finite-difference time-domain (3D-FDTD) method to simulate the light propagation in the present submicron-donut resonator. The grid sizes are chosen as x = z = 20nm, and y = 5nm, respectively. According to the analysis for the loss of a bent hybrid plasmonic waveguide, we choose h slot = 20nm, w co = 400nm, and R = 800nm # $15.00 USD Received 19 Aug 2011; revised 10 Oct 2011; accepted 10 Oct 2011; published 7 Nov 2011 (C) 2011 OSA 21 November 2011 / Vol. 19, No. 24 / OPTICS EXPRESS

257 as an example. Figure 8(a) shows the calculated wavelength responses for a submicron-donut resonator when the gap width w g is chosen as 60, 80, 100, and 120nm. In this example, the width of the pure dielectric access waveguide is chosen as 350nm to be singlemode. From this figure, it can be seen that there are four resonances in the wavelength range from 1200nm to 1800nm, and that the free spectral range (FSR) is not uniform due to the dispersion. The separation between the two adjacent resonances around 1550nm is about 148nm. Such a large FSR is due to the ultrasmall radius. Fig. 8. (a) The spectral responses of submicron-donut resonators with R = 800nm when the gap width w g is chosen as 60, 80, 100, and 120nm; (b) the extinction ratio at the resonance wavelength nm as the gap width varies. For a resonator with coupled waveguides, the Q value is given by 1/Q=1/Q c + 1/Q 0, where Q c is the Q-value due to the coupling, and Q 0 is the intrinsic Q-value. When critical coupling occurs, one has Q c = Q 0, and Q = Q 0 /2. For the present case, the intrinsic Q-value estimated by using the formula of Q = N g /(2n im ) is about 800 (see the curve for the case of R = 800nm shown in Fig. 7(b)). The Q-value for the submicron-donut with a coupled access waveguide is expected to be as high as 400. From the spectral response given in Fig. 8(a), the Q-value can be calculated by using Q = / 3dB, where 3dB is the 3dB bandwidth. The Q-value at the resonance around 1423nm is about 220, which is lower than the expected value (Q 0 /2 = 400). This might be due to some excess scattering loss at the coupling region between the straight access waveguide and the resonator (due to the very sharp bending). For a resonator with a single access waveguide, it is well known that there is a critical coupling that gives a maximal extinction ratio at resonances. In Fig. 8(b), the extinction ratio at the resonance wavelength nm is shown as the gap w g varies from 60nm to 120nm. The extinction ratio is defined as the ratio between the powers at the statuses of off-resonance and on-resonance. From this figure, one can see that a critical coupling is achieved when choosing the gap width about 80nm and the corresponding extinction ratio is close to 20dB. Figure 9(a) and 9(b) show the simulated electrical field distribution E y (x, z) in the hybrid plasmonic submicron-donut resonator when the input wavelength is chosen as nm (on-resonance), and 1437nm (off-resonance), respectively. The y-position of this xz plane is at the middle of the low-index slot region. From Fig. 9(a) and 9(b), one can see that there is a field enhancement in the submicron-donut due to the resonance, which is similar to the regular pure dielectric micro-resonator. Almost no bending leakage is observed from this FDTD simulation. With the present submicron-donut resonator, one can also realize some ultrasmall active hybrid plasmonic optoelectronics devices. For example, hybrid plasmonic optical modulators/switches could be realized by introducing some electro-optical material (e.g., EO polymer with a high EO efficiency [42]). It is also possible to realize submicron-donut lasers when a gain medium is introduced to achieve a net gain [32]. # $15.00 USD Received 19 Aug 2011; revised 10 Oct 2011; accepted 10 Oct 2011; published 7 Nov 2011 (C) 2011 OSA 21 November 2011 / Vol. 19, No. 24 / OPTICS EXPRESS

258 Fig. 9. The electrical field distribution E y(x, z) in a submicron-donut resonator with R = 800nm, w g = 80nm. (a) on-resonance; (b) off-resonance. 3. Conclusion We have given a characteristic analysis for ultra-sharp bent silicon hybrid plasmonic waveguides. It has shown that the hybrid plasmonic waveguide has the ability for submicron bending (e.g., 500nm) with very low leakage loss due to bending. This provides a way to realize submicron resonators. In this paper, we have proposed a silicon hybrid plasmonic submicron-donut resonator with pure dielectric access waveguides by utilizing the evanescent coupling between the pure dielectric waveguide and the submicron hybrid plasmonic resonator. The pure dielectric waveguide enables a long-distance optical interconnect due to its intrinsic loss. Furthermore, no additional mode converter is needed to combine the hybrid plasmonic circuits and the pure dielectric waveguides. Because of the relatively low loss of a hybrid plasmonic waveguide, the intrinsic Q-value of the present submicron-donut resonator is up to 2000 even when the bending radius is reduced to 800nm. Finally a 3D-FDTD simulation method has been used to calculate the spectral response of hybrid plasmonic submicron-donut resonators, which has a bending radius of 800nm and the corresponding loaded Q-value is about 220. The relatively high Q-value makes the present submicron-donut resonator very promising for realizing ultrasmall active hybrid plasmonic devices by introducing some active mediums, e.g., EO polymer with a high EO efficiency [42] for hybrid plasmonic optical modulators/switches, gain medium for submicron-donut laser [32]. Acknowledgment This project was partially supported by Zhejiang Provincial Natural Science Foundation (No. R ), the National Nature Science Foundation of China (No ), the 111 Project (No. B07031), a 863 project (Ministry of Science and Technology of China, No. 2011AA010301) and also supported by the Fundamental Research Funds for the Central Universities. # $15.00 USD Received 19 Aug 2011; revised 10 Oct 2011; accepted 10 Oct 2011; published 7 Nov 2011 (C) 2011 OSA 21 November 2011 / Vol. 19, No. 24 / OPTICS EXPRESS

259 36 IEEE PHOTONICS TECHNOLOGY LETTERS, VOL. 25, NO. 1, JANUARY 1, 2013 Realization of a Novel 1 N Power Splitter With Uniformly Excited Ports Daryl T. Spencer, Student Member, IEEE, Daoxin Dai, Member, IEEE, Yongbo Tang, Martijn J. R. Heck, Member, IEEE, and John E. Bowers, Fellow, IEEE Abstract The first experimental demonstration of a novel ring resonator-based 1 N optical power splitter is reported. We fabricate the device on a Si 3 N 4 waveguide platform utilizing a bonded thermal oxide upper cladding. Fiber coupling and nearfield-imaging experiments at 1550 nm show that a 1 16 power splitter achieves very low excess loss of 0.9 db in addition to excellent uniformity of 0.4 db. The resonances of the device show a loaded quality factor of 6 million and finesse of 100. The device is promising for high-port-count power splitters without the need for cascaded stages. We also discuss applications requiring the wavelength selectivity of the device. Index Terms Optical resonators, optical waveguides, power dividers. I. INTRODUCTION LOW LOSS, uniform optical power splitting is needed for increasingly complex optical networks and photonic integrated circuits. Typical power splitters, such as Y branch, multimode interferometer (MMI), and star couplers, can suffer from poor uniformity and higher excess/insertion loss as the number of ports increases [1] [3]. A system distributing a large number of clock signals with optical interconnects could benefit from lower losses and higher uniformity across ports [4], [5]. Future passive optical networks requiring wavelength and time division multiplexing (hybrid-pon) across multiple FTTx nodes could gain additional benefit from a device with wavelength selectivity [6]. In this letter, we demonstrate the realization of a novel 1 16 power splitter using a ring resonator. We realize this structure in a low loss, CMOS compatible Si 3 N 4 optical waveguide platform [7] to achieve a high splitting ratio and uniform outputs that can be scaled even further. While our current design is not directly compatible with data communication applications, it is very useful for narrow linewidth laser applications as well as arbitrary splitting ratios, such as in arrayed waveguide gratings (AWG) [8], to be discussed later. Manuscript received August 21, 2012; revised October 24, 2012; accepted October 29, Date of publication November 15, 2012; date of current version December 18, This work was supported in part by DARPA MTO under the iphod contract and the NSF Fellowship for DS under Grant DGE , and in part by LioniX BV, The Netherlands. D. T. Spencer, Y. Tang, M. J. R. Heck, and J. E. Bowers are with the University of California Santa Barbara, Santa Barbara, CA USA ( darylt@ece.ucsb.edu; ytang@ece.ucsb.edu; mheck@ece.ucsb.edu; bowers@ece.ucsb.edu). D. Dai is with the Center for Optical and Electromagnetic Research, State Key Laboratory of Modern Optical Instrumentation, Zhejiang University, Hangzhou , China ( dxdai@zju.edu.cn). Color versions of one or more of the figures in this letter are available online at Digital Object Identifier /LPT Fig /$ IEEE Schematic for a 1 N ring resonator-based power splitter. II. DEVICE DESIGN AND FABRICATION Fig. 1 illustrates the layout for a general 1 N wavelength selective power splitter. To demonstrate the usefulness of this device, we fabricate a 1 16 power splitter designed after the theoretical basis in [9]. N + 1 directional couplers are added tangent to a waveguide ring resonator. To design a critically coupled system in which we can reduce the excess loss, we use the following design rule τ 2 0 = γ 2 N i=1 τ 2 i (1) where γ is the round trip propagation loss in the ring and κ 0 (τ 0 ), κ i (τ i ) denote the amplitude coupling (transmission) of the input and i th output port, respectively. To achieve uniform coupling, we match the outputs at two neighboring couplers such that P i+1 P i = κ2 i+1 κ 2 i γ θ π τ 2 i (2) where γ θ π is the propagation loss from the i + 1 to the i-th directional coupler spaced by θ radians. To design a perfectly uniform splitter such that (2) equals unity, each coupler must be accurately fabricated to a designed coupling strength, which can be difficult to control. Our strategy is to reduce the coupling strength to avoid any large mismatch or 256

260 SPENCER et al.: REALIZATION OF A NOVEL 1 N POWER SPLITTER 37 nonideality and make identical output couplers. Fabrication using a resonator with Q values in excess of 1 million [10] allows us to assume γ θ π 1, and finally choose κ0 2 N κi 2. According to calculations based on a designed κ 0/κ i of 2%/0.1%, the theoretical nonuniformity is < 0.1 db when the waveguide loss is <0.5 db/cm. Operation at 1550 nm was targeted and the directional couplers optical bandwidth over which (1) would apply was not measured in this study. Fabrication of a 1 16 ring resonator power splitter begins with a silicon substrate having 15 μm of thermal oxide. A 45 nm Si 3 N 4 thin film is then deposited via low pressure chemical vapor deposition (LPCVD) and contact lithography defines the 7 μm wide waveguides. 9.8 mm radius rings (corresponding to 3.3 GHz free spectral range (FSR)) are fabricated to reduce bending loss due to the low index contrast of Si 3 N 4 /SiO 2 [10]. Three 1.1 μm layers of SiO 2 are deposited via LPCVD with a tetraethylorthosilicate precursor, annealed for 3 hours at 1150 C, and then the sample is chemically mechanically polished. After this step, a second silicon substrate with 15 μm of thermal oxide is bonded above the waveguides after both surfaces are activated in O 2 plasma. A final anneal step is performed at 950 C to strengthen the bond. The wafer bonding process was chosen over plasma enhanced CVD in an attempt to avoid hydrogen impurity bond absorption tones as well as less film deposition induced stress. Further details on the fabrication can be found in [7]. Fig. 2 is a photograph of a fabricated device (outer ring) without the top silicon substrate. Fig. 2. Photograph of the Si 3 N 4 ring resonator power splitter showing most of the 16 output drop ports along the outer edge. III. MEASUREMENT AND RESULTS To insure operation of the 1 16 ring resonator power splitter, two measurements were performed. In order to measure resonators with less than 100 MHz bandwidth, a 1550 nm narrow linewidth tunable laser source ( 100 khz, Agilent 81640A) was used for near field imaging and spectra analysis. For both measurements, the input polarization was controlled to excite the fundamental TE mode, which exhibits the highest extinction ratio and power coupling efficiency. First, a near field image of each output facet was taken using a 20 objective, collimating optics, and an infrared camera. The stitched images of all 16 ports are shown in Fig. 3, where an intensity mapping yields a uniformity of < 0.4 db. Second, to study the excess loss as well as confirm the uniformity, cleaved SMF28 optical fibers were butt coupled to the waveguides. Fiber alignment was performed with piezo translation stages and index matching fluid was used to decrease facet loss and reflection. The coupling loss was measured in reference to fiber to fiber coupling and found to be 1.4 db/facet assuming negligible straight waveguide loss. The laser was tuned through multiple resonances and a high speed oscilloscope was triggered to capture the through and drop port spectra. Each drop port was measured and assumed to have uniform collection efficiency. A typical spectrum of the through port (red curve) and one output port (blue curve) is shown in Fig. 4, which has a measured drop port extinction ratio of 25 db and bandwidth of 33 MHz. The corresponding finesse and loaded Q are 100 and 6 million, respectively. Fig. 3. Near-field intensity map of the 16 output port facets. Nonuniform output waveguide separation was allowed in the design. The power measured on resonance at each port is normalized to the through port transmission off resonance ( 1 for high Q). After subtracting the intrinsic splitting loss of 12 db (1/16), the ring power splitter shows excess loss of 0.9 db and maximum to minimum uniformity of 0.4 db. Most of the nonuniformity is due to 0.2 db alignment error when butt coupling the fiber and waveguides. The somewhat long propagation distance of 5 cm at 1 db/m (conservative estimate from loaded Q) yields a negligible loss of < 0.05 db that is within our measurement error. The results are plotted in Fig. 5 and compared to typical 1 16 MMI splitters, 257

261 38 IEEE PHOTONICS TECHNOLOGY LETTERS, VOL. 25, NO. 1, JANUARY 1, 2013 Fig. 4. Red: optical spectrum of the through port. Blue: a typical output drop port. Fig. 5. Transmission and uniformity device comparison between the 1 16 ring resonator power splitter of this letter and typical Y branch, MMI, and star couplers seen in literature. Y branches, and star couplers (excited from the center input waveguide). There is good improvement of 0.3 db excess loss and 0.2 db uniformity over cascaded Y branch power splitters [1]. More recent cascaded Y branch power splitters written with deep UV stepper lithography show 0.2 db uniformity improvement, yet suffer from a higher insertion loss by 1.3 db [11]. When compared to MMI and star couplers, there is a substantial improvement in excess loss and uniformity of 1.8 db and 1.1 db, respectively [12], [13]. It should be noted that the MMI in [12] could have a lower insertion loss by increasing the width of the MMI, as shown in [14]. Additionally, recent AWG devices on this platform have shown very low excess loss of 0.5 db using 2 star couplers with 16 channels [15]. Overall, the ring power splitter performs nearly the same as conventional broadband power splitters in terms of excess loss and uniformity, but has some special features to be discussed in the next section. IV. APPLICATIONS The ring based power splitter has some unique features as compared to the conventional splitters shown in Fig. 5. First of all the bandwidth is narrow and the transmission spectra show a set of discrete peaks, evenly spaced at the FSR of the ring. Although such narrow-band transmission rules out applications like data- and telecommunication routing, it is perfectly suitable for fields where spectrally pure laser lines and combs are required, e.g., in microwave photonics, metrology, biophotonics, and as a source for (D)WDM systems. A second unique feature is that the splitting ratio can be arbitrarily chosen by tuning the directional coupler strengths of the N outputs. This adds significant flexibility over the power splitters mentioned earlier. As an example, a ring based power splitter can replace a star coupler in an AWG. Such star couplers are inherently high loss due to the finite lithography and etch resolution [8]. Ring-based power splitters can be designed to impose a Gaussian profile over the array arms, ensuring low loss and low-crosstalk performance. When an integer FSR of the ring is matched to the AWG channel spacing, consecutive narrow passbands end up in adjacent channels. Fig. 6. Schematic of a narrow-linewidth multiwavelength laser. SOAs provide the gain, and the cavity is formed by the facets mirrors. A particularly interesting application of such an AWG is a multi-wavelength or digitally tunable laser [16], [17]. The concept is schematically shown in Fig. 6. The N outputs of the ring splitter feed the array arms which have a length difference L corresponding to an integer multiple of the ring FSR. A star coupler can be used to combine the array arms, just like a conventional AWG [8]. The star coupler should be used here since the resonance filtering is already achieved with the ring power splitter and using 1 broadband star coupler will avoid alignment of 2 narrowband splitters. The laser cavity is then defined by the facets. By individually biasing the semiconductor optical amplifiers (SOAs) in the output channels, lasing is obtained at the wavelength corresponding to the AWG filter position. Due to the narrow AWG bandwidth, resulting from the high Q ring, very narrow linewidths are feasible. Moreover the wavelength grid is defined by the ring and mode-hopping is eliminated. We are currently further investigating this design. V. CONCLUSION We demonstrate a novel splitter architecture based on a ring resonator that offers a uniform, low loss solution to wavelength selective power splitting. The fabricated devices show excess loss of 0.9 db and uniformity of 0.4 db across all 16 ports. In comparison to broadband power splitters, this approach offers improved uniformity and excess loss in a wavelength selective device that does not require cascaded stages. The narrowband nature of this device makes it especially useful for systems requiring high spectral purity, such 258

262 SPENCER et al.: REALIZATION OF A NOVEL 1 N POWER SPLITTER 39 as frequency combs. The layout and fabrication also make this device easily scalable to larger number of output ports while maintaining good uniformity. ACKNOWLEDGMENT The authors would like to thank S. Rodgers and D. Blumenthal for helpful discussions. REFERENCES [1] H. Hanafusa, N. Takato, F. Hanawa, T. Oguchi, H. Suda, and Y. Ohmori, Wavelength insensitive 2 16 optical splitters developed using planar lightwave circuit technology, Electron. Lett., vol. 28, no. 7, pp , Mar [2] Y. P. Li and Y. Wang, Low-loss optical power splitter for high definition waveguides, U.S. Patent , Apr. 28, [3] M. Olivero and M. Svalgaard, UV-written integrated optical 1 N splitters, Opt. Express, vol. 14, no. 1, pp , Jan [4] P. J. Delfyett, D. H. Hartman, and S. Z. Ahmad, Optical clock distribution using a mode-locked semiconductor laser-diode system, J. Lightw. Technol., vol. 9, no. 12, pp , Dec [5] A. Mule, E. Glytsis, T. K. Gaylord, and J. D. Meindl, Electrical and optical clock distribution networks for gigascale microprocessors, IEEE Trans. Very Large Scale Integr. (VLSI) Syst., vol. 10, no. 5, pp , Oct [6] L. Kazovsky, W. Shaw, D. Gutierrez, N. Cheng, and S. Wong, Next generation optical access networks, J. Lightw. Technol., vol. 25, no. 11, pp , Nov [7] J. F. Bauters, et al., Planar waveguides with less than 0.1 db/m propagation loss fabricated with wafer bonding, Opt. Express, vol. 19, pp , Nov [8] M. K. Smit and C. V. Dam, PHASAR-based WDM-devices: Principles, design and applications, IEEE J. Quantum Electron., vol. 2, no. 2, pp , Jun [9] D. Dai and S. He, Proposal of a coupled-microring based wavelengthselective 1 N power splitter, IEEE Photon. Technol. Lett., vol. 21, no. 21, pp , Nov. 1, [10] M. C. Tien, J. F. Bauters, M. J. R. Heck, D. T. Spencer, D. J. Blumenthal, and J. E. Bowers, Ultrahigh quality factor planar Si 3 N 4 ring resonators on Si substrates, Opt. Express, vol. 19, no. 14, pp , Jun [11] S. H. Tao, Q. Fang, J. F. Song, M. B. Yu, G. Q. Lo, and D. L. Kwong, Cascade wide-angle Y-junction 1 16 optical power splitter based on silicon wire waveguides on silicon-on-insulator, Opt. Express, vol. 16, no. 26, p , Dec [12] M. Zirngibl, C. Dragone, C. H. Joyner, M. Kuznetsov, and U. Koren, Efficient 1 16 optical power splitter based on InP, Electron. Lett., vol. 28, no. 13, pp , Jun [13] C. Dragone, C. H. Henry, I. P. Kaminow, and R. C. Kistler, Efficient multichannel integrated optics star coupler on silicon, IEEE Photon. Technol. Lett., vol. 1, no. 8, pp , Aug [14] A. Hosseini, D. N. Kwong, Y. Zhang, H. Subbaraman, X. Xu, and R. T. Chen, 1 N multimode interference beam splitter design techniques for on-chip optical interconnections, IEEE J. Sel. Topics Quantum Electron., vol. 17, no. 3, pp , May [15] D. Dai, et al., Low-loss Si 3 N 4 arrayed-waveguide grating (de)multiplexer using nano-core optical waveguides, Opt. Express, vol. 19, no. 15, p , Jul [16] G. Kurczveil, M. J. R. Heck, J. D. Peters, J. M. Garcia, D. Spencer, and J. E. Bowers, An integrated hybrid silicon multiwavelength AWG laser, IEEE J. Sel. Topics Quantum Electron., vol. 17, no. 6, pp , Nov [17] M. J. R. Heck, et al., Monolithic AWG-based discretely tunable laser diode with nanosecond switching speed, IEEE Photon. Technol. Lett., vol. 21, no. 13, pp , Jul. 1,

263 612 IEEE PHOTONICS TECHNOLOGY LETTERS, VOL. 25, NO. 6, MARCH 15, 2013 High-Q Microring Resonators With 2 2 Angled Multimode Interference Couplers Li Jin, Jianwei Wang, Xin Fu, Bo Yang, Yaocheng Shi, and Daoxin Dai, Member, IEEE Abstract High Q-factor microring resonators (MRRs) with 2 2 angled multimode interference (MMI) couplers are realized based on SU-8 polymer strip waveguides, which has an SU-8 polymer core, an SiO 2 buffer, and an air cladding. The present MRR has a small radius (150 μm) because of the high-index contrast of the SU-8 optical waveguides. The coupling ratio of the angled MMI couplers is adjusted to achieve a high-loaded Q-factor MRR by modifying the bending angle. When this bending angle is chosen as 3.25, the Q-factor of the fabricated MRR is about Index Terms Angled, microring resonator (MRR), multimode interference (MMI) coupler, Q-factor. Fig. 1. Cross section of the present SU-8 strip waveguide. Usually a directional coupler (DC) is used for the coupling I. INTRODUCTION region of an MRR [8]. However, in order to achieve sufficient AS a versatile element for photonic integrated circuits coupling, this DC usually has to have a narrow gap for the (PICs), microresonators (including microrings, microracetracks, microdisks, etc) have received much attention [1]. has small tolerance to the fabrication error. This makes the case with a high. And the coupling ratio of a DC usually People have developed various MRR (microring resonator)- fabrication relatively difficult because one probably has to use based functional components for optical communications [2]. expensive E-beam, deep-ultraviolet lithography or nanoimprint The potential high Q-factor also makes MRRs very attractive technique to form the patters precisely [9]. It is well known for highly sensitive optical sensing by measuring the resonant that using multimode interference (MMI) couplers instead of wavelength shift or the output power variation [3]. DCs is a good alternative because of the easy fabrication and Generally speaking, small radius is desired for MRRs to be large fabrication tolerance [10] [11]. compact, which can be realized by using optical waveguides However, a regular 2 2 MMI coupler can only provide a with a high index-contrast (i.e., the difference of the fixed coupling ratio (e.g., 50:50), which makes it inflexible refractive index between the core and the cladding). Many to achieve MRRs with different bandwidths and Q-factors types of optical waveguides have been demonstrated with [12]. In this letter, we utilize angled MMI couplers [13] [14] different materials, such as silicon [1], III-V semiconductors to work with an MRR and adjust the coupling ratio of the [4] and polymers [5]. Among them, polymer materials are MMI coupler by modifying the bending angle. This way, very attractive because of the advantages of flexibility, low MRRs with high Q-factors have been achieved theoretically cost and easy fabrication [5] [7]. SU-8 is one of the most and experimentally. popular polymer materials and an SU-8 optical waveguide with a high index-contrast is achieved by introducing an II. STRUCTURE AND DESIGN air cladding, which is then useful for realizing compact Fig. 1 shows the cross section of the present small SU-8 MRRs [8]. polymer strip waveguide, which has a SiO 2 buffer layer, an For an MRR, the coupling region is a key part, which air cladding, and a core of SU-8 (2015) polymer. The SU-8 influences the extinction ratio (ER) as well as the Q-factor. core is 2.1μm wide and 1.52μm high to achieve singlemode propagation. According to our previous experimental results Manuscript received November 15, 2012; revised December 30, 2012; accepted January 22, Date of publication January 13, 2013; date of [15], the bending radius R of the small SU-8 strip waveguide current version March 7, This work was supported in part by a 973 could be as small as 100μm for a negligible bending loss. In Project (2011CB503700), in part by the National Natural Science Foundation this letter, we choose R = 150μm for our MRR. of China under Grant , in part by the 863 Project under Grant 2011AA010301, in part by the Zhejiang Provincial under Grant Z The schematic configuration of the present MRR is shown and Grant 2011C11024, and in part by the Doctoral Fund of Ministry of in Fig. 2(a). Here 2 2 MMI couplers are used to replace Education of China under Grant DCs to realize light coupling between the access waveguide The authors are with the Centre for Optical and Electromagnetic Research, State Key Laboratory for Modern Optical Instrumentation, Zhejiang Provincial and the resonator. In this way, no small gap is needed in Key Laboratory for Sensing Technologies, Zhejiang University, Hangzhou the coupling region, which makes an easy fabrication. In , China ( dxdai@zju.edu.cn). order to achieve variable power coupling ratios, we utilize Color versions of one or more of the figures in this letter are available online at an angled MMI coupler instead of a standard MMI coupler, Digital Object Identifier /LPT as shown in Fig. 2(b). The angled MMI coupler consists of /$ IEEE 260

264 JIN et al.: HIGH-Q MICRORING RESONATORS WITH 2 2 ANGLED MULTIMODE INTERFERENCE COUPLERS 613 Input Through O #1 O #2 (a) Drop L MMI WMMI W 2 W L tp 1 I #1 W12 (b) I #2 Fig. 4. Photograph of the fabricated SU-8 MRR with angled MMI couplers. Fig. 2. Structures of (a) present MRR and (b) angled MMI couplers. (a) Fig. 3. (a) Normalization output powers from port #1 and port #2 for different bending angles. (b) Total power (= P 1 + P 2 ). (b) Output Power (dbm) Output Power (dbm) θ= Wavelength (nm) (a) θ= Wavelength (nm) (c) Output Power (dbm) Output Power (dbm) θ= Wavelength (nm) (b) θ= Wavelength (nm) (d) input/output waveguides, two identical rectangular multimode sections and a triangular section between them. The MMI width is W MMI = 10.2μm and the length of the rectangular MMI sections is chosen as L MMI = 215μm according to the self-imaging theory. The center-to-center horizontal separation between the input ports (#1 and #2) is 7.6μm. The initial and final widths of the tapers at the input/output ports are 2.1μm, and 2.6μm, respectively. The taper length is chosen as 10μm to be adiabatic. The coupling ratios of the angled MMI couplers are modified by varying the bending angle θ. Since the angled MMI coupler is slightly polarization sensitive due to the polarization dependence of the beat length, we consider TE mode in our designs and measurements. Fig. 3(a) shows the calculated output powers from the through port (#2) and the cross port (#1) as the bending angle θ varies from 0 to 5. Here a 3-D beam propagation method (3-D-BPM) [16] is used for the simulation and two operation wavelengths are considered (i.e., 1530 nm, and 1535 nm). From Fig. 3, it can be seen that the MMI coupler is dependent of the wavelength slightly. When θ = 0, the MMI coupler becomes a regular straight one and a mirror image is formed at the end of the MMI section and consequently the power at the cross port is close to 100% while the through port receives very little power, as shown in Fig. 3(a). As the bending angle increases from 0 to 3.5, it can be seen that the cross coupling ratio decreases while the through coupling ratio increases. In this case, the cavity loss decreases and consequently a higher Q-value is expected. Regarding that the reflection at the facets of a high-q cavity might introduce a significant influence due to the resonance [17], [18], we have also calculated the reflection in the MMI coupler and fortunately it is shown that the reflection is negligible. On the other hand, one should note that it is also very essential to have low excess loss for the MMI couplers when Fig. 5. Measured spectral responses at the drop port of the fabricated MRRs with different bending angles. (a) θ = 3. (b) θ = (c) θ = (d) θ = 4.5. a high Q-factor is desired. Fig. 3(b) shows the calculated total power output from the cross and through ports. It can be seen that the excess loss increases slightly as the angle θ increases. Due to such an excess loss, the Q-value of the cavity and the peak power at the drop port will decrease. This is a drawback of using MMI coupler in comparison with a DC. Fortunately, for the present example, one can achieve a maximal throughcoupling ratio for the angled MMI coupler with an acceptable excess loss. Therefore, there is an optimal bending angle for a high-q microring resonator, which is verified by our experimental results below. III. FABRICATION AND MEASUREMENT In our fabrication, a 6μm-thick SiO 2 buffer layer was deposited on a Si substrate by using the plasma-enhanced chemical vapor deposition (PECVD) system. A SU-8 film as thin as 1.52μm is obtained by spin-coating the diluted SU-8 solution. The silicon wafer with the SU-8 layer is then prebaked C and C) to evaporate the solvent. Then the pattern on the photo-mask is transformed to the SU-8 film by the direct I-line UV (385 nm) lithography. A 5-min post-baking is necessary to make the exposed SU-8 cross-linked sufficiently and the development process is followed to remove the unexposed part. Finally, a one-hour hard-bake (@120 C) is carried out to make SU-8 thin film stable. Fig. 4 shows the microscopic photograph of the fabricated SU-8 MRR with angled MMI couplers. For the characterization of the fabricated MRRs, a tunable laser is used as the light source in our measurement system. A polarization controller is used to obtain a polarized input 261

265 614 IEEE PHOTONICS TECHNOLOGY LETTERS, VOL. 25, NO. 6, MARCH 15, 2013 Q-factor Theoretical Experimental Angle ( ) (a) ER(dBm) Theoretical ER Experimental ER Theoretical Power Experimental Power Angle ( ) (b) Fig. 6. Theoretical and experimental results for the MRRs with different angles. (a) Q-factor. (b) ER and the peak power at the drop port. light, which is then butt-coupled to the chip through a polarization maintaining fiber (PMF). In order to improve the coupling efficiency, a tapered lens fiber (TLF) is used. Fig. 5(a)-(d) shows the measured spectral responses of the drop port in the wavelength band from 1530 to 1535nm when the bending angle is chosen as θ = 3, 3.25, 4.25, and 4.5, respectively. According to the measured spectral responses at the drop port, we extract the loaded Q-factor, the extinction ratio (ER) as well as the peak power for the resonance around 1532 nm as the angles θ varies from 2 to 5, as shown in Fig. 6(a) and 6(b). These figures also show the theoretical results, which are obtained from the spectral responses calculated with the theoretical coupling ratio shown in Fig. 3(a) as well as the measured waveguide loss ( 0.14dB/mm). From these figures, it can be seen that the experimental and theoretical results agree very well with each other. The loaded Q-factor of more than is achieved experimentally when choosing θ = 3.25, where the coupling ratio between the through port and the cross port is about 90.1: 5.1 and the excess loss of the angled MMI coupler is still relatively low (about 0.21dB), as shown in Fig. 3(a)-3(b). According to the theoretical result, a maximal loaded Q-factor should be achieved when choosing θ = 3.5, around which the through-coupling ratio of the angled MMI coupler is maximal. One should also note that the peak power (@1532 nm) becomes minimized when θ=3.5, as shown in Fig. 6(b). This can be easily seen from the expression for the response at the drop port, i.e., T [1-(1-e αl/2 )/ (1-t 2 e αl )] 2,whereα is the attenuation coefficient, t is the through-coupling ratio of the MMI coupler, L is the cavity length. This formula has been simplified with the assumption of κ =(1-t 2 ) 1/2,whereκ is the cross-coupling ratio. From this formula, it can be seen that the peak power becomes smaller for the case of α>0 as the through-coupling ratio t increases. Therefore, for the present case, the peak power becomes minimal when θ = 3.5 where there is a maximal throughcoupling ratio t, as shown in Fig. 3(a). In the measurement, the power at the drop port for the case of θ = 3.5 is close to the noise floor of the photodetecror used, and thus the measured response is very noisy. Therefore, the data for θ = 3.5 is not included in Fig. 6(a) and 6(b). IV. CONCLUSION In this letter, we have experimentally demonstrated high-q MRRs with 2 2 angled MMI couplers by using small SU-8 optical waveguides with an air cladding. For the 2 2 angled MMI couplers, the coupling ratios can be adjusted from 50:50 to 5.1:90.1 by modifying the bending angle. With an optimal Peak Power(dBm) coupling ratio, the fabricated MRR has a maximal loaded Q-factor of over when this bending angle is chosen as This scheme should be available for silicon-based devices with ultra-small footprint. It has also been shown that the theoretical and experimental results for the loaded Q-factor, the ER, and the peak power of the spectral responses of the fabricated MRRs agree very well with each other. The present high-q MRRs are useful for optical filtering as well as optical sensing, particularly in the visible light range, in which silicon nanowire waveguides do not work. REFERENCES [1] V. R. Almeida and M. Lipson, Optical bistability on a silicon chip, Opt. Lett., vol. 29, no. 20, pp , [2] Y. Kokubum, Y. Hatakeyama, M. Ogata, S. Suzuki, and N. Zaizen, Fabrication technologies for vertically coupled microring resonator with multilevel crossing busline and ultracompact-ring radius, IEEE J. Sel. Topics Quantum Electron., vol. 11, no. 1, pp. 4 11, Jan./Feb [3] C.-Y. Chao and L. J. Guo, Biochemical sensors based on polymer microrings with sharp asymmetrical resonance, Appl. Phys. Lett., vol. 83, no. 8, pp , [4] R. J. Deri and E. Kapon, Low-loss III-V semiconductor optical waveguide, IEEE J. Quantum Electron, vol. 27, no. 3, pp , Mar [5] L. Eldada and L. W. Shacklette, Advances in polymer integrated optics, IEEE J. Sel. Topics Quantum Electron., vol. 6, no. 1, pp , Jan./Feb [6] L. Eldada, Nanoengineered polymers for photonic integrated circuits, in Proc. SPIE, vol. 5931, Sep. 2005, p F. [7] J. S. Kim, J. W. Kang, J. J. Kim, Simple and low cost fabrication of thermally stable polymeric multimode waveguides using a UVcurable epoxy, Jpn. J. Appl. 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266 2134 OPTICS LETTERS / Vol. 38, No. 12 / June 15, 2013 Optical bistability in a high-q racetrack resonator based on small SU-8 ridge waveguides Li Jin, Xin Fu, Bo Yang, Yaocheng Shi, and Daoxin Dai* Centre for Optical and Electromagnetic Research, State Key Laboratory for Modern Optical Instrumentation, Zhejiang Provincial Key Laboratory for Sensing Technologies, Zhejiang University, Zijingang Campus, Hangzhou , China *Corresponding author: dxdai@zju.edu.cn Received April 2, 2013; revised May 6, 2013; accepted May 18, 2013; posted May 20, 2013 (Doc. ID ); published June 12, 2013 A racetrack resonator with a high Q value ( 34; 000) is demonstrated experimentally based on small SU-8 optical ridge waveguides, which were fabricated with an improved etchless process. Optical bistability is observed in the present racetrack resonator even with a low input optical power ( mw), which is attributed to the significant thermal nonlinear optical effect due to the high Q value and the large negative thermo-optical coefficient of SU-8. Theoretical modeling for the optical bistability is also given, and it agrees well with the experimental result Optical Society of America OCIS codes: ( ) Guided waves; ( ) Waveguides, planar; ( ) Polarization-selective devices. Among various materials for integrated photonics, polymer is one of the most attractive options because of the advantages of high flexibility, low cost, and easy fabrication [1 3]. As a kind of typical polymer material, SU-8 has been widely used for many passive photonic devices [4 7], including optical resonators. It is well known that an optical resonator is a versatile element for many optical functionality elements, e.g., filters [8], switches or modulators [5], sensors [9], and lasers [10]. Since there is a significant field enhancement when operating at the resonance wavelength, a high-q optical resonator is also very attractive for many nonlinear optical applications, e.g., optical bistability, which is very useful for all-optical operations [11,12], including logic, modulation, switching, and memory. People have demonstrated optical bistability by using, e.g., compound semiconductor materials with strong nonlinear optical properties [13], high-q silicon ring resonators with a thermal-optical nonlinear effect [12]. A similar thermal-optical nonlinear effect was also observed in our moderate-q ring resonator based on SU-8 strip waveguides [14]. In this Letter, a high-q SU-8 optical racetrack resonator fabricated with a novel etchless process is demonstrated experimentally and a significant optical bistability is observed due to the thermal nonlinear optical effect for the first time. A theoretical modeling and an analysis are also given for the optical stability. Figure 1 shows the developed SU-8 optical ridge waveguides consisting of an SU-8 ridge and an SU-8 slab on the top of a SiO 2 buffer layer. Usually a SU-8 ridge structure can be formed by etching a SU-8 thin film partially with an O 2 -plasmon etching process [15]. The ridge height can be varied by controlling the etching time. However, because of the additional dry etching process, the easyfabrication benefit of SU-8 loses. Furthermore, such an O 2 -plasmon etching process usually makes the waveguide surface pretty rough, and it is actually not easy to control the etching depth precisely. In this Letter, we developed an improved etchless process described as follows. First a 6 μm thick SiO 2 buffer layer is first deposited on a Si substrate by the plasma-enhanced chemical vapor deposition technology. The SiO 2 layer can also be formed using the thermal-oxidation process to be low cost. Then a layer of SU-8 thin film was formed on the SiO 2 buffer layer with a spin-coating process. A maskless UV lithography process is followed so that a SU-8 slab region is formed. The second SU-8 thin film was then formed on top of the SU-8 slab layer with a second spin-coating process, and SU-8 ridges were then formed with the masked UV lithography process. The refractive indices of SU-8 and SiO 2 are and (at 1550 nm), respectively. In our design, the ridge width and the ridge height are chosen as w 2.75 μm and h 1.72 μm, while the slab height h slab 1.0 μm. The measured propagation loss of the fabricated waveguide is about 0.16 db mm. Figure 2(a) shows the fabricated racetrack, which has 68 μm long directional couplers for sufficient coupling. The gap width is about 1.15 μm [see Fig. 2(b)], which is limited by the UV-lithography resolution. The bend radius is chosen as 550 μm to be large enough for a low bending loss. Figure 3 shows the measured responses for the through and drop ports of the racetrack resonator when the input power is low. From this figure, one sees that the extinction ratio is about 13 db for the drop port and the Q value at the resonance wavelength nm is about 34,700. Fig. 1. Scanning electron microscope (SEM) picture of the cross section of the fabricated SU-8 optical ridge waveguide /13/ $15.00/ Optical Society of America 263

267 June 15, 2013 / Vol. 38, No. 12 / OPTICS LETTERS 2135 Input Through R=550μm Drop Fig. 2. (a) Fabricated racetrack resonator. (b) SEM picture for the coupling region. Figure 4(a) shows the measured spectral responses by scanning the wavelength of the input tunable laser with different power levels. From this figure, it can be seen that the spectrum changes dramatically as the input power (P in ) at the input-fiber end increases. The response decays slowly in the wavelength range of λ > λ res while it drops sharply in the range of λ < λ res when the input power becomes high. This asymmetry is caused by the thermal nonlinear optical effect due to the large negative thermo-optical (TO) coefficient of SU-8. A similar phenomenon was also observed previously from the response of the through port of a nitride silicon all-passed filter [16]. The negative TO coefficient of SU-8 introduces a blue shift for the resonance wavelength λ res as predicted. Figure 4(b) shows that the resonance wavelength λ res decreases almost linearly with a slope of about Δλ P in 1.1 pm mw as the input power P in increases. The resonance wavelength shift is given by Δλ λ res Δn eff n g, where the group index n g n eff λ res λ n eff λ, and Δn eff is the effective index change due to the temperature variation ΔT. For the present case, one has n g and Δn eff CΔT, where the TO coefficient of the SU-8 waveguides is about C C [17]. According to this equation, it is estimated to have a linear wavelength shift Δλ ΔT 0.12 nm C. From Fig. 4(b), one sees that when the input power increases to 169 mw, the wavelength shift Δλ is about 0.18 nm, which indicates there is a temperature variation of 1.52 C. Figure 5(a) shows the measured optical bistability, which was characterized by measuring the output power P dropwg at the drop waveguide as the power P inwg at the input waveguide increases from 3.5 to 9 mw. These power values are obtained by excluding the fiber-chip coupling loss ( 10.2 db). The input wavelength is chosen as λ in 1562 nm to be slightly smaller than a resonance wavelength (λ res nm). The experimental setup (a) (b) Fig. 4. (a) Measured responses with increasing input powers (P in ) and (b) resonant wavelength as the input power P in varies. is shown in Fig. 5(b). To explain the bistability, one should realize that the output power P dropwg is dependent on the input power and the transmittance of the resonator simultaneously. As the input power is modified, the circulating optical power inside the resonator changes accordingly, which causes some temperature variation in the resonator. Thus the resonance wavelength has a shift due to the TO effect in SU-8 waveguides. Such a wavelength detuning between the optical source and the shifted resonance causes the transmittance of the resonator to be dependent on the input power. The combined effect of these interrelated mechanisms is the reason for producing the bistability [12]. From Fig. 5(a), one sees that the on-switch power is 7.3 mw while the off-switch power is 5.6 mw. Such a bistability based on the thermal effect is usually not very fast, and the response time is estimated to be at the order of microsecond [12]. Such a nonlinear effect in an optical cavity can be modeled as follows. The relationship between the output power P dropwg and the input power P inwg in the linear region is given by [18] P dropwg 1 x P inwg 1 λ λ res Γ 2 ; (1) where 2Γ is the 3 db bandwidth of the resonance peak, and x is a constant related to the excess loss. Here one has x and 2Γ nm by fitting the measured response as shown in Fig. 6. Fig. 3. Measured responses of the racetrack resonator when it is with a low input power: (a) the through port and (b) the drop port. Fig. 5. (a) Bistability for the SU-8 racetrack resonator with an input wavelength of nm and (b) experimental setup. 264

268 2136 OPTICS LETTERS / Vol. 38, No. 12 / June 15, 2013 Fig. 6. Fitting of the measured response with Eq. (1). Fig. 7. (a) Resonance-wavelength shift Δλ as P out increases and (b) calculated and measured results for the bistability. The nonlinear optical response is then given by [18] P dropwg 1 x P inwg 1 P dropwg P o Δ 2 ; (2) where Δ λ res λ p Γ, λ p is the probe wavelength, and P o is the so-called characteristic power of the cavity [18]. In the present case, one has Δ 2.36 when choosing λ p 1562 nm and λ res nm. According to the relationship between the resonance-wavelength shift Δλ and the output power P dropwg [19], one sees that the characteristic power P o is given by P o P dropwg Δλ Γ. From the resonance wavelengths extracted from the measured responses shown in Fig. 4(a), we can obtain the resonance-wavelength shift Δλ as the output power P dropwg increases [see Fig. 7(a)]. Then one has P dropwg Δλ mw pm and thus P o μw. With Eq. (2), the calculated bistability is then shown in Fig. 7(b). It can be seen that the calculation result agrees very well with the experimental result. In summary, a racetrack resonator based on small SU-8 ridge waveguides fabricated with an improved etchless process has been presented experimentally. The Q value is as high as 34,000, which provides an enhanced power density in the cavity. Because of the high Q value and the large negative TO coefficient of SU-8, a significant thermal nonlinear optical effect and an optical bistability have been observed with a low input optical power. Finally a theoretical modeling has also been given for the optical bistability, which gives calculation results close to measured results. This project was supported by a 863 project (no. 2011AA010301), a NSFC project (no ), Zhejiang provincial grants (no. Z and no. 2011C11024), and the Doctoral Fund of Ministry of Education of China (no ). References 1. C.-Y. Chao and L. J. Guo, Appl. Phys. Lett. 83, 1527 (2003). 2. J. Wang, C. Zawadzki, N. Mettbach, W. Brinker, Z. Zhang, D. Schmidt, N. Keil, N. Grote, and M. Schell, Opt. Express 19, (2011). 3. O. Castany, K. Sathaye, A. Maalouf, M. Gadonna, I. Hardy, and L. Dupont, Opt. Commun. 290, 80 (2013). 4. K. K. Tung, W. H. Wong, and E. Y. B. Pun, Appl. Phys. A 80, 621 (2005). 5. P. Rabiei, W. H. Steier, C. Zhang, and L. R. Dalton, J. Lightwave Technol. 20, 1968 (2002). 6. D. Dai, B. Yang, L. Yang, Z. Sheng, and S. He, IEEE Photon. Technol. Lett. 21, 254 (2009). 7. L. Yang, B. Yang, Z. Sheng, J. Wang, D. Dai, and S. He, Appl. Phys. Lett. 93, (2008). 8. B. E. Little, S. T. Chu, H. A. Haus, J. Foresi, and J.-P. Laine, J. Lightwave Technol. 15, 998 (1997). 9. J. Wang and D. Dai, Opt. Lett. 35, 4229 (2010). 10. M. K. Gonokami, R. H. Jordan, A. Dodabalapur, H. E. Katz, M. L. Schilling, R. E. Slusher, and S. Ozawa, Opt. Lett. 20, 2093 (1995). 11. M. Notomi, A. Shinya, S. Mitsugi, G. Kira, E. Kuramochi, and T. Tanabe, Opt. Express 13, 2678 (2005). 12. V. R. Almeida and M. Lipson, Opt. Lett. 29, 2387 (2004). 13. H. M. Gibbs, Optical Bistability: Controlling Light with Light (Academic, 1985). 14. L. Yang, D. Dai, J. He, and S. He, Proc. SPIE 7631, 76310B (2009). 15. G. Hong, A. S. Holmes, and M. E. Heaton, Microsyst. Technol. 10, 357 (2004). 16. A. Gondarenko, J. S. Levy, and M. Lipson, Opt. Express 17, (2009). 17. B. Yang, Y. Zhu, Y. Jiao, Z. Sheng, S. He, and D. Dai, J. Lightwave Technol. 29, 2009 (2011). 18. J. Bravo-Abad, A. Rodriguez, P. Bermel, S. G. Johnson, J. D. Joannopoulos, and M. Soljacic, Opt. Express 15, (2007). 19. M. Soljacic, M. Ibanescu, S. G. Johnson, Y. Fink, and J. D. Joannopoulos, Phys. Rev. E 66, (R) (2002). 265

269 6304 OPTICS LETTERS / Vol. 39, No. 21 / November 1, 2014 High-order microring resonators with bent couplers for a box-like filter response Pengxin Chen, Sitao Chen, Xiaowei Guan, Yaocheng Shi, and Daoxin Dai* Centre for Optical and Electromagnetic Research, State Key Laboratory for Modern Optical Instrumentation, Zhejiang Provincial Key Laboratory for Sensing Technologies, Zhejiang University, Zijingang Campus, Hangzhou , China *Corresponding author: dxdai@zju.edu.cn Received September 1, 2014; revised October 5, 2014; accepted October 7, 2014; posted October 10, 2014 (Doc. ID ); published October 28, 2014 High-order microring resonator (MRR) filters with bent directional couplers are proposed and demonstrated to achieve a box-like filter response. When using bent couplers, the coupling ratio can be adjusted easily by choosing the length of the coupling region, and the excess loss is almost zero while the perimeter of the microring length is unchanged. For the present fabricated five-microring filters with bent directional couplers, the excess loss is less than 1.0 db, the out-of-band extinction ratio is 36 db, and the response has rising and falling edges as sharp as 48 db nm. The thermal tunability of the high-order MRR filter with a Ti-microheater is also demonstrated and the thermally tuning efficiency is about 0.10 nm mw Optical Society of America OCIS codes: ( ) Integrated optics devices; ( ) Resonators; ( ) Coupled resonators. Wavelength-division multiplexing (WDM) is a key technique developed to achieve high capacity for an optical interconnect link and a wavelength-division-multiplexer is one of the most important key components in a WDM system. In the past decades, various WDM filters have been demonstrated [1], such as Bragg gratings [2], microring resonators (MRRs) [3 8], Mach Zehnder interferometers [9], and arrayed-waveguide gratings [10,11]. Among them, the MRR-based optical filter is one of the most popular choices because of the simple structure, the compact footprint, as well as the flexible scalability. For an optical filter, a box-like filtering response is often desired so that it can tolerate a wavelength shift due to any environmental change. For optical filters based on MMRs, this response can be synthesized with multiple rings [3 8,12,13]. When using multiple microrings to achieve a box-like filtering response, all the couplers involved should be designed optimally to achieve the coupling coefficients as desired [14]. For example, for the ultra-compact fifthorder MRR optical filters demonstrated in Ref. [4], the power coupling coefficients κ 2 while κ itself defined as the field coupling coefficient for all the couplers are designed to be 0.45, 0.09, 0.05, 0.05, 0.09, and 0.45, respectively. With this design, the ripples in the passband of the fifth-order MRR filter are smaller than 0.15 db, and the out-of-band rejection ratio is larger than 40 db theoretically. In order to achieve the sufficient power coupling coefficient of 0.45 between the access waveguide and the side-microring, one usually has to use the design of race-track resonators so that the coupling can be enhanced by increasing the length L of the coupling region or reducing the gap w gap in the coupling region. However, a longer coupling region causes a smaller free-spectral range (FSR), which limits the channel number available in WDM systems and consequently is not desired. Alternatively, when choosing a narrow gap (e.g., 20 nm), the beating length becomes small to realize a large FSR. However, the fabrication (e.g., the lithography and etching processes) becomes difficult, and the coupling ratio is very sensitive to the beating length variation [4]. In order to overcome these issues, multimode interference (MMI) couplers were used as the coupler with a power ratio of between the two output ports in Ref. [4]. One should note that there are some disadvantages when introducing MMI couplers. First, an MMI coupler usually has a few percent of excess loss during this splitting process [4], and there is also mode conversion loss between the straight section and the bending section of a microring. This might introduce some notable excess loss for an MRR filter, particularly for the case with utlrasharp bending. Second, the power splitting ratio of an MMI coupler is fixed [15], and thus it is not available when one wants to choose another value for the power splitting ratio. Third, the length L MMI of the MMI section is usually several microns (e.g., L MMI 3.5 μm [4]), and the cavity length is increased by 2 L MMI, which increases the microring length and thus reduces the FSR in some degree. In order to solve these problems, in this Letter, we introduce bent directional couplers for high-order MRR optical filters to have a box-like filtering response. The SEM image of five-microring filter with bent coupler as shown in Fig. 1(a). In the present design, bent couplers are used for light coupling between the access waveguides and the side-microring. With bent couplers, the coupling ratio can be chosen flexibly by choosing the length of the coupling region appropriately even when Input (a) Drop Bent coupler (b) R 1 R 2 Bent coupler W gap Fig. 1. (a) SEM image of the present five-microring filter with bent couplers. (b) SEM image of the bent coupler used here. W 2 W /14/ $15.00/ Optical Society of America 266

270 November 1, 2014 / Vol. 39, No. 21 / OPTICS LETTERS 6305 the gap width is relatively large. Furthermore, there is no excess loss theoretically, and the cavity length is the same as a regular microring. Figure 1(b) shows the structure of the bent couplers, in the coupling region of which there are two parallel bent waveguides, i.e., the bent access waveguide and the microring waveguide. In order to have efficient coupling between the access waveguide and the microring, the two parallel bent waveguides are designed to be with different widths w 1 ;w 2 according to the phase matching condition [16], n eff1 R 1 n eff2 R 2, where n eff1 and n eff2 are the effective indices of the fundamental modes of the two bent waveguides, respectively, R 1 and R 2 are the corresponding bending radii, and R 1 R 2 w 1 w 2 2 w gap.in our design, a relatively large gap (w gap > 150 nm) is chosen so that the fabrication is not difficult. The design with the phase matching condition also helps minimize the excitation of higher-order modes in the microring waveguides (which might be multimode). In this Letter a silicon-on-insulator (SOI) wafer with a 220-nm-thick top silicon and a 2-μm-thick buried-oxide layer is used, and there is a 1-μm-thick SiO 2 uppercladding layer for the SOI nanowires used here. The refractive indices of Si and SiO 2 are n Si 3.45 and n SiO2 1.45, respectively. As an example, we choose the widths w 1 ;w 2 to be around 450 nm and the radii R 1 ;R 2 to be around 5 μm regarding the single-mode condition as well as the bending loss. Figure 2 shows the calculated value of n eff R for bending waveguides with different core widths (w 350; 375; ; 500 nm) as the radius R increases. Here the effective index n eff is obtained by using a full-vectorial finite-difference method (FV-FDM) mode-solver numerically. According to the resonant equation for MRRs 2πn eff R mλ, where m is the resonant order of the microring and λ is the wavelength in the vacuum, one has the product n eff2 R μm (as indicated by the dash-dotted line in Fig. 2) when assuming that the resonant order m 45 and λ 1.55 μm. From this figure, one can easily have many solutions for w 2 ;R 2 to satisfy the equation n eff2 R μm. According to phase matching condition, finally we choose the parameters w μm, R μm, w μm, and R μm for the bent coupler so that the gap is relatively large (w gap 182 nm) to make the fabrication not difficult. Figure 3(a) shows the simulated power coupling coefficients of the designed bent coupler for the case with light launched from the access waveguide as the angle Power coupling ratio Thru Total Thru Cross Input 0.2 Cross Input Cross (a) (degree) (b) w gap ( m) θ of the coupling region increases. Here the light propagation is simulated with a three-dimensional finite-difference time-domain (3D-FDTD) method. The simulation shows that the excess loss of this structure is as low as 0.04 db in theory. The coupling ratio between the access waveguide and the microring is 0.45 as required when choosing θ As indicated by Ref. [3], the power coupling coefficients should be [0.45, 0.09, 0.45] for a two-ring filter, [0.45, 0.09, 0.09, 0.45] for a three-ring filter and [0.45, 0.09, 0.05, 0.05, 0.09, 0.45] for a five-ring filter, respectively. For the inter-ring coupler between two adjacent microrings, the coupling coefficients can be controlled by adjusting the gap between them, as shown in Fig. 3(b). For example, the gap widths are about 116 and 156 nm to achieve the power coupling coefficients of 0.09 and 0.05, respectively. The sensitivity of the power coupling ratios to the core/gap width deviation is also analyzed with a 3D- FDTD simulation for the designed three couplers for the five-ring filter as an example (see Fig. 4). Assuming that there is a deviation Δw for the waveguides, one has w w 0 Δw and w gap w gap0 Δw for the waveguide width and the gap width, respectively, where w 0 and w gap0 are the designed values. From Fig. 4(a) (see the curve with circles), the power coupling ratio for the bent coupler is not sensitive to the deviation Δw, which is an advantage and has been also proposed to realize a broad-band 3 db coupler in Ref. [17] recently. In contrast, the inter-ring coupler is more sensitive to the deviation Δw (see the curves with squares and diamonds). When jδwj < 20 nm, the coupling ratios Thru Thru Cross Total Fig. 3. (a) Simulated power coupling ratio of the bent coupler as the angle θ of the coupling region increases when w μm, R μm, w μm, and R μm. (b) Coupling ratio of the inter-ring coupler as the gap width w gap varies when choosing R μm and w μm. w gap neffr (μm) w=350:25:500nm R (μm) Fig. 2. Calculated value of n eff R for the bent waveguides with different core widths (w 350; 375; ; 500 nm) as the radius R increases. Power coupling ratio Bent coupler Inter-ring coupler #1 Inter-ring coupler # (a) Δw (μm) Power (db) Δw=20, 10, 0, -10, -20nm (b) Wavelength (nm) Fig. 4. (a) Sensitivity of the coupling ratio to the waveguide deviation Δw. (b) Calculated spectral responses for a five-ring filter when there is a deviation Δw. 267

271 6306 OPTICS LETTERS / Vol. 39, No. 21 / November 1, 2014 for the two inter-rings varies in the ranges of , and , respectively. The spectral responses for a five-ring filter are also simulated when assuming that there is a deviation Δw, as shown in Fig. 4(b). From this figure, it can be seen that the spectral response is still box-like even when the deviation Δw is as large as 20 nm. One should note that the 3-dB bandwidth changes and the ripples increase slightly. The designed devices were then fabricated with a regular process for passive silicon photonic devices. First an E-beam lithography (Raith II) with 300 nm-thick electronic resist was used for the patterning, and an inductively coupled plasma (ICP) etching process was followed to etching through the top silicon layer and form the silicon core region. Grating couplers at the ends of the input/output waveguides were made with a second etching process to have a high fiber-chip coupling efficiency. Finally, 1-μm-thick SiO 2 upper-cladding is formed with a plasma-enhanced chemical vapor deposition (PECVD) process. The fabricated devices were then measured with a setup with a tunable laser (Agilent 81940A) as the source. A polarization controller is used to achieve TE-polarized incident light, which is then coupled from an optical fiber to the chip through a grating coupler. The output light from the chip is received by a power meter (Agilent 81618A). Figures 5(a) 5(c) show the measured spectral responses of the fabricated optical filters with two, three, and five microrings (see the thin curves). The theoretical spectral responses are also calculated by using the analytical formulas given in Ref. [18] (see the thick curves). For this calculation, the coupling ratios are chosen as the values designed above. It can be seen that the measured results agree well with the calculated results. Their FSRs are about 18.4 nm, and the 3-dB bandwidths are 2.0, 2.6, and 2.38 nm, respectively. The measured out-of-band rejection ratios for the fabricated two-microring, threemicroring, and five-microring filters are about 25, 30, and 36 db, respectively. The out-of-band rejection ratio of five-microring filter might be higher than the measurement result shown in Fig. 5(c) due to the limit of the sensitivity of the powermeter used in our measurement setup. Nevertheless, it can be seen that higher out-ofband rejection ratio is obtained by introducing more microrings. Both the measurement and simulation results also show that the spectral response is more box-like (with sharp transitions) when more microrings are cascaded. The response for the five-microring filter has rising and falling edges as sharp as 48 db nm. From the measured spectral responses, one can also see that the fabricated two-microring, three-microring, and fivemicroring filters have an excess loss of <1.0 db (at 1550 nm), which is beneficial from the low excess loss of the bent couplers in comparison with the MMI Power (db) Calculated Measured (a) Wavelength (nm) Power (db) Calculated Measured (b) Wavelength (nm) Power (db) Calculated Measured (c) Wavelength (nm) Fig. 5. Measured (thin curves) and simulated (thick curves) responses of the optical filters with two microrings (a), three microrings (b), and five microrings (c). The insets are the microscope images of the filers. Fig. 6. (a) SEM image of a five-microring filter with a Ti microheater. The measured responses of the filters with (b) two microrings, (c) three microrings, and (d) five microrings when applying different electrical powers. (e) The central wavelength shifts as the electrical power increases. 268

272 November 1, 2014 / Vol. 39, No. 21 / OPTICS LETTERS 6307 couplers or traditional straight-bend coupler used in race-track resonators demonstrated in e.g. [19]. As thermal-tuning is often used to make tunable optical filters, which is important for achieving flexible optical systems, here we also demonstrate the thermal insensitivity of the MRR-based filters by introducing a titanium micro-heater on the top of microrings. The micro-heater is made of 100 nm -thick and 1-μm-wide titanium strip [see Fig. 6(a)]. The resistances of the micro-heaters for the two-microring, three-microring, and five-microring filters are about 3.6, 4.8, and 6.7 kω. The corresponding spectral responses measured for the tunable optical filters are shown in Figs. 6(b) 6(d), respectively, as the applied electrical power increases. Since the refractive index variation due to the temperature increase is small (e.g., <1% of the index of the silicon core), the coupling ratios are not temperature-sensitive. Therefore, the shapes of the measured responses do not change almost, except that there is an expected red-shift for the central wavelength, as shown in Figs. 6(b) 6(d). We note that the transmissions have some slight drops when the chip is heated, which might be due to the slight misalignment of input/output fiber. Figure 6(e) shows the measured central wavelengths for the two-microring, three-microring, and five-microring filters as the applied electrical power increases. From this figure, one sees that the two-microring filter has the highest thermally tuning efficiency of Δλ ΔT 0.17 nm mw, while thermally tuning efficiency for the five-microring filter is about 0.1 nm mw. This reason is that the two-microring filter has the smallest heating volume. It is possible to improve the thermally tuning efficiency by reducing the bending radius of the microrings, or introducing some special structures, e.g., thermal isolation grooves, or suspended waveguides [20]. In summary, we have proposed and demonstrated high-order MRR optical filters with a box-like filtering response by introducing bent directional couplers to have sufficient coupling between the access waveguide and the microrings. With the present design, there is no excess loss theoretically, and the cavity length is the same as a regular microring, which is promising to achieve low-loss MRR filter with a large FSR. For the present high-order MRR filters, the FSR is 18 nm, and the excess loss is less than 1.0 db. Furthermore, the coupling ratio can be chosen flexibly by choosing the length of the coupling region appropriately even when the gap width is relatively large. Ti micro-heaters have also been made on the upper-cladding of the microrings, and thermally tunable MRR filters have been realized with an efficiency of 0.10 nm mw for the five-microring filter. This project was supported by a 863 project (2011AA010301), and NSFC ( , ). References 1. D. Dai and J. E. Bowers, Nanophoton. 3, 283 (2014). 2. J. H. Song, J. H. Lim, R. K. Kim, K. S. Lee, K.-Y. Kim, J. Cho, D. Han, S. Jung, Y. Oh, and D.-H. Jang, IEEE Photon. Technol. Lett. 17, 2607 (2005). 3. B. Little, S. Chu, P. Absil, J. Hryniewicz, F. Johnson, F. Seiferth, D. Gill, V. Van, O. King, and M. Trakalo, IEEE Photon. Technol. Lett. 16, 2263 (2004). 4. F. Xia, M. Rooks, L. Sekaric, and Y. Vlasov, Opt. Express 15, (2007). 5. R. Grover, V. Van, T. A. Ibrahim, P. P. Absil, L. C. Calhoun, F. G. Johnson, J. V. Hryniewicz, and P.-T. Ho, J. Lightwave Technol. 20, 900 (2002). 6. B. E. Little, S. T. Chu, J. V. Hryniewicz, and P. P. Absil, Opt. Lett. 25, 344 (2000). 7. Q. Xu, B. Schmidt, J. Shakya, and M. Lipson, Opt. Express 14, 9431 (2006). 8. X. Luo, J. Song, S. Feng, A. Poon, T.-Y. Liow, M. Yu, G.-Q. Lo, and D.-L. Kwong, IEEE Photon. Technol. Lett. 24, 821 (2012). 9. M. Uenuma and T. Motooka, Opt. Lett. 34, 599 (2009). 10. K. Okamoto, K. Takiguchi, and Y. Ohmori, Electron. Lett. 31, 723 (1995). 11. D. Dai, X. Fu, Y. Shi, and S. He, Opt. Lett. 35, 2594 (2010). 12. L. Y. M. Tobing, P. Dumon, R. Baets, and M.-K. Chin, Opt. Lett. 33, 2512 (2008). 13. A. Melloni, Opt. Lett. 26, 917 (2001). 14. B. Little, S. Chu, H. Haus, J. Foresi, and J. P. Laine, J. Lightwave Technol. 15, 998 (1997). 15. M. Bachmann, P. A. Besse, and H. Melchior, Appl. Opt. 33, 3905 (1994). 16. D. Dai and J. E. Bowers, Opt. Express 19, (2011). 17. H. Morino, T. Maruyama, and K. Iiyama, J. Lightwave Technol. 32, 2188 (2014). 18. C.-S. Ma, Y.-Z. Xu, X. Yan, Z.-K. Qin, and X.-Y. Wang, Opt. Commun. 262, 41 (2006). 19. F. Xia, L. Sekaric, and Y. A. Vlasov, Opt. Express 14, 3872 (2006). 20. P. Dong, W. Qian, H. Liang, R. Shafiiha, D. Feng, G. Li, J. E. Cunningham, A. V. Krishnamoorthy, and M. Asghari, Opt. Express 18, (2010). 269

273 IEEE PHOTONICS TECHNOLOGY LETTERS, VOL. 18, NO. 21, NOVEMBER 1, Novel Ultracompact Triplexer Based on Photonic Crystal Waveguides Yaocheng Shi, Daoxin Dai, and Sailing He, Senior Member, IEEE Abstract Two stages of directional couplers based on photonic crystal waveguides are cascaded to form an ultracompact triplexer. The directional couplers are decoupled at the wavelength of 1310 nm. The length of the coupling region in the first directional coupler is chosen to separate the other two wavelengths (i.e., 1490 and 1550 nm), and the coupling region is tapered to improve the extinction ratios. The second directional coupler separates the wavelengths of 1490 and 1310 nm. For the channel of 1550 nm, an additional directional coupler is used to reduce the crosstalk from the channels of 1490 and 1310 nm. The total size of the present triplexer is only 50 m 20 m, and the good performance is verified with finite-difference time-domain simulation. Index Terms Directional coupler, photonic crystal (PC), triplexer, waveguide. I. INTRODUCTION ATRIPLEXER [1], [2], which is a (de)multiplexer for three specific wavelengths, plays a very important role in a fiber-to-the-home (FTTH) system. According to ITU G.983 standard, the three commonly used wavelengths are 1310, 1490, and 1550 nm, for upstream digital, downstream digital, and downstream analog channels, respectively. Typically there are two different types of triplexers. One is of bulky type realized by cascading, e.g., thin-film filters [1] (expensive for packaging and difficult to integrate with other devices). The other type is based on planar lightwave circuits (PLCs), and is more promising due to their reliability, high integration density, and suitability for mass-production, etc. Some PLC-based triplexers have been reported [2] [4] and their typical size is about several millimeters. In this letter, we introduce a triplexer based on a photonic crystal (PC), which is more compact. A PC [5] is a periodic arrangement of dielectric or metallic materials. The interest in the research of PCs is increasing due to their unique ability in controlling the propagation of lightwave. Many photonic devices based on PC waveguides (PCWs) have been introduced, such as a PCW-based directional cou- Manuscript received June 1, 2006; revised July 24, This work was supported by the Provincial Government of Zhejiang Province of China (R and 2004C31095). Y. Shi and D. Dai are with the Centre for Optical and Electromagnetic Research, State Key Laboratory for Modern Optical Instrumentation, Zhejiang University, Joint Research Center of Photonics, Royal Institute of Technology (Sweden) and Zhejiang University, Zhejiang University, Hangzhou , China. S. He is with the Centre for Optical and Electromagnetic Research, State Key Laboratory for Modern Optical Instrumentation, Zhejiang University, Joint Research Center of Photonics, Royal Institute of Technology (Sweden) and Zhejiang University, Zhejiang University, Hangzhou , China, and also with the Division of Electromagnetic Engineering, School of Electrical Engineering, Royal Institute of Technology, S Stockholm, Sweden ( sailing@kth.se). Color versions of Figs. 1 7 are available online at Digital Object Identifier /LPT Fig. 1. Band diagram for guided modes of two parallel PCWs. pler used as a dual-wavelength (de)multiplexer [6], [7]. In this letter, we present a novel ultracompact triplexer, which includes two stages of PCW-based directional couplers. The directional couplers are decoupled at the wavelength of 1310 nm. For the first directional coupler, the length of the coupling region is optimally chosen so that the other two wavelengths (i.e., 1490 and 1550 nm) are separated and the wavelengths of 1490 and 1310 nm are output from the same port (separated later by the second directional coupler). If the first directional coupler is a conventional PCW directional coupler, it is difficult to achieve high extinction ratios (defined as the ratio of the power at the desired output port to the power at an undesired port for a specific wavelength) for the wavelengths of both 1490 and 1550 nm since the coupling length of the two parallel PCWs is always an integer of the period. This problem is solved in this letter by introducing a tapered coupling region. For the channel of 1550 nm, an additional directional coupler is used to reduce the crosstalk from the channels of 1490 and 1310 nm. II. TRIPLEXER DESIGN AND OPTIMIZATION In this letter, we consider a PC with a triangular lattice of dielectric rods (with a period of ) in the air. In order to compare the device performances (e.g., the extinction ratio) with those of the dual-wavelength demultiplexer proposed in [6], we choose the same parameters for the basic PC structure as those in [6]. The radius and the dielectric constant of the rods are and, respectively. For this PC, there is a bandgap ranging from 0.26 to 0.45 for TM polarization. The directional coupler considered in this letter consists of two parallel PCWs with a separation of one period (as shown in the inset of Fig. 1). The band diagram of the guided modes in such a directional coupler is shown in Fig. 1. From Fig. 1, one sees that there are two guided modes (i.e., the even and odd modes). The coupling length of the two parallel PCWs is given by [6], where are the /$ IEEE 270

274 2294 IEEE PHOTONICS TECHNOLOGY LETTERS, VOL. 18, NO. 21, NOVEMBER 1, 2006 TABLE I OUTPUT POWERS OF THREE WAVELENGTHS AT THREE PORTS OF THE TRIPLEXER SHOWN IN FIG. 2 Fig. 2. Schematic configuration for a triplexer based on PCW directional couplers (with nontapered coupling region). Fig. 4. First directional coupler with a tapered coupling region. Fig. 3. Output power for two different wavelengths (1550 and 1490 nm) as the length of the coupler varies. wavevectors of the even and odd modes at a given frequency, respectively. At Point D (with in Fig. 1), where, the coupling length is infinitely long and, thus, Point D is called a decoupling point [9]. This decoupling property has been utilized in the design of a dual-wavelength demultiplexer [6]. In this letter, we use this decoupling property to design a triplexer. The schematic configuration of Fig. 2 shows the basic principle of a triplexer utilizing PCW directional couplers. There are two stages of PCW-based directional couplers. These directional couplers are decoupled at the wavelength of 1310 nm. Thus, wavelength (1310 nm) propagates through the input PCW (PCW #1) without any coupling to the other output port. The length for the coupling region of the first directional coupler (Coupler #1) is chosen to separate the other two wavelengths (i.e., 1490 and 1550 nm) and the wavelength of 1490 nm is also output at PCW #1. should satisfy and, where is an odd integer, is an even integer, and are the coupling lengths at 1550 and 1490 nm, respectively. Finally, the second directional coupler (Coupler #2) separates the wavelengths of 1310 and 1490 nm to Ports #1 and #2, respectively. When we choose the decoupling point (see Fig. 1) at nm, we have normalized frequency at nm and at nm. According to formula for the coupling length, we obtain the coupling lengths and. Fig. 3 shows the output powers from PCW #1 for wavelengths and as the length of the coupling region varies. From Fig. 3, one sees that the two wavelengths are almost separated when. For this value of, wavelength nm can be separated from the other two wavelengths (which are output from the same port, i.e., PCW #1). Wavelengths and Fig. 5. Extinction ratios of the first coupler for the three different wavelengths as radius R varies. are then separated by the second direction coupler (Coupler #2). We choose length for Coupler #2 and wavelength ( nm) is output from Port #2 while wavelength ( nm) goes through PCW #1 without any coupling to PCW #2. Table I shows the powers output at different ports for the three wavelengths (calculated with a two-dimensional (2-D) finite-difference time-domain (FDTD) method [8]). From Table I, one sees that the extinction ratio for nm is close to 30 db (as expected). The extinction ratios for the other two wavelengths nm and nm are not so good (the worst one is about 8 db for 1490 nm, and 10 db for 1550 nm). The reason for this bad crosstalk is that the chosen length does not satisfy exactly relations and. To improve the extinction ratios, we taper the coupling region symmetrically, as shown in Fig. 4. The radii of the rods in the coupling region decrease linearly from (at the left edge) to at the center of the coupling region and then increase back to (at the right edge), i.e., ( at the center). Fig. 5 shows the extinction ratios for the three wavelengths as radius (at the center of the first directional coupler) varies. In our design, the length of the coupling region is fixed to

275 SHI et al.: NOVEL ULTRACOMPACT TRIPLEXER BASED ON PCWs 2295 TABLE II OUTPUT POWERS OF THREE WAVELENGTHS AT THREE PORTS OF THE TRIPLEXER SHOWN IN FIG. 6 Fig. 6. Schematic configuration for the present triplexer with tapering in the first directional coupler. shown in Fig. 7 and Table II. The extinction ratios for the wavelengths of 1490 and 1550 nm are improved to more than 18.0 and 16.0 db, respectively (better than the results for a dual-wavelength demultiplexer [6]). Compared with the results shown in Table I, one sees the performances of the triplexer with tapering are improved greatly. The 1-dB bandwidths of the spectral responses for the three channels (at Ports #1, #2, #3) are about 48, 20, 15 nm, respectively (note that the bandwidth will be very narrow if one uses PC cavities [10] to drop/separate wavelengths). Fig. 7. Field distributions simulated with an FDTD method for the present triplexer at (a) = 1310 nm; (b) = 1490 nm; (c) = 1550 nm. From Fig. 5, one sees that the extinction ratio for each wavelength can vary continuously when one adjusts radius. One can obtain an optimal radius of so that the extinction ratios for all the three wavelengths are acceptably high. For this example, we choose an optimal value (around the peaks of the extinction ratios for the wavelengths of 1490 and 1550 nm; see the dashed vertical line in Fig. 5). For this optimal design, the extinction ratios for the wavelengths of 1490 and 1550 nm are about and db, respectively, which are much better than those for the conventional PCW directional coupler without tapering (i.e., in Fig. 5). On the other hand, the decoupling property is no longer satisfied at 1310 nm in the tapered coupling region and some power is coupled from PCW #1 to PCW #3, and this introduces an inevitable reduction of the extinction ratio (from to db) for nm. In order to improve the extinction ratio for 1310 nm, we filter out the power at wavelength 1310 nm from Port #3 (which is for the channel of 1550 nm) by introducing an additional directional coupler (Coupler #3) (see Fig. 6). Coupler #3 has a decoupling point at wavelength nm and the wavelength of 1550 nm is almost coupled to PCW #4. With such a design, the residual power of 1310 nm is output from an auxiliary port (as shown in Fig. 6). Therefore, this introduces only a small excess loss of about 0.45 db for (1310 nm). The second PCW directional coupler (Coupler #2; see Fig. 6) remains the same as in Fig. 2. The total size of the present triplexer is about 50 m 20 m, which is only 1/100 of the conventional PLC-based triplexer [2]. Finally, we use a 2-D FDTD method [8] to simulate the field propagation in the whole triplexer and the results are III. CONCLUSION In this letter, we have proposed a novel PCW-based triplexer formed by two cascaded directional couplers. A tapered coupling region has been introduced to the first directional coupler to improve the extinction ratios for the wavelengths of 1490 and 1550 nm. By introducing an additional directional coupler, all three wavelengths are (de)multiplexed with acceptable extinction ratio. The present triplexer is very compact and the total size of the chip is about 50 m 20 m. It is possible to integrate the present ultracompact triplexer with laser diodes and photodetectors for the realization of a triplexer transceiver for FTTH networks. REFERENCES [1] M. Yanagisawa, Y. Inoue, M. Ishii, T. Shibata, Y. Hibino, H. Kawata, and T. Sugie, Low-loss and compact TFF-embedded silica-waveguide WDM filter for video distribution services in FTTH systems, in Proc. OFC 2004, Los Angeles, CA, Feb. 2004, Paper TuI4. [2] X. Li, G.-R. Zhou, N.-N. Feng, and W. P. Huang, A novel planar waveguide wavelength demultiplexer design for integrated optical triplexer transceiver, IEEE Photon. Technol. 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