SILICON-BASED waveguides [1] [5] are attractive for

2428 JOURNAL OF LIGHTWAVE TECHNOLOGY, VOL. 24, NO. 6, JUNE 2006 Bilevel Mode Converter Between a Silicon Nanowire Waveguide and a Larger Waveguide Daoxin Dai, Sailing He, Senior Member, IEEE, and Hon-Ki Tsang, Senior Member, IEEE Abstract A bilevel mode converter is analyzed for providing low-loss coupling between the small fundamental mode of a silicon nanowire waveguide and the larger mode of a conventional siliconon-insulator (SOI) rib waveguide. The bilevel converter can also be used to improve the coupling efficiency between a lensed fiber and a silicon nanowire waveguide. The mode converter consists of two tapers formed at different levels. The top taper comprises a parabolic and sine taper, which is optimized to improve the mode conversion efficiency. Numerical analyses are given by using a three-dimensional semivectorial beam propagation method. The design has good tolerance against misalignment of the two masks needed for the double etch. Index Terms Bilevel, mode converter, nanowire waveguide, silicon, taper. I. INTRODUCTION SILICON-BASED waveguides [1] [5] are attractive for planar lightwave circuits (PLCs) because of their potential compatibility with CMOS. Furthermore, the large difference between the refractive indexes of the core (Si) and the cladding/insulator (air or SiO 2 ) enables the realization of optical waveguides with submicrometer dimensions, known as silicon nanowire waveguides, which allows an ultrasmall bending radius. Thus, very compact PLC devices can be realized by using silicon nanowire waveguides. Due to the large refractive index contrast, the width and height of the core for a singlemode silicon nanowire waveguide can have dimensions of a few hundred nanometers. This small size introduces two main challenges for silicon nanowire waveguides. The first one is how to reduce the large scattering loss due to the roughness of the sidewall. Some groups have reported low-loss silicon nanowire waveguides [6] [10] by reducing the roughness via an additional fabrication process such as wet chemical oxidation [6] Manuscript received November 30, 2005; revised February 23, 2006. This work was supported by Research Grants Council (RGC) Earmarked Grant 415905 and the provincial government of Zhejiang Province of China under Research Grant 20044131095. D. Dai is with Centre for Optical and Electromagnetic Research, State Key Laboratory of Modern Optical Instrumentation, Zhejiang University, Joint Research Center of Photonics of the Royal Institute of Technology (Sweden) and Zhejiang University, Hangzhou 310058, China, and also with the Department of Electronic Engineering, the Chinese University of Hong Kong, New Territories, Hong Kong (e-mail: dxdai@ee.cuhk.edu.hk). S. He is with Centre for Optical and Electromagnetic Research, Zhejiang University, Joint Research Center of Photonics of the Royal Institute of Technology (Sweden) and Zhejiang University, Zijingang Campus, Hangzhou 310058, China, and also with the Division of Electromagnetic Engineering, School of Electrical Engineering, Royal Institute of Technology, S-100 44 Stockholm, Sweden (e-mail: sailing@kth.se). H.-K. Tsang is with the Department of Electronic Engineering, the Chinese University of Hong Kong, New Territories, Hong Kong (e-mail: hktsang@ ee.cuhk.edu.hk). Digital Object Identifier 10.1109/JLT.2006.874554 Fig. 1. Three-dimensional view of the present bi-level mode converter. and losses of about 0.2 db/mm have been reported [7]. Furthermore, the total loss is alleviated by the size reduction of the PLC device [9]. The second challenge is how to couple light from optical fibers into the ultrasmall PLC devices based on silicon nanowire waveguides. Practical silicon nanowires are becomingly increasingly attractive [11], [12]. For conventional micrometer-sized waveguides, such as silicon-on-insulator (SOI) rib waveguide with large cross section, low-loss coupling from/to a single-mode fiber have been routinely achieved. Bilevel tapers [13], [14], formed by a top cheese wedge-shaped taper to expand the mode vertically, have been employed to improve the coupling efficiency for micrometer-sized SOI waveguides. However, there has been no work to date on scaling the bilevel tapers to provide efficient coupling between a silicon nanowire waveguide from/to a waveguide with large mode size (such as a single-mode fiber, a SOI rib waveguide). For the nanowire waveguides, it is necessary to expand the mode size to several micrometers to improve the coupling efficiency. Other approaches for mode converters have been developed, such as a waveguide grating [1], [15], an inverse taper [3], [16] [18], and a dual-gratingassisted directional coupler [19]. Some of these methods (e.g., grating-based coupler [15]) are polarization dependent and need to introduce other materials (such as polymer, Si 3 ON 4, or SiON) and additional steps of deposition. The inverse taper approach has shown good performance. In this paper, we study the bilevel mode converter to realize the transform between the fundamental modes of a silicon nanowire waveguide and the SOI rib waveguide with a large cross section (or a fiber). The bilevel taper includes a bottom taper and a top taper. This taper is polarization insensitive and has a broadband. Furthermore, only SOI wafer is needed for the fabrication. It is well 0733-8724/$20.00 2006 IEEE

DAI et al.: BILEVEL MODE CONVERTER BETWEEN A SILICON NANOWIRE WAVEGUIDE AND A LARGER WAVEGUIDE 2429 Fig. 2. (a) Four types of conventional tapers. (b) Power propagation in the tapers. (c) Position of reference points z 1 and z 2. known that a taper of linear shape is inefficient and there have been many theoretical and experimental investigations on the design of nonlinear tapering shapes [20], [21]. In this paper, we present a top taper with two sections (a parabolic taper and a followed sine taper) in order to improve the mode conversion efficiency. II. STRUCTURE AND DESIGN Fig. 1 shows the structure of the present bilevel mode converter, which includes two layers of tapers (i.e., a bottom taper and a top taper). The slab height h of the SOI rib waveguide is the same as the core height h co of the silicon nanowire waveguide. By using a bottom taper, the width of the slab is tapered from a width w tp to the core width w co of the of the silicon nanowire waveguide. The rib of the SOI waveguide is tapered from a width w r to a tip by using the top taper. With such a bilevel taper, a gradual transformation between the SOI rib waveguide and a silicon nanowire waveguide is obtained and thus the fundamental modes can be converted. In order to give an optimal design for the present bilevel mode converter, we use a three-dimensional (3-D) semivectorial beam propagation method (BPM) [22] to simulate the light propagation in the taper with a perfectly matched layer boundary treatment [23]. The coordinate system is shown in Fig. 1, where the origin is at the center of the Si core layer. The grid size for the BPM simulation is chosen as x = y =0.01 µm and z =0.1 µm. Our numerical simulation has shown such a grid size is fine enough to give convergent results. The refractive indexes for the buffer layer (SiO 2 ), the core layer (Si), and the cladding layer (air) are 1.46, 3.455, and 1.0, respectively. First, we consider the mode conversion of the TE polarization. Actually, this bilevel taper is polarization insensitive (which will be shown later). As an example, we choose the width and height of the silicon nanowire waveguide as w co = 500 nm and h co = 350 nm. For the SOI rib waveguide, H = 4.1 µm, w r =2.4 µm, and the slab height h is equal to the core height h co of the silicon nanowire waveguide. Such an input rib waveguide is multimode because of the deep etching. In our BPM simulation, the fundamental modal field of the SOI rib waveguide is chosen as the initial input field. Our simulation results have shown that the bottom taper does not influence much the mode conversion efficiency and we choose a parabolic bottom taper with w tp =7.0 µm and L bt = 700 µm. In the following part, we focus on the optimal design of the top taper. First, we consider four kinds of conventional tapers [as shown in Fig. 2(a)]: 1) the first kind of parabolic

2430 JOURNAL OF LIGHTWAVE TECHNOLOGY, VOL. 24, NO. 6, JUNE 2006 Fig. 3. Present top taper. (a) Structure. (b) Power propagation for different w 1 with fixed w 2 = 200 nm. (c) Power propagation situations for different w 2 with fixed w 1 = 600 nm. taper; 2) the second kind of parabolic taper; 3) a linear taper; and 4) a sine taper. Here, we choose the lengths of the top taper as L top = 600 µm. The power in these four kinds of tapers at different propagation distance (z) is shown in Fig. 2(b). From this figure, one sees that the linear taper (c) has a conversion efficiency of about 60%. The conversion efficiency for the second kind of parabolic taper is about 40%, which is the lowest among these four kinds of tapers. From the curves of power P (z), one sees that the power changes quickly at two special points z 1 and z 2. At point z 1, the power begins to decrease and at point z 2, the power drops rapidly. For different type of tapers, the positions of z 1 and z 2 are different [see the marks o in Fig. 2(b)]. However, we find that the taper widths at points z 1 and z 2 are about 0.6 and 0.2 µm for all the four kinds of tapers, respectively [see the marks o in Fig. 2(c)]. This can be explained from the mode confinement of the tapered waveguide. In this example, the fundamental modal field of the deeply etched SOI rib waveguide is chosen as the initial input field for the BPM simulation. When the rib width decreases from 2.4 to 0.6 µm, the intensity peak of the fundamental mode moves down only slightly and is located almost at the middle of the rib due to the strong confinement. Consequently, a good mode conversion is obtained and the fundamental mode is predominantly excited. When the rib is tapered from 0.6 µm to a smaller width, the mode conversion is not complete and some power is coupled to the higher order leaky modes if the width at point z 1 varies fast. In this case, the field in the SOI rib waveguide has two peaks. One peak corresponds to the fundamental mode and the other is formed by the power remaining in the rib. The power remaining in the rib is coupled to the higher order leaky modes instead of the fundamental mode and thus introduces a reduction of power. When the rib width is reduced to a value smaller than 0.2 µm, the light cannot be confined well in the rib and more power is coupled to the higher order leakage modes with larger leakage losses and thus a rapid reduction of power is introduced. Therefore, we should let the taper vary more slowly at point z 1 (where the taper width is 0.6 µm) to allow more mode conversion and reduce the power coupled to the higher order leakage modes. In the following part, we analyze an optimal design for the top taper, which is shown in Fig. 3(a). The shape of the top taper under consideration includes two parts: First, a parabolic taper is used to taper the rib to a certain width w 1, and then, the rib tapers to a smaller width w 2 by using a sine taper. The

DAI et al.: BILEVEL MODE CONVERTER BETWEEN A SILICON NANOWIRE WAVEGUIDE AND A LARGER WAVEGUIDE 2431 Fig. 4. Field distributions at different planes. (a) y = (H h). (b)z =0.(c)z = 200 µm. (d) z = 400 µm. (e) z = 600 µm. (f) z = 800 µm. dependence of the taper width on the propagation distance z is given by the following equation: w(z) (w r w 1 )(1 z/l top1 ) 2 + w 1, z L top1 = (w 1 + w 2 )+(w 1 w 2 ) cos [π(z L top1 )/L top2 ], L top1 z L top where L top1 and L top2 are the lengths of the parabolic taper and the sine taper, respectively, and we choose L top1 = 400 µm and L top2 = 200 µm. We also choose w 1 =0.6 µm (600 nm) and w 2 =0.2 µm (200 nm). Therefore, z 1 = L top1 and z 2 = L top2 (the taper widths at points z 1 and z 2 are 0.6 and 0.2 µm, respectively). With this design, the taper width changes very slowly around z = z 1 (i.e., w = 600 nm). Consequently, more power will be converted to the fundamental mode. As a comparison, we also calculate the conversion efficiency as the widths w 1 and w 2 varies. Fig. 3(b) shows the power along the propagation distance for the cases of w 1 = 500, 600, and 700 nm when w 2 = 200 nm. One sees that a maximum mode conversion efficiency of about 78.9% is obtained when w 1 = 600 nm. Fig. 3(c) shows the power along the propagation distance as the width w 2 varies (w 2 = 100, 200, 300, and 400 nm) and the width w 1 is fixed at w 1 = 600 nm. From this figure, one sees that the mode conversion efficiency is more than 78% and changes slightly when the width w 2 varies from 100 to 300 nm. When a large w 2 (e.g., 400 nm) is chosen, the mode conversion efficiency is reduced greatly and is only about 58%. Therefore, the width w 2 should be smaller than 300 nm. Since a sharp tip is difficult to fabricate, we choose w 2 = 200 nm to relax the critical requirement for fabrications. From Fig. 3(b) and (c), one can also see that the mode conversion efficiency is not very sensitive to the changes of the waveguide widths w 1 and w 2. This indicates that our structure has a relative large tolerance of fabrication. Fig. 4 shows the distributions of the field intensity at plane of y = (H h) and several planes perpendicular to the propagation direction z, i.e., z = 0, 200, 400, 600, and 800 µm. From this figure, one sees the fundamental mode is converted successfully. As mentioned before, when the taper width is about 600 nm, the peak of the fundamental mode moves down and the field distribution has two peaks. Even for our optimal design, there is still a minor peak in the rib, which can be seen in Fig. 4(d). This power leaks to the free space [see Fig. 4(e)], which results in a decrease of power, as shown in Fig. 3(b). Finally, the fundamental mode of the silicon nanowire waveguide is obtained [see Fig. 4(e)]. In Fig. 5, the power propagation in the bilevel taper for different wavelengths (λ = 1500, 1550, and 1600 nm) are shown. One sees that when the wavelength increases from 1500 to 1600 nm, the change of the coupling efficiency is less than 0.3 db. The bilevel taper thus has low wavelength dependent loss and can operate over a wideband. For the fabrication of the present bilevel mode converter, two separate etching processes are needed. The bottom and top tapers are formed by using the first and second masks in sequence. Here, we consider the required alignment tolerance of the used two masks. In order to obtain a larger alignment tolerance, the distance D from the tip of the top taper to the edge of the bottom taper should be large enough [see Fig. 6(a)]. In Fig. 6(a), the power propagation in the taper with

2432 JOURNAL OF LIGHTWAVE TECHNOLOGY, VOL. 24, NO. 6, JUNE 2006 Fig. 5. Power propagation in the bilevel taper for different wavelengths. Fig. 7. Power propagation when h co = 350, 500, and 800 nm. (about 4%). A misalignment of 0.2 µm for the two masks is not critical, and thus there is good fabrication tolerance. If the scattering loss due to the roughness becomes insignificant (for a perfect fabrication process), we can choose a silicon nanowire waveguide with a larger height and a smaller width for a more efficient use of the wafer area. For example, we consider the cases of h co = 350, 500, and 800 nm. We choose 350 nm for the core width to make the silicon nanowire waveguide quasi-single mode. Fig. 7 shows the corresponding power propagation in this taper. One sees that the converted efficiency is improved greatly when the core height increases. The conversion efficiency is about 96% (corresponding to an excess loss of 0.18 db) when h co = 800 nm. The reason is that it becomes easier to push down the power peak in the rib as the slab height h (the same as the core height h co ) increases, and thus, the power remaining in the rib decreases. On the other hand, the single-mode condition is a limitation for choosing a larger height, and one should consider this in the design of the mode converter. We also calculate the power propagating in the present bilevel taper for both polarizations. Our simulations show that the polarization dependent loss is less than 0.3 db. Fig. 6. (a) Power propagation in the bilevel taper with a misalignment of 200 nm. (b) Intensity at plane y = (H h). a misalignment x ma =0.2 µm is shown. Fig. 6(b) shows the field intensity at plane y = (H h). One sees the reduction of the conversion efficiency due to the misalignment is small III. CONCLUSION We have proposed a bilevel mode converter for the mode transformation between a silicon nanowire waveguide and the SOI rib waveguide with a large cross section. The bilevel taper comprises two layers of tapers, i.e., the bottom taper and the top taper. When one uses a conventional (such as linear, parabolic, and sine) type of taper as the top taper, the mode conversion efficiency is no more than 60%. Based on our analysis of the power propagation in the tapers, we have proposed a top taper (including a parabolic taper and a sine taper) and give an optimal design for the top taper to improve the mode conversion efficiency. The efficiency for the optimized mode converter has been improved to about 78.9% (estimated by using a 3-D semivectorial BPM) when the height of the silicon nanowire waveguide is 350 nm. The conversion efficiency can be improved further to about 96% if we can choose a larger

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Thurston, E. Kapon, and A. Shahar, Two-dimensional control of mode size in optical channel waveguide by lateral channel tapering, Opt. Lett., vol. 16, no. 5, pp. 306 308, Mar. 1991. [21] F. Payne, Semiconductor optical waveguide device, U.S. Patent 6 853 775, Feb. 8, 2005. [22] P.-L. Liu and B.-J. Li, Semivectorial beam-propagation method for analyzing polarized modes of rib waveguides, IEEE J. Quantum Electron., vol. 28, no. 4, pp. 778 782, Apr. 1992. [23] W. P. Huang, C. I. Xu, W. Lui, and K. Yokoyama, The perfectly matched layer boundary condition for modal analysis of optical waveguides: Leaky mode calculations, IEEE Photon. Technol. Lett., vol. 8, no. 5, pp. 652 654, May 1996. Daoxin Dai was born in Jiangxi, China, in 1979. He received the B.Eng. and the Ph.D. degrees from the Department of Optical Engineering, Zhejiang University, Zhejiang, China, in 2000 and 2005, respectively. He has authored about 30 papers and holds five patents in optical waveguide devices. His research interests include modeling and fabrication of integrated photonic devices. Sailing He (M 92 SM 98) received the Licentiate of Technology degree and the Ph.D. degree, both in electromagnetic theory, from the Royal Institute of Technology, Stockholm, Sweden, in 1991 and 1992, respectively. Since 1992, he has been in the faculty of the Royal Institute of Technology. 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 the Royal Institute of Technology and Zhejiang University. He has first-authored one monograph (Oxford University Press), authored/coauthored about 200 papers in refereed international journals, and has been granted a dozen of patents in optical communications. Hon-Ki Tsang (M 90 SM 04) received the B.A. degree in engineering (electrical and information sciences) and the Ph.D. degree in engineering from the University of Cambridge, Cambridge, U.K., in 1987 and 1991, respectively. His dissertation was entitled Optical Nonlinearities in MultiQuantum Well Waveguides. He was a Research Visitor with Bellcore, Red Bank, NJ, in 1990 and was a Science and Engineering Research Council Postdoctoral Fellow with the University of Bath, Bath, U.K., before joining the Chinese University of Hong Kong, Sha Tin, Hong Kong, in 1993 as a Lecturer in the Department of Electronic Engineering. He was with Bookham Technology PLC, Oxfordshire, U.K., in 2002 and returned to the Chinese University of Hong Kong in 2003. He has published about 170 papers in refereed journals or conference proceedings on modulators, all-optical signal processing, nonlinearities in optical waveguides, and planar lightwave components.