All-fiber Fourier filter flat-top interleaver design with specified performance parameters

Transcription

1 All-fiber Fourier filter flat-top interleaver design with specified performance parameters Qijie Wang Tong Liu Yeng Chai Soh Nanyang Technological University School of Electrical and Electronic Engineering Nanyang Avenue Singapore Ying Zhang, MEMBER SPIE Singapore Institute of Manufacturing Technology Nanyang Drive Singapore Abstract. A minimax method for designing a Fourier filter flat-top (F 3 T) interleaver is proposed and demonstrated. Given a passband range, the proposed minimax method is able to produce an F 3 T interleaver with a specified bandwidth, minimal insertion loss, and higher isolation. In comparison with current interleaver design methods, the proposed approach has the advantage that the design parameters and the performance parameters of the interleaver can be obtained analytically Society of Photo-Optical Instrumentation Engineers. [DOI: / ] Subject terms: Fourier filter flat-top interleaver; interleaver; minimax; dense wavelength division multiplexing; all-fiber filter. Paper received Jan. 7, 2003; revised manuscript received Apr. 2, 2003; accepted for publication Apr. 9, Introduction To meet the explosive bandwidth demand in optical communications, dense wavelength division multiplexing DWDM systems must offer increasingly higher channel counts or channel speeds. Two solutions are being pursued. One is to broaden the bandwidth by reducing the attenuation peak around 1400 nm. The other is to achieve narrower channel spacings in the currently used bands supported by erbium-doped fiber amplifier EDFA amplifiers. From the perspective of cost effectiveness, the second solution is preferred, because the existing optical components designed for wide channel spacing can still be used. In this solution, interleaver technology plays a critical role. Today s DWDM systems with interleavers can be upgraded with much narrower channel spacings and more channel counts for very large capacity applications. 1 3 Several techniques have already been proposed for implementing optical interleavers, and these include the F 3 T interleaver, 1 3 Michelson-Gires-Tournois interleaver, 4 Birefrigent Gires-Tournois interleaver, 5,6 Etalon interleaver, 7 and so on. The key performance parameters used to evaluate their performance include insertion loss, square-like passband/stopband, channel phase symmetry, and channel isolation. Among these techniques, the F 3 T interleaver demonstrates several advantageous properties over other techniques. As it adopts the all-fiber implementation, the F 3 T interleaver has a low-loss, uniform response over a wide wavelength range, low chromatic dispersion, and minimal polarization-dependence effects. To ensure that the F 3 T interleaver is practically useful, the thermal stability of the all-fiber F 3 T interleaver was investigated and a thermal controller has been devised. 8 The results of Ref. 8 have shown that the F 3 T interleaver can achieve good temperature stability under testing conditions in accordance with the standards of Bellcore Telcordia GR In addition to these merits, another attractive and important feature of the F 3 T interleaver is its ability to achieve symmetrical passband and stopband with flat tops. Thus, the F 3 T interleaver has attracted intensive interest in the optical engineering community. It is worthy to mention that Etalon-based interleavers do have a better performance in providing flat-top passbands or stopbands. This is not surprising, because from the signal processing prospective, the Etalon interleavers are essentially infinite impulse response IIR type filters and the F 3 T interleavers are finite impulse response FIR type filters. However, it is the IIR structure 9 that makes it difficult for the Etalon interleaver to obtain /2 phase shift symmetry between the bar-state and cross-state channels of the interleaver. As an FIR filter, the F 3 T interleaver exhibits the advantage of phase performance. 10 For an F 3 T interleaver, the design parameters are the coupling ratios of fiber couplers, and the important performance parameters are the passband/stopband shape, isolation, and insertion loss. 11 It is desired that the insertion loss be as low as possible, the channel isolation as high as possible, and the passband/stopband shape be wide and squarelike. Currently, F 3 T interleavers are designed by numerically optimizing certain integration criteria. 12,13 As integration criteria are chosen heuristically, it is difficult to specify an explicit relationship between the design parameters and the performance of the designed interleaver. Thus, tedious trial-and-error steps have to be performed to obtain an interleaver with the desired specifications. It is therefore of practical and theoretical interest to develop a quantitative approach capable of specifying the key performance parameters in the design stage. This work addresses this problem. A minimax method is proposed to design F 3 T interleavers under a given passband/stopband bandwidth. The basic idea is to minimize worst-case performance in terms of insertion loss and isolation over the given bandwidth. Describing the insertion loss and isolation as passband and stopband ripples, respectively, the interleaver performance can be specified by a kind of H norm of the power spec Opt. Eng. 42(11) (November 2003) /2003/$ Society of Photo-Optical Instrumentation Engineers

2 Hence, the transfer functions H 0 from port 1 to port 3 and H 1 from port 1 to port 4, which are usually termed as the bar-state and the cross-state transfer functions, respectively, can be expressed in the following two equations: H 0 c 1 c 2 c 3 exp j3 s 1 s 2 c 3 exp j c 1 s 2 s 3 exp j s 1 c 2 s 3 exp j3, 2 tral transfer function of the interleaver. Then, the interleaver design is treated as a minimax filtering problem and all design parameters are obtained by resolving the H norm. It is shown that given a passband/stopband bandwidth, the proposed approach can produce F 3 T interleavers with minimal insertion loss and maximal isolation. When compared with the traditional interleaver design approaches, the proposed approach has the advantage that the influence of the design parameters on the performance parameters can be evaluated analytically instead of being solved via numerical methods. Thus, the proposed minimax filter scheme gives a quantitative approach to the design of interleavers with given specifications. The rest of the work is organized as follows. Section 2 briefly introduces the F 3 T interleaver and its transfer functions. Section 3 illustrates the proposed minimax design method and its properties. In Sec. 4, a simulation study is carried out to verify that the performance of interleavers can be specified by the proposed approach. In Sec. 5, the proposed design approach is experimentally demonstrated. Section 6 concludes the work. 2 F 3 T Interleaver A Fourier filter flat-top (F 3 T) interleaver device is a generalized unbalanced Mach-Zehnder interferometer, as shown in Fig. 1. It consists of three cascaded couplers linked by two differential delays. Denote the phase delay as L n/ that corresponds to half of L, where L is the physical length of the differential delay, is the wavelength of the wave propagating through free space, and n is the refractive index of the optical fiber. The normalized electric field transfer function from the two inputs to the two outputs can be expressed by the following matrix transfer function 14 : E 3 E M 3 M M 2 M M 1 4 E 1 E 2 c 3 js 3 js 3 c 3 e 2 j 0 j 0 e 2 c 1 js 1 js 1 c 1 E 1 E 2, Fig. 1 F 3 T interleaver. c 2 js 2 js 2 c 2 e j 0 j 0 e where c i k i and s i 1 k i, with k i as the bar-state intensity coupling ratio of the i th directional coupler. 1 H 1 j c 1 c 2 s 3 exp j3 s 1 s 2 s 3 exp j c 1 s 2 c 3 exp j s 1 c 2 c 3 exp j3. The interleaver design is to choose appropriate parameters c i and s i, such that the interleaver spectrum responses H 0 and H 1 have performance specified by passband/stopband shape, passband bandwidth, isolation, and insertion loss. This work addresses the interleaver design under a given passband bandwidth. In this case, the task of interleaver design is aimed at achieving a prespecified passband bandwidth with as low an insertion loss and as high an isolation as possible. 3 F 3 T Interleaver by H Filter Design The basic requirement on an interleaver is to obtain identical passband/stopband shape for both the bar-state and the cross-state output. 13 To this end, it is required that H 0 2 H 1 /2 2, where H 0 2 H 0 H 0 * is the bar-state power transfer function and H 1 ( /2) 2 H 1 ( /2)H 1 *( /2) is the cross-state power transfer function with a phase shift of /2. From the definitions of H 0 and H 1, it is easy to obtain c 1 s 1 &/2. Denote c i (i 1,2,3) by cos i, and s i by sin i, where i is in the interval 0, /2. The output response of H 0 and H 1 can be expressed in the frequency spectrum by H 0 w & 2 cos 2 cos 3 exp j3w sin 2 cos 3 exp jw sin 2 sin 3 exp jw cos 2 sin 3 exp j3w, H 1 w & 2 cos 2 sin 3 exp j3w sin 2 sin 3 exp jw sin 2 cos 3 exp jw cos 2 cos 3 exp j3w, where w /T, T is the unit delay time corresponding to half of the first phase delay of the interleaver. Let s0 denote the stopband ripple of H 0 (w), p1 the passband ripple of H 1 (w), B s0 and B p0 the stopband and passband bandwidth of H 0 (w), and similarly, B s1 and B p1 the stopband and passband bandwidth of H 1 (w), respectively. Here, the ripple is defined as the amplitude difference within the passband or stopband, and the passband Optical Engineering, Vol. 42 No. 11, November

3 Fig. 2 Scheme of bar-state and cross-state intensity. or stopband bandwidth is defined as the range between the two points where a line tangential to the ripple bottom or the ripple peak for the stopband cuts the boundary of the spectrum curve. 15 See Fig. 2 for illustration. With these denotations and definitions, applying the energy conservation principle given by H 0 (w) 2 H 1 (w) 2 1, we have p s0 1/2, 7 and B s0 B p1. As the bar-state and the /2 shifted cross-state power spectral transfer functions are identical, the passband and stopband ripples are identical for H 0 (w) and H 1 (w), and so are the passband and stopband bandwidths, as defined before. And from Eq. 8, we have p0 p1 and s0 s1, 9 B s0 B s1 B p0 B p1. Therefore, Eq. 7 can be abbreviated as p 1 1 s 2 1/2, where 1 s corresponds to the isolation of the interleaver and p is the passband ripple, as illustrated in Fig. 2. Equation 11 gives the relation between s and p, from which it can be seen that if s is minimized, then p also achieves its minimum. As seen from Fig. 2, the passband ripple p actually specifies the worst insertion loss of the interleaver when the spectral response of the interleaver can reach a transmission spectrum of one at some wavelength in the passband. This is the theoretical value, and in practice some extra insertion loss will be introduced by other factors. Thus the objective of interleaver design can be stated as follows. Given the stopband/passband bandwidth B s /B p for the interleaver, find the coupling ratios of those fiber couplers in the interleaver, such that the worst case of the stopband ripple s of the interleaver is controlled at the minimal level over the stopband. Now we describe the problem in a more quantitative way by using the minimax method. The details of this method can be found in chapter 14 of Ref. 15. As the power transfer functions of the bar-state and the /2 shifted crossstate are identical, it suffices to consider one channel. Without loss of generality, we select H 0 (w). By definition, s specifies the worst case of the stopband ripple, that is, s max H 0 w 2, w s1 w w s2 12 where w s1 and w s2 are the lower and upper limits of the stopband of H 0 (w), respectively, and w s2 w s1 B s when the desired bandwidth is given by B s. Then the interleaver design problem is to resolve a H norm of H 0 (w) is given by H min max H 0 w 2. w s1 w w s2 2, 3 13 It is actually an optimization problem of finding a set of i to resolve the norm. Denote E(w) H 0 (w) 2. Using Eq. 5, we have 3174 Optical Engineering, Vol. 42 No. 11, November 2003

4 E w sin 2 2 sin 2 3 sin 2 2 cos 2 3 cos 2w 1 2 cos 2 2 sin 2 3 cos 6w. 14 After a careful examination of all the stationary points of E given by E/ w 0 and their associated Hessian matrix 2 E/ w 2, the maximum of H 0 (w) is reached only when w /2, and the maximum value in the stopband is obtained by E s max H 0 w 2 w s1 w w s2 H sin It is clear from Eq. 14 that the frequency response is symmetrical with respect to /2. Thus, w s1 and w s2 are determined by w s1 ( B s )/2 and w s2 ( B s )/2, with the stopband bandwidth being specified by B s. In addition, E(w s1 ) E(w s2 )atw s1 and w s2. Thus, we only need to calculate w s1 that falls into the range /4, /2. Now the minimax problem reduces to Minimize E sin 2 2 3, 2, 3 subject to 1 2 sin 2 2 sin 2 3 sin 2 2 cos 2 3 cos 2w s cos 2 2 sin 2 3 cos 6w s This problem is a constrained optimization problem. By using the Lagrange method, the analytical solutions can be obtained. As i (i 2,3) are limited to the boundary 0, / 2, we have Fig. 3 With the same bandwidth, only the solid curve derived by the proposed method is tangential to the boundary. Straight line is and ; dashed line is and ; and dashed dotted line is and It is interesting to note that the top of H 0 ( /2) 2 is always tangential to the transmission spectrum of 1 when the optimal value is achieved. To see this, we consider the other two stationary points, given by E/ w 0. Also by examining the associated Hessian matrix at these two points, it concludes that the power spectral response E(w) reaches its maximal value at these two stationary points and the maximal values are one. It shows that at the stationary points, except for w /2, the curve is always tangential to the unity transmission spectrum boundary when the optimal solutions are obtained. Figure 3 illustrates the three curves that possess the same bandwidth, with the solid curve depicting the optimal results obtained by the proposed design method. It can be seen that only the solid curve touches the boundary. This result also justifies the 2 arctan ) 2 cos 2w s1 1 3, arctan ) 2 cos 2w s1 1, 19 where w s1 ( B s )/2, with B s as a prespecified bandwidth. So far, we have obtained a formalized approach to the design of an interleaver with a given passband bandwidth. More specifically, it is summarized as follows. First, considering channel symmetry, the coupling ratio of the first fiber coupler in the F 3 T interleaver always takes a value of 50:50, i.e., 1 /4. Second, using the given passband bandwidth B s, the optimal parameters i (i 1,2,3) for the second and third coupler are derived by Eqs. 18 and 19. With these optimal parameters i (i 1,2,3), the insertion loss of the interleaver reaches its minimum, while the isolation reaches its maximum, under the given bandwidth. Fig. 4 Comparison with different passband bandwidth. Straight line is w s ; dashed line is w s ; and dashed dotted line is w s Optical Engineering, Vol. 42 No. 11, November

5 Table 2 Comparison of key optical performance parameters designed by different approaches. Specification Parameter Mach-Zehnder F 3 T in Ref. 3 Proposed F 3 T Insertion loss 0.2 db 0.3 db 0.3 db 0.5-dB passband 20 GHz 28 GHz 31.2 GHz 25-dB isolation 4 GHz 14 GHz 15 GHz bandwidth Ripple 0.1 db 0.1 db 0.01 db Dispersion 10 ps/nm 10 ps/nm 10 ps/nm Fig. 5 Detailed illustration of Fig. 4. Straight line is w s ; dashed line is w s ; and dashed dotted line is w s assertion that the insertion loss can be specified by p or s ). 4 Performance Study by Simulation In this section, we compare the performance of interleavers designed by different approaches. We shall also examine the performance of our proposed approach with different bandwidth specifications. First, we use the proposed approach to design interleavers with 50-GHz channel spacing. Suppose that the desired passband bandwidth is 32.5, 20, and 7.5 GHz, respectively. Applying the proposed approach, the lower boundary of passband w s1 shall take the values of , , and in radians, correspondingly. Using Eqs. 18 and 19, the desired interleavers are obtained with spectral responses, as shown in Fig. 4. To see the details of the passband, the top portions of these responses are magnified in Fig. 5. It is clear that among these three cases, although the passband/stopband bandwidth is the widest when w s rad, the insertion loss in the passband and the isolation are the worst in this case. On the other hand, when w s rad, the interleaver possesses the best isolation and insertion loss, but the bandpass bandwidth is the Table 1 The relationship between the performance parameters. B s w s1 2 3 Ripples in Passband Isolation 50 GHz db 3 db 45 GHz db 5 db 40 GHz db 7.3 db 35 GHz db 10 db 30 GHz db 13.1 db 25 GHz db 16.6 db 20 GHz db 20.8 db 15 GHz db 26 db 10 GHz db 33.3 db 5 GHz db 45.4 db narrowest. A compromise is achieved with w s rad. This result indicates that the performance parameters are interrelated. Table 1 lists several typical cases with different bandwidths. The corresponding values of w s1, the optimal solution of 2 and 3, the ripples in the passband, and the associated isolation are given in the table. The data in the table again confirms the interdependence of the three key performance parameters of the passband bandwidth, the insertion loss, and the channel isolation. That is, one performance indicator is improved at the expense of another indicator. Next, we compare the performance of 50/100-GHz interleavers designed by different approaches. The key optical performance parameters of these interleavers are summarized in Table 2, from which it is shown that the 0.5-dB passband width of the proposed F 3 T interleaver is about 31 GHz, as compared to 28 GHz for the F 3 T interleavers in Ref. 3 and 20 GHz for a single unbalanced Mach Zehnder interferometer MZI interleaver. Also, the proposed F 3 T interleaver provides 15 GHz of 25-dB stopband width, which is larger than 14 GHz for the integration F 3 T interleaver and 4 GHz for a single unbalanced MZI interleaver. These simulation results demonstrate that the proposed approach can be used to design interleavers with a specified performance here passband/stopband bandwidth is prespecified, and the designed interleavers possess superior performance when compared to other existing interleavers. 5 Experiment Results The proposed approach has been used to design an all-fiber 25/50-GHz F 3 T interleaver, or equivalently, an interleaver with 0.2-nm channel spacing. The passband bandwidth is selected as 50% to the channel spacing, i.e., 12.5 GHz. Using the design formula given by Eqs. 18 and 19, the corresponding values of 2 and 3 are obtained as and , respectively. With these coupling ratios, the F 3 T interleaver is fabricated. The bar-state and cross-state spectral responses of the F 3 T interleaver are observed on an optical spectrum analyzer OSA. Figures 6 a and 6 b show the responses on an OSA in a display resolution of 0.2 and 0.5 nm, respectively. By moving the display window, the same spectral interleaving responses can be observed over the whole C band. To measure key optical performance parameters, we take one channel response and display it in Figs. 6 c and 3176 Optical Engineering, Vol. 42 No. 11, November 2003

6 Fig. 6 Responses of the F 3 T interleaver: (a) responses of bar- and cross-states in a narrower band; (b) responses of bar- and cross-states in a broader band; (c) passband/stopband width of the interleaver; and (d) passband/stopband ripple and the isolation of the interleaver. 6 d, where the passband bandwidth and the passband ripple are measured, respectively. From the OSA readings, as shown in the figures, the channel spacing is nm and the passband bandwidth is about nm, which is nearly 50% to the channel spacing. It is also observed that the passband ripple is lower than 0.2 db, and the isolation of the interleaver is around 18 db. All these parameters are comparable to the single stage 50/100-GHz F 3 T interleaver in Ref. 3. This again proves the effectiveness of the proposed design approach. 6 Conclusion We describe a new approach for the design of F 3 T interleavers with specified performance passband/stopband bandwidth. In the proposed approach, the performance of the interleaver is described by a H norm of the power transfer function of the interleaver. It is shown that with the proposed design approach, the bar-state and the crossstate intensity transmittance spectra of the designed interleaver gives a flat top with minimal ripple interleaving response under the given passband/stopband bandwidth. Unlike the existing interleaver design approaches, the analytical expressions of the optimal coupling ratios 2 and 3 are obtained in the proposed design scheme. Moreover, it is noted from the analysis in the work that the proposed design scheme can also be extended to interleaver design under other specifications. Thus the proposed approach provides a quantitative means to interleaver design. Acknowledgments The research was supported by the Singapore Institute of Manufacturing Technology within a collaboration research project U01-A-008CRP. References 1. J. Chon, H. Luo, C. H. Huang, R. Huang, J. Chen, and J. Bautista Expandable 50-GHz and 100-GHz dense wavelength division multiplexers based on unbalanced and cascaded-fiber Mach-Zehnder architecture, NFOEC 99, Chicago, IL Available on: J. C. Chon, B. Jian, and J. R. Bautista, High capacity and high speed DWDM and NWDM optical devices for telecom and datacom applications, Proc. SPIE 4289, C. H. Huang, Y. Li, J. Chen, E. Sidick, J. Chon, K. G. Sullivan, and J. Bautista, Low-loss flat-top 50-GHz DWDM and Add/Drop modules using all-fiber Fourier filters, NFOEC 2000, Denver, CO, pp , Telcordia Technologies B. B. Dingel and M. Izutsu, Multifunction optical filter with a Michelson-Gires-Tournois interferometer for wavelength-divisionmultiplexed network system applications, Opt. Lett , S. Cao and X. F. Simon, Fiber optic dense wavelength division multiplexer with a phase differential method of wavelength separation utilizing a polarization beam splitter and a nonlinear interferometer, U.S. Patent No. 6,130, Optical Engineering, Vol. 42 No. 11, November

7 6. S. Cao, C. Lin, C. Yang, E. Ning, J. Zhao, and G. Barbarossa, Birefringent Gires-Tournois interferometer BGTI for DWDM interleaving, OFC 2002, pp L. P. Ghislain, R. Sommer, R. J. Ryall, R. M. Fortenberry, D. Derickson, P. C. Egerton, M. R. Kozlowski, D. J. Poirer, S. DeMange, L. F. Stokes, and M. A. Scobey, Miniature solid etalon interleaver, NFOEC 2001, pp J. Chon, A. Zeng, P. Peters, B. Jian, A. Luo, and K. Sullivan, Integrated interleaver technology enables high performance in DWDM systems, NFOEC 2001, pp E. M. Dowling and D. L. MacFarlane, Lightwave lattice filters for optically multiplexed communication systems, J. Lightwave Technol. 12 3, G. Lenz, B. J. Eggleton, C. K. Madsen, C. R. Giles, and G. Nykolak, Optimal dispersion of optical filters for WDM systems, IEEE Photonics Technol. Lett. 10 4, B. Shine and J. Bautista, Interleavers make high-channel-count systems economical, Lightwave 2000, pp , available on Y. Li, C. Henry, E. Laskowski, H. Yaffe, and R. Sweatt, Monolithic optical waveguide filters based on Fourier expansion, U.S. Patent No. 5,596, T. Liu, Y. C. Soh, Y. Zhang, and Z. P. Fang, Parameter optimization of all-fiber F 3 T interleaver, Opt. Eng , C. K. Madsen and J. H. Zhao, Optical Filter Design and Analysis: A Signal Processing Approach, John Wiley and Sons, New York A. Antoniou, Digital Filters: Analysis, Design, and Applications, McGraw-Hill, New York Qijie Wang received his BE degree from the University of Science and Technology of China, in He is currently pursuing his PhD degree at Nanyang Technological University, Singapore. technology, optical measurement, surface plasmon resonance, image processing, and machine vision. Yeng Chai Soh received the BEng degree in electrical and electronic engineering from the University of Canterbury, New Zealand, in 1983, and the PhD degree in electrical engineering from the University of Newcastle, Australia, in From 1986 to 1987, he was a research assistant in the Department of Electrical and Computer Engineering, University of Newcastle. He joined the Nanyang Technological University, Singapore, in 1987, where he is currently a professor in the School of Electrical and Electronic Engineering. Since 1995, he has been the Head of the Control and Instrumentation Division. His current research interests are in the areas of robust system theory and applications, signal processing, estimation and filtering, model reduction, and hybrid systems. Ying Zhang received his BE, ME, and PhD degrees from Southeast University, in 1989, 1992, and 1995, respectively. Since 1995, he has held various research positions at Tsinghua University, China, Melbourne University, Australia, and Nanyang Technological University, Singapore. He is currently with the Singapore Institute of Manufacturing Technology. He has authored 50 scientific journal papers and one monograph Robust Identification of Uncertain Systems. He was also the recipient of the National Outstanding Doctorial Dissertation Award issued by the State Council of China in His current research interests include adaptive signal processing and control, image processing and computer vision, and optical measurement. Tong Liu received his BS and MS degrees in applied optics in 1988 and 1991, respectively, from the Department of Modern Applied Physics, Tusinghua University, China. He obtained his PhD degree in mechanical engineering in 2002 from Nanyang Technological Univeristy(NTU), Singapore. Before he joined NTU in 1998, he was an associate professor at Tsinghua University. Currently he is working with the School of Electrical and Electronic Engineering, NTU, as a research fellow. His interests include photonics, laser 3178 Optical Engineering, Vol. 42 No. 11, November 2003