Integrated grating-assisted coarse/dense WDM multiplexers

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1 Integrated grating-assisted coarse/dense WDM multiplexers Linping Shen *a, Chenglin Xu b, and Wei-Ping Huang b a Apollo Inc., 1057 Main Street W., Hamilton, ON, Canada L8S 1B7 * lpshen@apollophotonics.com; phone ext 242; fax b Department of ECE, McMaster University, 1280 Main Street W., Hamilton, ON, Canada L8S 4K1 ABSTRACT In wavelength division multiplexing (WDM) systems, coarse and dense WDM (CWDM/DWDM) are two key technologies. In general, it takes two steps to accomplish this mixing (coarse/dense) WDM function. In order to make the WDM device compact and low loss, it is necessary to integrate these two WDM functions into one step. In this paper, we propose two typical designs of the coarse/dense multiplexers, which multiplex the coarse/dense-wdm (C/D-WDM) signals simultaneously. We believe that, although their operation principle is simple, the proposed structures simplify the design of integrated photonic devices and will be the guideline in the development of future WDM devices. Keywords: WDM multiplexer, photonic integrated circuit, Mach-Zehnder interferometer, wideband coupler 1. INTRODUCTION In optical WDM systems and networks, such as the fiber-to-the-home (FTTH) service (e.g., wavelength 1.31/1.55/1.49 µm in the EPON and wavelength 1.31/1.545/1.5x µm in the APON), coarse WDM (e.g., channel spacing 0.2/0.4 nm) and dense WDM (e.g., channel spacing 0.04/0.08 nm) are two key technologies. In current WDM systems, with different WDM devices, the mixing (coarse/dense) WDM functions are accomplished separately. By considering the advantage of photonic integrated circuit (PLC), i.e., compact and low loss, it is necessary to integrate these two WDM functions into one step. In this paper, we propose two typical designs of the coarse/dense multiplexers based on a grating-assisted Mach-Zehnder interferometer (MZI) with two couplers. With the combination of two well-known devices [1,2]: the wavelength selective coupler and the grating-assisted MZI, we are able to multiplex/demultiplex the coarse/dense-wdm (C/D-WDM) channels simultaneously. The proposed structures simplify the design of integrated photonic C/D-WDM devices and circuits. The proposed devices consist of a grating-assisted symmetrical or asymmetrical Mach-Zehnder interferometer with the wideband coupler (WBC) and/or the 3dB coupler. In first design, the C/D-WDM multiplexer/demultiplexer utilizes a grating-assisted asymmetrical (unequal arm) MZI with one wideband 3dB WBC coupler and one general 3dB coupler. In the second design, the C/D-WDM multiplexer/demultiplexer utilizes a grating-assisted symmetrical (equal arm) MZI with two wavelength selective couplers (WSCs). Depending on different operation principles, the wideband coupler operates as a 3dB coupler in two wavelength bands or operates as a 3dB coupler in one wavelength band and a crossstate coupler in another one. Without loss of generality, an example of multiplexing three signals (λ 1 /λ 2 /λ 3 ) in two wavelength bands is considered, where λ 1 (e. g., 1.31 µm) belongs to the first band and λ 2 /λ 3 (e. g., 1.55/1.5x µm) belong to the second band. In this paper, firstly, the operation principles of the proposed C/D-WDM Multiplexers are demonstrated. Then, based on the hierarchy software platform of Apollo photonics solution suite (APSS) [3], the design procedures are demonstrated and the simulation results of those C/D-WDM multiplexers and related components such as the couplers and planar gratings are given. Finally, some related issues such as polarization dependence and material dispersion are discussed. 2. THEORY The proposed multiplexer/demultiplexers are shown in Fig. 1. The WDM signals from an input waveguide, with three wavelengths (λ 1 /λ 2 /λ 3, i.e. 1.3/1.55/1.5x µm), are lunched at port 2, and demultiplexed into different ports. In the first design as shown in Fig. 1a, the asymmetrical MZI device consists of a wideband 3dB coupler (WBC), a general 3dB 698 Photonics North 2004: Optical Components and Devices, edited by John C. Armitage, Simon Fafard, Roger A. Lessard, George A. Lampropoulos, Proceedings of SPIE Vol (SPIE, Bellingham, WA, 2004) X/04/$15 doi: /

2 coupler, and Bragg gratings with a Bragg wavelength λ 1. The WBC is a device that operates as a 3dB coupler in two wavelength bands. In the second design as shown in Fig. 1b, the MZI symmetrical device consists of two wavelength selective couplers (WSCs) and Bragg gratings with a Bragg wavelength λ 2. The WSC is a wavelength selective device that operates as a 3dB coupler in one wavelength band (i.e., λ 2 /λ 3 ) and a cross-state coupler in another band (i.e., λ 1 ). Fig. 1 shows the configuration of a demultiplexer, in which the device demultiplexes the wavelengths λ 1, λ 2 and λ 3 from port 2 to ports 1, 3 and 4, respectively. Because the proposed device acts as a multiplexer, a demultiplexer, or a multiplexer/demultiplexer with the direction of light propagation reversed from one configuration to the other for each port, only the demultiplexers, as shown in Fig. 1, are considered in detail throughout this paper. (a) First design with an asymmetrical MZI and Bragg grating at wavelength of λ 1 (b) Second design with a symmetrical MZI and Bragg grating at wavelength of λ 2 Fig. 1. The proposed WDM Demultiplexer (DeMUX) for two wavelength bands. The operation theory of the C/D-WDM DeMUXs is as follows: The WDM signals, with wavelengths λ 1, λ 2 and λ 3, enter from port 2. Here, optical channels with wavelengths λ 2 and λ 3 are dense wavelength signals and belong to one wavelength band, and optical channel with wavelength λ 1 belongs to another wavelength band. In the first design as shown in Fig. 1a, the WBC coupler operates as a 3dB coupler for all wavelengths (i.e., λ 1, λ 2 and λ 3 ). The channel signal with wavelength λ 1 is reflected by the Bragg gratings and coupled from the port 2 to port 1 due to the π/2 phase difference of the 3db coupler and the equal phase of the Bragg gratings on both arms. Also, the channel signals with wavelengths λ 2 and λ 3 are transmitted by the Bragg gratings and, due to the zero and π phase difference of the asymmetrical MZI structure for the corresponding wavelengths, coupled from the port 2 to port 3 and port 4, respectively. The length difference L meets the following condition (assuming the wavelength λ 2 > λ 3 ): ( m 0.5) λ 2 mλ L = = n n 0, λ 2 3, and 0, λ 3 n λ 1 0, λ m = (1 ) (1) 2 n0, λ 3λ 2 Proc. of SPIE Vol

3 where m is the diffraction order, and n 0,λ2 and n 0,λ3 are the effective indices at the corresponding wavelengths. We find that the narrower the wavelength spacing ( λ = λ 2 - λ 3 ), the longer the length difference L (also the larger the diffraction order). In the second design as shown in Fig. 1b, the MZI symmetrical device consists of two wavelength selective couplers (WSCs) and Bragg gratings with a Bragg wavelength λ 2. The WSC coupler is a wavelength selective device that operates as a 3dB coupler in one wavelength band (i.e., λ 2 /λ 3 ) and a cross-state coupler in another band (i.e., λ 1 ). Like the first design as shown in Fig. 1a, the channel signal with wavelength λ 2 is reflected by the Bragg gratings and coupled from the port 2 to port 1 and the channel signals with wavelengths λ 3 and λ 1 are transmitted by the Bragg gratings. Unlike the first design, due to the zero phase difference of the symmetrical MZI structure, the channel signal at wavelength λ 3 is coupled by the WSC coupler from the port 2 to the port 4, and the channel signal at wavelength λ 1 is switched from the port 2 to the port 3 due to the cross-state operation of the WSC coupler. In general, with the help of the symmetrical/asymmetrical grating-assisted MZIs with some specific couplers, we are able to demultiplex the coarse/dense WDM channels simultaneously. For the sake of simplicity, only three C/D WDM signals (λ 1 /λ 2 /λ 3 ) in two wavelength bands and the directional coupler based on the typical silica buried channel waveguide are considered. In general, by utilization of MZI wavelength selective properties, we can increase the number of channels. For example, the path from port 2 and port 4 may contain more than one WDM signals. Also the extension from typical four-port MZI to generalized MZI such as array waveguide grating (AWG) and etched diffraction grating (EDG), from silica material system to other material system such as semiconductor, polymer, and silicon-on-insulator (SOI) is conceptually straightforward. 3. DESIGN OF WIDEBAND COUPLER In this section, we present the design of the wideband coupler (WBC) and walength selective coupler (WSC), which are an important part in the proposed device. Generally, several integrated photonic devices such as the cross coupler, the directional coupler [5] and the Multimode interferometer (MMI) [6] can be used as the WBC and WSC couplers by their wavelength dependence properties. The detail selection of the couplers is determined by the specific requirement of the C/D-WDM demultiplexers. In order to demonstrate the design theory of the couplers, the simple 2x2 directional coupler based on the buried channel waveguide is selected, which is built on the mode coupling phenomena, as shown in Fig. 2. As shown in Fig. 2a, the coupler consists of two parallel waveguides I and II with the separation S and length L. With the help of the well-know effective index method (EIM), the three-dimensional devices can be simplified to the twodimensional device consisting of equivalent slab waveguides with the equivalent cladding index n o, and the equivalent core n 1 as shown in Fig. 2b. (a) Top view 700 Proc. of SPIE Vol. 5577

4 (b) Equivalent index distribution Fig. 2. The schematic of the directional coupler For the WBC coupler, in order to perform the 3dB coupler for all wavelengths λ 1, λ 2 and λ 3, (here λ 2 and λ 3 belong to the same wavelength band), the total length of the coupler meets the following equations: (2p -1)π L WBC = = 4 k λ1 (2q -1)π 4 k, p and q = 1, 2, 3,.. (2) λ2/λ3 where p and q are a positive integer (number), and k λ1 and k λ2/λ3 are coupling coefficients at corresponding wavelength bands. It is noted that p or q =1 for the convention 3dB coupler. Usually the coupling coefficient is weak at the shorter wavelength, so we have that q > p. The coupling coefficient ratio (CCR) for the WBC coupler is expressed as kλ1 2 p 1 C CR WBC = = (3) k 2q 1 λ2/λ3 Similarly for the WSC coupler, in order to perform the cross state coupler for λ 1 and the 3 db coupler for λ 2 and λ 3, the total length of the coupler has the following equations: (2p -1)π L WSC = = 2 k λ1 (2q -1)π 2 k, p and q=1,2,3,.. (4) λ2/λ3 where we have that q > 2p-1/2. The coupling coefficient ratio (CCR) for the WSC coupler is expressed as k 2(2 1) CR λ1 p C WSC = = (5) k 2q 1 λ2/λ3 For the 1.3/1.55 µm demultiplexer, the reasonable range of the coupler CCR is around The possible combination of p and q for the minimum length L is that p=3 and q=4 for the WBC coupler, and p = 1 and q = 2 for the WSC coupler. As we know from the next section, by adjusting the separation S of the directional coupler, the corresponding coupling coefficient ratios (i.e., for the WBC coupler and for the WSC coupler) are obtained. Proc. of SPIE Vol

5 4. SIMULATION RESULTS After understanding the operation principle of the proposed devices, we are ready to show their initial simulation results. By utilization of the hierarchy software platform of APSS [3, 4], we can divide the whole design procedure of the complicated device into four stages: material, waveguide (i.e., cross-section), device (i.e., top-view) and circuit, in which each stage focuses on own specific targets. Therefore, some typical effects such as material dispersion, polarizationindependence, and mixture of analytical and numerical solvers are easily considered. In order to illustrate the guidelines for the design of the C/D-WDM, We begin to present the simulation results from the silica material, in which the core and cladding are GeO 2 doped glass and pure silica glass, respectively. In this model, the material dispersion with threeterm Sellmeier formula is considered and the refractive index difference 0.6 % (or 6.3 % mol GeO 2 doping composition) is selected [2]. After finishing the design of the silica material, the typical buried silica channel waveguide with 6.0 µm wide and 6.0 µm high is built and analyzed. The calculated effective and equivalent indices of silica waveguide structure and are shown in Fig. 3. Fig. 3 shows that the silica waveguide is polarization independent (or difference between X and Y polarizations is indistinguishable) and effective indices for both X (i.e., quasi-te) and Y (i.e., quasi-tm) polarizations are quasi-linearly dependent with wavelength. It is worth to note that some other waveguide modal properties such as near/far field, overlap integral with fiber, group delay, and effective area are also obtained. (a) The effective indices for both polarization (b) The equivalent indices for both polarization Fig. 3. The effective and equivalent indices of waveguide structure After building the waveguide project, we can start to analyze the direction coupler with some analytical and numerical methods such as well-known coupled mode theory (CMP), beam propagation method (BPM), and finite difference time domain (FDTD) method. For example, the coupling coefficient ratio (CCR) of the directional coupler as a function of the separation S for both polarizations is shown in Fig. 4. Because the different confinement factors and coupling coefficients are different between TE and TM polarizations within wideband wavelength range, the proposed directional coupler is actually polarization dependent. However, as can been seen from Fig. 4, the waveguide separations for the exact coupling coefficient ratio for the WBC coupler are almost the same for both polarizations: µm (X pol.) and µm (Y pol.). So are the waveguide separations for the coupling coefficient ratio 0.667: µm (X pol.) and µm (Y pol.). Therefore, from the design point of view, through further optimization of the waveguide structure, we can design the proposed directional coupler as polarization independent. Here, according to the relationship between the waveguide separation S and CCR as shown in Fig. 4, we select the waveguide separation S = 8.05 µm for the WBC coupler and S = 8.55 µm for the WBC coupler, respectively. 702 Proc. of SPIE Vol. 5577

6 CCR ratio X Y Separation S (µm) Fig. 4. The relationship between DC separation S and the CCR From (2), the wideband (p = 3) and general (p = 1) 2x2 directional couplers are selected with the coupler lengths L = µm and L = µm, respectively. The performance of the WBC coupler for both polarizations is shown in Fig. 5a. Similarly from (4), the general 2x2 WSC coupler is selected with the coupler length L = µm. Its corresponding performance is shown in Fig. 5b Normal. power X_Bar X_Cross Y_Bar Y_Cross Normal. power X_Bar X_Cross Y_Bar Y_Cross Wavelength λ (µm) Wavelength λ (µm) (a) The WBC coupler (b) The WSC coupler Fig. 5. The simulation results of the wideband directional coupler Owing to recent progress in the index modulation of silica waveguides by UV-induced or surface etching [8, 11], planar Bragg gratings, which can be easily integrated with other functions discussed previously, are used as the wavelength selective elements to select narrow wavelength spacing or wide band WDM signals. Theoretically, according to the different channel spacing specifications, the 3dB bandwidth of the filter spectrum can be made wider or narrower depending on the length and index profiles of the gratings. To reduce the side-lobes of the grating spectrum, some kind Proc. of SPIE Vol

7 of apodization, such as the Hamming or raised cosine, may be used. For the sake of simplicity, here we select the UVinduced Bragg gratings with the uniform index modulation as the wide band filter. Though the proper design by using the couple mode theory [7] and the transfer matrix method [8] select the uniform index modulation with a length of 0.04 mm (about 100 periods) and a relative index difference of 3%, which has a 3dB bandwidth of 32.6 nm to realize the selection of the coarse WDM signals. The typical transmission and reflection characteristics of the planar Bragg gratings are shown in Fig. 6a. Similarly for the narrow band characteristic of the Bragg grating, we select the raised cosine index modulation of 5.0 mm with an induced index change of ~ [9, 10], which has a 3dB bandwidth of 0.8 nm to realize the selection of the dense WDM signals. The typical transmission and reflection characteristics of the planar Bragg gratings are shown in Fig. 6b Normal. power (db) Reflection Transmission Normal. power (db) Reflection Transmission Wavelength λ (nm) Wavelength λ (nm) (a) The wideband filter (b) The narrowband filter Fig. 6. The transmission and reflection of Bragg gratings After obtaining the performance parameters (i.e., the scattering matrix) of individual device, the overall performance of the proposed circuit can be effectively calculated by the Circuit module of APSS [3]. In this module, the scattering matrices of individual device and connector (i.e., S bend and straight line), which is used to connect the devices, are cascading together. By breaking the complicated circuit into devices and connectors, which can be simulated by individual proven modeling methods, the performance of the circuit is obtained easily. Fig. 7 shows the characteristics of the first proposed C/D-WDM demultiplexer, where only X polarization is considered and the length difference L = µm with 200 GHz (i.e., λ = 1.6 nm) wavelength spacing is used. It can be seen from Fig. 7 that the proposed C/D-WDM demultiplexer works well and acts as the wavelength interleaver for dense WDM signals. Similarly, the overall performance of the second proposed C/D-WDM demultiplexer is obtained by cascading the scattering matrices of the WSC coupler and Bragg grating with those of connectors. Fig. 8 shows the characteristics of the second proposed W/D-WDM demultiplexer, where only X polarization is considered. As expected, the proposed C/D-WDM demultiplexer works well and acts as the wavelength add-drop device for dense WDM signals. 704 Proc. of SPIE Vol. 5577

8 1.0 Normal. power Port 1 Port 3 Port Wavelength λ (nm) Fig. 7. The characteristics of the first proposed C/D-WDM DeMUX 1.0 Normal. power Port 1 Port 3 Port Wavelength λ (µm) Fig. 8. The characteristics of the second proposed C/D-WDM DeMUX 5. DISCUSSION As the guideline in the development of future WDM devices, only operation principles of proposed devices are demonstrated through a simple type of coupler: directional coupler. In order to optimize the performance of proposed device, some other kinds of couplers should be considered. For the sake of simplicity, we neglect some effects involved in the integrated circuits, which, however, may make themselves difficult to be developed as a practical device. For example, in Bragg gratings, the coupling between the guided and cladding modes will cause a series of loss band on the Proc. of SPIE Vol

9 short wavelength side of the main Bragg band. This loss can be quite pronounced in strong gratings. We should avoid this loss band to stay in the operation range of wavelength. Based on the hierarchy platform of APSS, some related design issues such as polarization dependence and material dispersion are easily considered. However, when we design the practical devices, some extra effects related to the fabrication process, such as stress, thermal fluctuation, and fabrication tolerance, should be considered. For example, in order to eliminate the polarization dependence of Bragg grating-based circuits, we should consider the UV-induced birefringence to compensate the natural waveguide birefringence of the integrated circuits [10]. Therefore, more detailed optimizations of the performance parameters of the proposed circuit, such as crosstalk, are needed. 6. CONCLUSION We proposed two methods to multiplex/demultiplex the coarse/dense WDM channels simultaneously by combining the symmetrical/asymmetrical grating-assisted MZIs with some specific wavelength selective couplers. In first design, the C/D-WDM multiplexer/demultiplexer utilizes a grating-assisted asymmetrical MZI with one wideband 3dB WBC coupler and one 3dB coupler. In the second design, the C/D-WDM multiplexer/demultiplexer utilizes a grating-assisted symmetrical MZI with two WSC couplers. The operation principles of the proposed C/D-WDM Multiplexers are demonstrated. Finally, with the help of APSS, the simulation results of those C/D-WDM multiplexers and related components such as the couplers and planar gratings are obtained. ACKNOWLEDGEMENTS Dr. Linping Shen thanks the Natural Sciences and Engineering Research Council of Canada (NSERC) to support his work as an Industrial Research Fellow (IRF). REFERENCES 1. D. Marcuse, Theory of dielectric optical waveguides. New York: Academic press, K. Okamoto, Fundamentals of optical waveguides, New York: Academic Press, Apollo Inc., Apollo photonic solution suite (APSS), W.-P. Huang, CAD tools speed complex component design, Laser Focus World, no.11, C. M. Ragdale, T. J. Reid, D. C. J. Reid, A. C. Carter, and P. J. Wiliams, Narrowband GaInAsP/InP waveguide grating-folded directional coupler multiplexer /demultiplexer, Electron. Lett., vol. 24, No.3, pp , L. B. Soldano and C. M. Pennings, Optical multimode interference devices based on self-imaging: principles and applications, J. Lightwave Technol., vol.13, no.4, pp , H. A. Haus and W.-P Huang, Coupled mode theory, Proceedings of IEEE, vol. 79, no. 10, pp , J. Hong, W.-P. Huang, and T. Makino, On the transfer matrix method for distributed feedback waveguide devices, J. Lightwave Technol., vol.10, no.12, pp , J.-M. Jouanno, D. Zauner, and M. Kristensen, Low crosstalk of planar optical add-drop multiplexer fabricated with UV-induced gratings, Electron. Lett., vol.33, no.25, pp , J. Albert, F. Bilodeau, D. C. Johnson, K. O. hill, S. J. Mihailov, D. Stryckman, T. Kitagawan and Y. Hibino, Polarisation-independent strong Bragg gratings in planar lightwave circuits, Electron. Lett., vol.34, no.5, pp , G. E. Kohnke, C. H. Henry, E. J. Laskowski, M. A. Cappuzzo, T. A. Strasser, and A. E. White, Silica based Mach- Zehnder add-drop filter fabricated with UV induced gratings, Electron. Lett., vol.32, no.17, pp , Proc. of SPIE Vol. 5577

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