Design and simulation of multimode interference based demultiplexers aided by computer-generated planar holograms

A 1.31/1.55 μm multimode interference based wavelength demultiplexer aided by computer-generated planar holograms is proposed. The device length is not limited to the common multiples of the beat lengths for the two wavelengths. The demultiplexer length is chosen as the first selfimaging length for 1.55 μm input, and a computer-generated holographic pattern is used to image the 1.31 μm input to the cross output port. The design and optimization of the holographic pattern is presented. The device performance is investigated using the beam propagation method. ©2010 Optical Society of America OCIS codes: (130.3120) Integrated optics devices; (230.7380) Waveguides, channeled; (230.7408) Wavelength filtering devices; (090.1760) Computer holography. References and links 1. G. Keiser, Optical Fiber Communications (McGraw-Hill, MA, 2000). 2. H. Kawata, T. Ogawa, N. Yoshimoto, and T. Sugie, “Multichannel video and IP signal multiplexing system using CWDM technology,” J. Lightwave Technol. 22(6), 1454–1462 (2004). 3. L. B. Soldano, and E. C. M. Pennings, “Optical multi-mode interference devices based on self-imaging: principles and applications,” J. Lightwave Technol. 13(4), 615–627 (1995). 4. 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 Technol. 12(6), 1004–1009 (1994). 5. K.-C. Lin, and W.-Y. Lee, “Guided-wave 1.3/1.55 [micro sign]m wavelength division multiplexer based on multimode interference,” Electron. Lett. 32(14), 1259–1261 (1996). 6. B. Li, G. Li, E. Liu, Z. Jiang, J. Qin, and X. Wang, “Low-loss 1×2 multimode interference wavelength demultiplexer in silicon-germanium alloy,” IEEE Photon. Technol. Lett. 11(5), 575–577 (1999). 7. M. R. Paiam, C. F. Janz, R. I. MacDonald, and J. N. Broughton, “Compact planar 980/1550-nm wavelength multi/demultiplexer based on multimode interference,” IEEE Photon. Technol. Lett. 7(10), 1180–1182 (1995). 8. T. W. Mossberg, “Planar holographic optical processing devices,” Opt. Lett. 26(7), 414–416 (2001). 9. Y. Sakamaki, T. Saida, T. Hashimoto, and H. Takahashi, “New optical waveguide design based on wavefront matching method,” J. Lightwave Technol. 25(11), 3511–3518 (2007). 10. Y. Tsuji, and K. Hirayama, “Design of optical circuit devices using topology optimization method with functionexpansion-based refractive index distribution,” IEEE Photon. Technol. Lett. 20(12), 982–984 (2008). 11. S.-Y. Tseng, Y. Kim, C. J. K. Richardson, and J. Goldhar, “Implementation of discrete unitary transformations by multimode waveguide holograms,” Appl. Opt. 45(20), 4864–4872 (2006). 12. S.-Y. Tseng, C. Fuentes-Hernandez, D. Owens, and B. Kippelen, “Variable splitting ratio 2 x 2 MMI couplers using multimode waveguide holograms,” Opt. Express 15(14), 9015–9021 (2007), http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-15-14-9015. 13. S.-Y. Tseng, S. K. Choi, and B. Kippelen, “Variable-ratio power splitters using computer-generated planar holograms on multimode interference couplers,” Opt. Lett. 34(4), 512–514 (2009). 14. S.-Y. Tseng, “Diffraction engineering of multimode waveguides using computer-generated planar holograms,” Opt. Express 17(24), 21465–21471 (2009), http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-17-24-21465. 15. S.-Y. Tseng, and M.-C. Wu, “Adiabatic mode conversion in multimode waveguides using computer-generated planar holograms,” submitted (2010). 16. The Dow Chemical Company, “CYCLOTENE Advanced Electronics Resins,” www.dow.com/cyclotene 17. R. W. Boyd, Nonlinear Optics (Academic, CA, 1992). #127003 $15.00 USD Received 15 Apr 2010; revised 7 May 2010; accepted 11 May 2010; published 12 May 2010 (C) 2010 OSA 24 May 2010 / Vol. 18, No. 11 / OPTICS EXPRESS 11270


Introduction
Wavelength division multiplexing (WDM) is a key technology in optical fiber communication systems [1].In WDM transmission systems, wavelength multiplexers/demultiplexers play essential roles in combining/separating information carried by different wavelengths.Of particular interests to optical telecommunications are the 1.31 µm and 1.55 µm windows.In fiber-to-the-home (FTTH) services, these two windows are used to carry data/voice and video, respectively [2].Several integrated optical devices have been proposed or demonstrated for the demultiplexing of 1.31 and 1.55 µm wavelengths.Devices based on the application of multimode interference (MMI) phenomenon [3] are particularly attractive because of their large fabrication tolerance, low loss, and compact size [4].
In the past, several groups [5,6] have demonstrated wavelength demultiplexers for the 1.31 and 1.55 µm based on MMI.The operation of these MMI based demultiplexers relies on the self-imaging (SI) effect in multimode waveguides [3].The SI length is wavelength dependent, and two wavelengths can be separated if the device length is at the direct image length for one wavelength while at the mirror image length for the other.As a result, the device length needs to be a common multiple of the beat lengths for the two wavelengths [7], which could result in a long device length.To achieve a shorter device length, careful selection of device width and length through numerical simulations is required [6].For a particular material platform, the available device geometry in terms of width and lengths is thus restricted.A MMI based multiplexer/demultiplexer with fewer restrictions on its geometry would be desirable in terms of design freedom.
Recently, planar optical waveguide devices with computer calculated refractive index distributions have received a lot of attention [8][9][10].The ability to design and fabricate these index perturbation on optical waveguides has opened up new possibilities in designing functional devices that are no longer limited by the traditional device geometries.In the past, we have proposed a class of devices using computer-generated planar holograms (CGPHs) on multimode waveguides to perform various functionalities [11][12][13][14][15].These CGPHs are multiplexed long-period gratings that couple and transform the guided modes of the multimode waveguides.In this letter, we propose a 1.31/1.55µm wavelength demultiplexer using CGPH on MMI devices.The design and optimization procedure of the CGPH is presented, and the device performance is investigated with numerical simulations.

Principle of operation
Figure 1 shows the operation schematic of the CGPH aided MMI wavelength demultiplexer.Two wavelengths, 1.31 and 1.55 µm, coupled into the input port are demultiplexed to the cross and bar output ports.For a conventional MMI, the length L of the multimode section needs to be a common multiple of the beat lengths for these two wavelengths such that the MMI is in cross and bar states at 1.31 and 1.55 µm, respectively.The beat length L π,λ is related to the waveguide effective width W e and the operating wavelength λ as 2 ,

4
, 3 where n e is the core effective index.As shown in ref [5], specific ratios of the beat lengths can be used to reduce L.  For the CGPH aided MMI wavelength demultiplexer, we choose an arbitrary waveguide width W, and the waveguide length L is chosen as the first self-imaging length for 1.55 µm as shown by beam propagation method (BPM) simulation in Fig. 2(a).For the BPM simulations, we employ a polymer ridge waveguide structure described in the next section.Since W is chosen arbitrarily, L does not correspond to a mirror image length at 1.31 µm [Fig.2(b)].We show in the next section that, with a properly designed CGPH on the MMI, the 1.31 µm input can be imaged to the cross output port.As will be explained in the next section, the wavelengths 1.31 and 1.55 µm are sufficiently separated such that the CGPH designed at 1.31 µm has little or no effect at 1.55 µm, as a result, the 1.55 µm wavelength still images to the bar output port.The two wavelengths can thus be demultiplexed.Next, we use a specific example to explain the design and optimization of the CGPH.

CGPH design
We choose a polymer ridge waveguide structure for the BPM simulations.The design parameters are chosen as follows: 3 µm thick SiO 2 on a Si wafer is used for the bottom cladding layer, the core consists of a 2.4 µm layer of Cyclotene TM (BCB), the upper cladding is air, the width W of the multimode section is 18 µm, the width of the access waveguide is 3 µm, and the centers of access waveguides are placed at ± 7.5 µm from the center of the multimode section.The refractive indices of BCB at 1.31/1.55µm can be found in [16].Subsequent CGPH design and BPM simulations are performed on the 2D structure obtained from the 3D structure using the effective index method.
For the TE polarization at 1.55 µm, we use the BPM simulation to find the first selfimaging length and set it as the length of the multimode section length L = 2720 µm [Fig.2(a)].Next, we calculate the CGPH that images the 1.31 µm input to the cross output port.The 1.31 µm optical field E 1 (z) do not image at L [Fig.2(b)], and we wish to transform E 1 (z) to an optical field E 2 (z) which images to the cross output port.E 2 (z) is obtained by taking the conjugate of the mirrored image of E 1 (L) and using it as the input to the multimode waveguide.Because E 2 (0) is the phase conjugate replica of the mirrored image of E 1 (L), we expect E 2 (L) to form an image at the cross output port.This is verified by the BPM simulation shown in Fig. 3. Here, we explain the design of a CGPH that diffract the E 1 input field to the E 2 field, which images to the cross output port.In the MMI without the CGPH, the fields E 1 and E 2 obey the wave equation where ε = ε 0 n 0 2 , and n 0 is the refractive index profile of the unperturbed waveguide.Using modal expansion, E 1 and E 2 can be written using the superposition of the unperturbed waveguide modes as ( ) , where N is the number of modes, c's are the modal amplitudes, φ's represent the modal profiles, and β's are the propagation constants.The CGPH is generated by calculating the interference pattern of E 1 (z) [Fig.2(b)] and E 2 (z) (Fig. 3) as which is shown in Fig. 4. The interference pattern in Fig. 4 is then normalized to a maximum index perturbation ∆n and used as a perturbation to the effective index of the multimode waveguide.The CGPH can thus be written using Eq. ( 3) and Eq. ( 4) as , which can be viewed as multiplexed long-period gratings coupling modes m and n.Writing the total field in the CGPH aided MMI as E 1 + E 2 and substituting into the wave Eq. ( 2) along with the index perturbation described by Eq. ( 5), we can obtain the following coupled equations by collecting the synchronous terms [17] where the coupling coefficient κ is proportional to ∆n.By solving Eq. ( 6), we obtain the diffraction efficiency of   4).The interference pattern is normalized to a maximum index perturbation ∆n and used as a perturbation to the multimode waveguide.
To find the optimal index perturbation, we monitor the cross and bar port outputs as a function of ∆n using 1.31 µm as the input.As shown in Fig. 5, the cross port output varies in a sinusoidal manner with ∆n as indicated by Eq. ( 7).The result is not exactly described by Eq. ( 7) since we monitor the power at the cross output port rather than |E 2 (L)| 2 .From Fig. 5, we find that the optimal ∆n to image the 1.31 µm input to the cross output port is 1.4 × 10 −3 , and the corresponding field intensity simulation is shown in Fig. 6(a).With the properly designed CGPH, the 1.31 µm input is imaged to the cross output port.As shown in Eq. ( 5), the CGPH has wavelength selectivity since the grating periods designed for 1.31 µm would not satisfy the phase matching conditions at 1.55 µm.Figure 6(b) shows the field intensity simulation of the same CGPH aided MMI with 1.55 µm input.The CGPH has little effect on its selfimaging property as expected.The CGPH loaded MMI can thus be used to demultiplex 1.31 and 1.55 µm.In the subsequent analysis, a ∆n of 1.4 × 10 −3 is used to evaluate the performance of the proposed wavelength demultiplexer.Across the investigated spectral range, the MMI basically retains its spectral response except for the peak at 1.31 µm induced by the CGPH.Using the conventional approach, we have estimated that the MMI demultiplexer length needs to be three times the current device length of 2720 µm in order to be at a mirror image length for 1.31 µm.The proposed approach offers more flexibility in device geometry without sacrificing the compactness of the device.Further reduction of the device length to the first mirror image length for 1.55 µm is feasible provided that the amount of index modulation could be increased to obtain maximum diffraction efficiency in Eq. ( 7).In conclusion, we have proposed a MMI wavelength demultiplexer aided by the CGPH.Unlike conventional MMI demultiplexers, the device width and length are not limited to specific values as determined by the self-imaging properties.Using a design example, the design procedure for the CGPH is illustrated.BPM simulations are used to design the demultiplexer and analyze its performance.The same design principle can be applied to demultiplexers for different wavelengths.

Fig. 3 .
Fig. 3. BPM simulations showing that the phase conjugate of the mirrored image of E1(L) images to the cross port at 1.31 µm.

Fig. 4 .
Fig. 4. The calculated CGPH as described by Eq. (4).The interference pattern is normalized to a maximum index perturbation ∆n and used as a perturbation to the multimode waveguide.

Fig. 5 .
Fig. 5.The variation of bar/cross ports output at 1.31 µm as a function of maximum index perturbation ∆n.

Fig. 7 .
Fig. 7. Wavelength dependence of the cross and bar ports contrast defined by −10log (Pcross / Pbar) with and without the CGPH.