Optimum Access Waveguide Width for 1xN Multimode. Interference Couplers on Silicon Nanomembrane

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1 Optimum Access Waveguide Width for 1xN Multimode Interference Couplers on Silicon Nanomembrane Amir Hosseini 1,*, Harish Subbaraman 2, David Kwong 1, Yang Zhang 1, and Ray T. Chen 1,* 1 Microelectronic Research Center, Department of Electrical and Computer Engineering, University of Texas, Burnet Rd. Austin, TX USA 2 Omega Optics, Inc., Sausalito Dr., Austin, TX USA * Corresponding authors: ahoss@mail.utexas.edu; raychen@uts.cc.utexas.edu An analytical formula for the optimum width of the access waveguides of 1xN multimode interference (MMI) couplers is derived. Eigenmode decomposition based simulations show that the optimum width relation corresponds to the points of diminishing returns in both insertion loss and output uniformity versus access waveguides width. We fabricate and characterize 1x12 MMIs on a nanomembrane of silicon on insulator (SOI) substrate. The experimental investigations demonstrate that the analytical results can be reliably used as a design rule for MMI couplers with large number of outputs Optical Society of America OCIS codes: , Introduction Multimode interference (MMI) devices based on self-imaging are key components in photonic integrated circuits (PICs). 1xN MMI-based beam splitters have been theoretically and experimentally investigated [1-6]. The resolution and contrast of the images formed in the 1

2 multimode waveguide determine the uniformity and insertion loss of MMI splitter devices [1]. By analyzing the phase errors due to deviations of the higher order mode dispersion relations from those required for ideal self-imaging, one can show that MMI couplers with large number of outputs (N) normally result in poorer output uniformity and higher insertion loss [2]. There have been two major techniques proposed to enhance MMI performance: optimizing the index contrast [2,3] and increasing the input/output access waveguide width [4]. Other approaches, such as using genetic algorithm [5] and tuning the input taper angle [6] were also investigated. Tuning the index contrast may not be an option based on the choice of the substrate and the geometry of the splitter. Also, use of genetic algorithm or input taper angle tuning does not provide insight into the nature of the poor MMI performance at large N values. Increasing the input/output access waveguide width to enhance the self-imaging quality proposed in [4] is a practical approach especially for cases such as photonic integrated circuits, where the index tuning is a challenge. In this study, we investigate the effect of the input/output access waveguide width on the MMI performance and derive an analytical relation for the optimum width for minimizing the insertion loss and enhancing the output uniformity. Experimental results for a 1x12 MMI based on a silicon nanomembrane confirm the analytical conclusions. Fig. 1. A schematic of a 1xN MMI beam splitter. Inset is a cross section schematic of the SOI waveguiding structure. n Si =3.47, n SiO2 =1.45, n SiO2(PECVD) =

3 2. Optimum channel width derivation The theory of self-imaging in multimode optical waveguides has been the subject of several studies [1,7,8,9]. Figure 1 shows a schematic of a 1xN MMI splitter. The multimode waveguide section consists of a W MMI wide and L MMI long core with refractive index n c. In the case of channel waveguides, an equivalent 2D representation can be made by techniques such as the effective index method or the spectral index method [7]. Assume that n eff is the effective index of the fundamental mode of an infinite slab waveguide with same thickness and claddings. For each mode p (0 p M) of a MMI that can support (M+1) modes, the dispersion relation is given as [1] β + κ 2 p 2 yp 2πn = λ0 eff 2, (1) where, β p is the propagation constant of the p th mode, λ 0 is the free-space wavelength. Throughout this letter, λ 0 =1.55μm. κ yp is the lateral wavenumber of the p th mode given as κ yp =(p+1)π/w e, where W e is the effective width, which includes the penetration depth due to the Goose-Hahnchen shift [7]. In the MMI theory, β p is approximated from Eq. (1) as [1] β p p( p 2) β0, (2) 3L π where, L π =π/(β 0 -β 1 ) 4n eff W 2 e /3λ 0. In the case of symmetric excitations, such as a 1xN MMI coupler excited by the fundamental mode of the input waveguide, using the approximation in Eq. (2), one can show that the required length for such a coupler is L MMI =3IL π /4N, where I is an integer. However, MMIs with length derived using the approximation in Eq. (2) suffer from high insertion loss and poor output uniformity as discussed in [2]. The approximation in Eq. (2) becomes increasingly inaccurate for larger mode numbers (p), which results in larger accumulated modal phase errors in the multimode section at the output with regard to the values 3

4 required for ideal self-imaging. It was shown before that increasing the input/output waveguide width (W w ) improves the image quality by reducing the accumulated modal phase errors at the output of the multimode section [4]. However, the maximum W w is limited by the geometry as well as the coupling between the output waveguides. Also larger W w results in longer tapers when the output channels are adiabatically tapered down for single mode operation. Our goal is to find the minimum W w for which the MMI performance is still acceptable. The error in the calculated propagation constant when using Eq. (2) can be estimated by the third term in the Taylor Expansion of β p given by Eq. (1) as Δβ p 2 (κ yp λ 0 /4πn eff ) 4. After propagating along the MMI, the resulting modal phase errors at the output are given as 2 4 πλ0 ( p + 1) Δϕ p = Δβ plmmi =. (3) Nn W For a high quality image at the output of MMI, we restrict the maximum Δφ p to π/2, because if Δφ p is more than π/2, the sign of mode field p is changed by the phase error. Let q be the maximum mode number (p) for which Δφ p <π/2. We choose W w so that the highest order mode excited in the multimode region can satisfy this restriction. To do so, we pick W w to be equal to the lateral wavelength (2π/κ yq ) of the highest allowed mode given by Δφ p <π/2. This also guarantees negligible excitation of all higher order modes since several periods of these modes fall within the input excitation field and the resulting overlap integrals are thus small. By equating W w,opt =2π/κ yq we get eff e W w, opt 1 λ0we =. (4) 4 2N n eff When W w W w,opt, the Δφ p <π/2 condition holds for all the modes in the multimode section that receive significant excitation. Therefore, we expect that W w,opt corresponds to the point of 4

5 diminishing returns (or the knee point) in 1xN MMIs performance in terms of insertion loss and output uniformity as functions of W w. Fig. 2. (a) and (b) variations of the insertion loss and output uniformity, respectively, versus MMI length. The MMI is 1x12 (N=12), W MMI =60μm, h=230nm and different W w values. (c) and (d) variations of the insertion loss and output uniformity, respectively, versus W w for 1x2, 1x3, 1x6 and 1x12 MMIs. Due to symmetry, uniformity is 0 db for all W w values in the case of the 1x2 MMI. W w,opt values for each MMI are indicated by crosses ( ). 3. Simulations and discussions In order to investigate the effect of W w on the image quality we used the 3D full vectorial eigenmode expansion simulator in the FIMMPROP TM module from Photon Design. We calculated MMI outputs from the transfer matrix coefficients of the fundamental mode in the output channels. We assumed silicon nanomembrane on oxide as shown in Figure 1 inset, where the thickness of the silicon slab is h=230nm (n eff =2.85). For given W MMI and W w, one can tune L MMI to achieve better uniformity [5]. In order to demonstrate that tuning the MMI length to achieve high output uniformity and high transmission is an inefficient method, let us consider a 1x12 MMI with W MMI =60μm. For this MMI, the 5

6 theoretical predictions give L MMI =553.4μm and W w,opt =2.58μm. Figures 2(a) and (b) show the insertion loss and output uniformity, respectively, for varying L MMI and for W w =0.5μm, W w =1.25μm, W w =2.6μm and W w =3.5μm. Uniformity is calculated as 10log(P min /P max ), where P max and P min are the maximum and minimum power (norm of the fundamental mode) of the MMI output channels, respectively. In the case of W w =1.25μm and W w =0.5μm, highest uniformity does not occur at the lowest insertion loss, and the resulting optimized MMI length is different from the theoretical predictions as shown in Figure 2. For W w =2.6μm and W w =3.5μm, the optimum lengths are closer to L MMI =553.4μm at which the total insertion loss is also much smaller than that for W w =1.25μm and W w =0.5μm. Also, the MMI performance is almost the same for W w =2.6μm and W w =3.5μm. In order to verify the W w,opt values predicted by Eq. (4), we simulated MMIs with different N values. Figure 2(c) and (d) show the insertion loss and the output uniformity, respectively, versus the W w for 1x2, 1x3, 1x6 and 1x12 MMIs. The MMIs dimensions are shown in the figure, and the MMIs lengths are 4n eff W 2 e /3λ 0 in all cases. Using Eq. (4), the corresponding W w,opt values are 1.16, 1.82μm, 2.17μm and 2.58μm for the 1x2, 1x3, 1x6 and 1x12 MMIs, respectively. One can see that these numbers correspond to the points of diminishing returns in both the total output power and uniformity versus W w. Also note that when the access waveguide width (W w ) is less than the W w,opt value, larger MMIs have worse permanence than smaller MMIs. Thus, it is more crucial to apply W w W w,opt as a design rule for larger MMIs. 4. Experimental Results We fabricated 1x12 MMIs (W MMI =60μm, L MMI =553.4μm) with W w =0.50μm, W w =1.25μm, W w =2.60μm and W w =3.50μm [See Figure 3]. The MMIs are fabricated on a silicon-on-insulator 6

7 (SOI) substrate with 3µm buried oxide layer (BOX). The MMIs are patterned using electron beam lithography, followed by reactive ion etching (RIE), lift-off pattern inversion, and plasmaenhanced chemical vapor deposition (PECVD) of a 1µm thick silicon dioxide film for the top cladding. The details of the fabrication process will be reported separately. The output waveguides are fanned out for 30μm center-to-center separation. Fig. 3. (a) SEM picture of 1x12 MMIs with W MMI =60μm, L MMI =553.4μm and different W w. Transverse-electric (TE) field from an external cavity tunable laser source is coupled into the input waveguides through a tapered and lensed polarizations maintaining fiber (PMF). A CCD camera captured top-down images of the scattered light at the cleaved output waveguide facets as shown in Fig. 4(a-b). For the same input power we observed significantly brighter outputs for the W w =2.60μm and W w =3.50μm MMIs compared to W w =0.50μm and W w =1.25μm MMIs. To calculate the output uniformity, a single-mode output fiber is scanned at output side across each output waveguide cross-section for maximum output coupling. In order to cancel out the fabrication errors, we use the average of output fiber measurement results from two sets of the four MMIs. Figures 4(c) and (d) compare the measured insertion loss and output uniformity values with those from the simulation results shown in Figures 2(c) and (d). The results from 7

8 both simulation and experimental data indicate that W w =2.60μm, which is predicted from Eq. (4), is in fact the point of diminishing returns for the MMI performance as a function of the width of the access waveguides. 5. Conclusion An analytical formula for optimum 1xN multimode input/output access waveguide width is derived for improved performance based on the insertion loss and the output uniformity. Eigenmode decomposition based simulations and experimental investigations of SOI based 1x12 MMIs confirm the analytical results. The results can be used as a design rule for high performance MMI based beam splitters. Fig. 4. Top-down IR-images of MMI outputs for (a) W w =0.50μm, (b) W w =2.60μm. (c) and (d) insertion loss and uniformity measurement results for 1x12 MMIs with W MMI =60μm, L MMI =553.4μm and different W w values, respectively. 6. Acknowledgement This research is supported by the multi-disciplinary university research initiative (MURI) program through the AFOSR, contract # FA

9 References: [1] R. Ulrich and T. Kamiya, Resolution of self-images in planar optical waveguides, J. Opt. Soc. Am. 68, (1978). [2] J.Z. Huang, R. Scarmozzino, and R.M. Osgood Jr., A new design approach to large input/output number multimode interference couplers and its application to low-crosstalk WDM routers, IEEE Photon. Technol. Lett. 10(9), (1998). [3] R. Yin, J. Yang, X. Jiang, J. Li, and M. Wang, Improved approach to low-loss and highuniformity MMI devices, Opt. Commun. 181, (2000). [4] Y. Shi, D. Dai, and S. He, Improved performance of a silicon-on-insulator-based multimode interference coupler by using taper structures, Optics Communications 253, (2005). [5] Q. Wang, J. Lu, S. He, Optimal design of a multimode interference coupler using a genetic algorithm, Opt. Commun. 209, (2002). [6] R. M. Lorenzo, C. Llorenle, E. J. Abril, and M. López, Improved self-imaging characteristics in 1xN multimode couplers, Proc. Inst. Elect. Eng. Optoelectron. 145(1), (1998). [7] L. Soldano and E. Pennings, Optical multi-mode interference devices based on selfimaging: principles and applications, J. Lightwve Technol. 13(4), , (1995). [8] M. Rajarajan, B. Rahman, T. Wongcharoen, and K. Grattan, Accurate analysis of MMI devices with two-dimensional confinement, J. Lightwave Technol., 14(9), (1996). 9

10 [9] A. Hosseini, D. N. Kwong, C.-Y. Lin, B. S. Lee, and R. T. Chen, Output Formulation for Symmetrically-Excited one-to-n Multimode Interference Coupler, IEEE J. of Sel. Topics in Quant. Elect. 6(1), (2010). 10