Self-focusing Appearance in Ultra-compact 3x3 Multimode Interference Coupler Based on Silicon on Insulator

The study of multimode interference (MMI) couplers in silicon waveguides is limited by the high index contrast, especially when operated in nonlinear regime. In low index contrast, the common method is beam propagation method (BPM) that is based on several algorithms which propose a simple numerical method, but, in nonlinear high index contrast, the modal propagation analysis based on finite difference method (FDM) is a rigorous method, and high index contrast is a super benefit to confine the wave in waveguide in the maximum rate to appearance the self-focusing in highly ultra-compact size. In this paper, we investigate the nonlinear effect in high index contrast structure of silicon on insulator (SIO) 3x3 multimode coupler. Moreover, by simulation of the wave propagation while the input intensities are increasing simultaneously, the appearance of self-focusing are demonstrated. The results show capability of nonlinear modal propagation by FDM numerical solution. Wave propagation in multimode region accomplished with the output electric field indicate the good efficiency for the considered purposes.