Semi-vectorial analysis of a compact wavelength demultiplexer based on the tapered multimode interference coupler

Based on a parabolically tapered multimode interference (MMI) coupler with a deep-etched SiO₂/SiON rib waveguide, a compact wavelength demultiplexer operating at 1.30 and 1.55\mum wavelengths is proposed and analysed by using three-dimensional semi-vectorial finite-difference beam propagation method (3D-SV-FD-BPM). The results show that a MMI section of 330.0\mum in length, which is only 76% length of a straight MMI coupler, is achieved with the contrasts of 42.3 and 39.2dB in quasi-TE mode, and 38.4 and 37.8dB in quasi-TM mode at wavelengths 1.30 and 1.55\mum, respectively, and the insertion losses below 0.2dB at both wavelengths and in both polarization states. The alternating direction implicit algorithm with the Crank--Nicholson scheme is applied to the discretization of the 3D-SV-FD-BPM formulation along the longitudinal direction. Moreover, a modified FD scheme is constructed to approximate the resulting equations along the transverse directions, in which the discontinuities of the derivatives of magnetic field components H_y and H_x along the vertical and horizontal interfaces, respectively, are involved.