Analysis of optical waveguide devices using the FD‐TD method based on the principles of multidimensional wave digital filters

Abstract

We present a finite difference time domain (FD‐TD) method with the perfectly matched layers (PMLs) absorbing boundary condition based on the multidimensional wave digital filters (MD‐WDFs) for discrete‐time modeling of Maxwell's equations and show its effectiveness. First we propose modified forms of Maxwell's equations in the PMLs and their MD‐WDFs representation by using the current‐controlled voltage sources. Second we evaluate the numerical errors about phase velocity in the plane wave propagation problem by examining the numerical dispersion relation and show an advantage of the FD‐TD method based on MD‐WDFs over the Yee algorithm. As a numerical example, we analyze two typical optical waveguide devices and design a low‐insertion‐loss polarizer composed of a multiple‐quantum‐well waveguide and a right‐angle bend waveguide using a photonic crystal whose size is on the order of the wavelength of light.