Finite-difference-based mode-matching method for 3-D waveguide structures under semivectorial approximation

A finite-difference-based mode-matching method (FD-MMM) is developed and demonstrated for three-dimensional (3-D) optical waveguide structures with arbitrary index profiles and multiple scattering interfaces along the waveguide axis. The computation domain is enclosed by a perfectly conducting box coated by a perfectly matched layer (PML). Semivectorial approximation is employed to simplify the formulations and calculations. Tradeoff and guidelines for choice of the PML parameters in the mode-matching analysis are discussed by comparison with known benchmark solutions for a two-dimensional (2-D) structure. The method is subsequently applied to and validated for 3-D structures in which both single and multiple scattering interfaces are simulated.