A numerical mode matching method for wave scattering in a layered medium with a stratified inhomogeneity

TL;DR

This paper introduces an advanced numerical mode matching method for wave scattering in layered media, effectively handling complex incident waves and improving computational efficiency with theoretical convergence guarantees.

Contribution

A novel NMM approach with Robin-type boundary conditions and a fast reference solution computation method for cylindrical waves, enhancing accuracy and efficiency in layered media wave scattering.

Findings

The new NMM method achieves exponential convergence.

It effectively handles complex incident waves and total internal reflection.

Numerical experiments validate improved performance and accuracy.

Abstract

Numerical mode matching (NMM) methods are widely used for analyzing wave propagation and scattering in structures that are piece-wise uniform along one spatial direction. For open structures that are unbounded in transverse directions (perpendicular to the uniform direction), the NMM methods use the perfectly matched layer (PML) technique to truncate the transverse variables. When incident waves are specified in homogeneous media surrounding the main structure, the total field is not always outgoing, and the NMM methods rely on reference solutions for each uniform segment. Existing NMM methods have difficulty handing gracing incident waves and special incident waves related to the onset of total internal reflection, and are not very efficient at computing reference solutions for non-plane incident waves. In this paper, a new NMM method is developed to overcome these limitations. A Robin-type boundary condition is proposed to ensure that non-propagating and non-decaying wave field components are not reflected by truncated PMLs. Exponential convergence of the PML solutions based on the hybrid Dirichlet-Robin boundary condition is established theoretically. A fast method is developed for computing reference solutions for cylindrical incident waves. The new NMM is implemented for two-dimensional structures and polarized electromagnetic waves. Numerical experiments are carried out to validate the new NMM method and to demonstrate its performance.