A RIGOROUS NUMERICAL ANALYSIS OF THE TRANSFORMED FIELD EXPANSION METHOD FOR DIFFRACTION BY PERIODIC, LAYERED STRUCTURES

Abstract

Boundary perturbation methods have received considerable attention in recent years due to their ability to simulate solutions of differential equations of applied interest in a stable, robust, and highly accurate fashion. In this contribution we study the rigorous numerical analysis of a recently proposed high-order perturbation of surfaces method for scattering of electromagnetic waves by a doubly layered, periodic medium in transverse electric polarization. The algorithm in question is a transformed field expansion method which is discretized with a Fourier-Legendre-Galerkin, Taylor series approach. We prove not only results on existence and uniqueness of solutions but also theorems indicating that solutions of our scheme converge to these solutions with high-order spectral accuracy.