Analysis of time-domain Maxwell's equations in biperiodic structures

Abstract

This paper is devoted to the mathematical analysis of the diffraction of an electromagnetic plane wave by a biperiodic structure. The wave propagation is governed by the time-domain Maxwell equations in three dimensions. The method of a compressed coordinate transformation is proposed to reduce equivalently the diffraction problem into an initial-boundary value problem formulated in a bounded domain over a finite time interval. The reduced problem is shown to have a unique weak solution by using the constructive Galerkin method. The stability and a priori estimates with explicit time dependence are established for the weak solution.