Analysis of Time-Domain Scattering by Periodic Structures

TL;DR

This paper provides a rigorous mathematical analysis of electromagnetic scattering in the time domain by periodic diffraction gratings, establishing well-posedness, stability, and energy estimates with minimal data regularity.

Contribution

It introduces an exact transparent boundary condition to reduce the scattering problem and proves well-posedness and stability for the resulting initial-boundary value problem.

Findings

Proves well-posedness of the time-domain scattering problem.

Establishes stability and energy estimates with minimal data regularity.

Provides explicit dependence of solutions on time.

Abstract

This paper is devoted to the mathematical analysis of a time-domain electromagnetic scattering by periodic structures which are known as diffraction gratings. The scattering problem is reduced equivalently into an initial-boundary value problem in a bounded domain by using an exact transparent boundary condition. The well-posedness and stability of the solution are established for the reduced problem. Moreover, a priori energy estimates are obtained with minimum regularity requirement for the data and explicit dependence on the time.