Time Dependent Scattering from a Grating

TL;DR

This paper develops a method for computing time-dependent electromagnetic scattering from periodic gratings, incorporating frequency-dependent materials, with proofs of existence, uniqueness, and error estimates, supported by numerical validation.

Contribution

It introduces a novel approach combining Convolution Quadrature with wave equation solutions for frequency-dependent materials in periodic structures, providing theoretical guarantees and numerical evidence.

Findings

Proved existence and uniqueness for frequency-dependent materials

Established error estimates for the time-stepping scheme

Numerical results demonstrate convergence and stability

Abstract

Computing the electromagnetic field due to a periodic grating is critical for assessing the performance of thin film solar voltaic devices. In this paper we investigate the computation of these fields in the time domain (similar problems also arise in simulating antennas). Assuming a translation invariant periodic grating this reduces to solving the wave equation in a periodic domain. Materials used in practical devices have frequency dependent coefficients, and we provide a first proof of existence and uniqueness for a general class of such materials. Using Convolution Quadrature we can then prove time stepping error estimates. We end with some preliminary numerical results that demonstrate the convergence and stability of the scheme.