Electromagnetic scattering by periodic structures with sign-changing coefficients

Abstract

We analyze the well-posedness of a scattering problem of time-harmonic electromagnetic waves by periodic structures with sign-changing coefficients. Transmission problems for Maxwell's equations with sign-changing coefficients in bounded domains have been recently studied by Bonnet-Ben Dhia and co-workers in the so-called T-coercivity framework. In this article, we generalize such a framework for periodic scattering problems relying on an integral equation approach. The periodic scattering problem is formulated by a hypersingular integral equation of Lipmann–Schwinger type. We prove that the integral equation satisfies a Gårding-type estimate, which allows us to establish the well-posedness of the problem in the sense of Fredholm.