Variational Approach to Electromagnetic Scattering by Layers above a Perfectly Conducting Surface for TM Polarization

In this paper, we study the scattering of time harm-onic electromagnetic waves by a homogeneous layer above a perfectly conducting surface in the case of TM polarization. We first, propose a variational formulation, and establish its equivalence to the boundary value problem. Then we prove, via Lax-Milgram theorem, the well-posedness of this problem for small wave number, and obtain a stability estimation about the solution, which show explicitly the dependence on wave number and the maximum surface elevation. Finally, we consider the case of conducting layer, and show the problem is still uniquely solvable based on the results of dielectric case.