Scattering of electromagnetic waves by rough interfaces and inhomogeneous layers

We consider a two-dimensional problem of scattering of a time-harmonic elec tromagnetic plane wave by an infinite inhomogeneous conducting or dielectri c layer at the interface between semi-infinite homogeneous dielectric half- spaces. The magnetic permeability is assumed to be a fixed positive constan t. The material properties of the media are characterized completely by an index of refraction, which is a bounded measurable function in the layer an d takes positive constant values above and below the layer, corresponding t o the homogeneous dielectric media. In this paper, we examine only the tran sverse magnetic (TM) polarization case. A radiation condition appropriate f or scattering by infinite rough surfaces is introduced, a generalization of the Rayleigh expansion condition for diffraction gratings. With the help o f the radiation condition the problem is reformulated as an equivalent mixe d system of boundary and domain integral equations, consisting of second-ki nd integral equations over the layer and interfaces within the layer. Assum ptions on the variation of the index of refraction in the layer are then im posed which prove to be sufficient, together with the radiation condition, to prove uniqueness of solution and nonexistence of guided wave modes. Rece nt, general results on the solvability of systems of second kind integral e quations on unbounded domains establish existence of solution and continuou s dependence in a weighted norm of the solution on the given data. The resu lts obtained apply to the case of scattering by a rough interface between t wo dielectric media and to many other practical configurations.