Electromagnetic scattering by unbounded rough surfaces, submitted

This paper is concerned with the mathematical analysis of the solution for the wave prop-agation from the scattering by an unbounded penetrable rough surface. Throughout the wavenumber is assumed to have a nonzero imaginary part which accounts for the energy ab-sorption. The scattering problem is modeled as a boundary value problem governed by the Helmholtz equation with transparent boundary conditions proposed on plane surfaces confin-ing the scattering surface. The existence and uniqueness of the weak solution for the model problem are established by using a variational approach. Furthermore, the scattering problem is investigated for the case when the scattering profile is a sufficiently small and smooth de-formation of a plane surface. Under this assumption, the problem is equivalently formulated into a set of two-point boundary value problems in the frequency domain, and the analytical solution, in the form of an infinite series, is deduced by using a boundary perturbation tech-nique combined with the transformed field expansion approach. Key words. Helmholtz equation, variational formulation, rough surface scattering, boundary perturbation method, transformed field expansion AMS subject classications. 78A45, 78M30, 78M35