Scattering from a periodic medium with a rough interface

A hybrid technique that utilizes the finite-element method (FEM) and an analytic solution is presented for the analysis of the scattering of a plane wave from a periodic inhomogeneous medium, having arbitrary geometry and material properties. This medium is overlaid with a homogeneous one that presents a rough interface with the space from which the incident plane wave originates. The rough interface is studied with a perturbative method, whereas the inhomogeneous medium is examined with the finite-element procedure. The two methods are matched imposing the continuity of the fields into the homogeneous medium.