Scattering From Two Rough Surfaces With Inhomogeneous Dielectric Profiles

A rigorous analytical technique to derive the scattering coefficients of three-dimensional (3-D) two rough surfaces with arbitrary dielectric profiles is presented. The proposed method applies a perturbation approach to a surface integral equation (IE) formulation that is derived from the extended boundary conditions (EBC). First, using EBC or the surface equivalence principle (SEP) and the dyadic Green´s functions of the resulting simpler geometries, a system of IEs for the surface fields of the two rough interfaces is established. Then, the Fourier-domain surface fields are derived using a perturbation method. The scattered fields are subsequently determined by a second application of SEP. In general, the approach could be used to present the general formulation for multiple rough layers and also higher order solutions. But, the focus of this paper is on deriving compact closed-form solutions for inhomogeneous dielectric profiles and thus, only two rough interfaces are considered. Accordingly, the first-order closed-form scattered fields are represented in a remarkably compact form that is suitable for physical interpretation and also extension to higher orders. Finally, the derived expressions are compared to known solutions of special cases, available in the literature. The results are shown to be exactly consistent with existing ones and hence validated analytically and numerically.