The Local Spectral Expansion Method for Scattering From One-Dimensional Dielectric-Dielectric Rough Interfaces

In this paper we generalize the local spectral expansion method (previously developed for perfectly conducting rough surfaces) to the scattering from dielectric-dielectric interfaces rough in one dimension. The method for perfectly conducting surfaces is recovered from the present formulation in the limit when one of the dielectric constants increases to infinity. We obtain the first order approximation using the tangent plane approximation. It is shown analytically that the present approximation reduces to first order perturbation theory in the appropriate limit. On the other hand, since the only approximation in our formulation is the tangent plane approximation, the present results are expected a priori to coincide with the Kirchhoff approximation when this is accurate. A numerical comparison for Gaussian random rough surfaces with other first order theories is presented.