Like‐ and cross‐polarized transmission scatter cross sections for random rough surfaces: Full wave solutions

Abstract

In this work full wave expressions are derived for the incoherent diffuse scatter cross sections (per unit area) for waves transmitted across rough surfaces. Both the like‐ and cross‐polarized cross sections are considered since the surfaces are rough in two dimensions. The full wave solutions are compared with the small perturbation solutions as well as with the physical/geometrical solutions. It is shown that when the heights and slopes are of the same order of smallness, the full wave solutions are in agreement with the small perturbation solution, while in the high‐frequency limit the full wave solution is in agreement with physical/geometrical optics solutions, provided that specular (stationary phase) points exist on the surface. Several illustrative examples are considered and the refractive index is assumed to be larger or smaller than unity. The critical angle for total internal reflection has a significant impact on diffuse scattering in the nonspecular direction. Since the full wave solutions account for specular point scattering as well as Bragg type scattering in a uniform, self‐consistent manner, it is not necessary to adopt the two‐scale model for the rough surfaces.