Electromagnetic Scattering from Periodic Rough Surfaces.

A simple scalar model involving propagation transverse to a cylindrical periodic (two dimensional) surface is developed. By using a perturbation analysis, a general expression is obtained for the amplitude of the scattered waves which is valid for all spectral and all perturbation orders. In addition, the general expression permits one to discern some important properties of the amplitudes for a purely sinusoidal surface. Among other things, it shows that all odd perturbation orders are zero for the specular mode. An improved vector model is outlined which incorporates a proposed alternative to the Rayleigh hypothesis which is used to obtain the modal expansion of the solution used in the simple model. All of the models developed are illustrated and compared by numeric examples. This includes consideration of the convergence of the numerical point-matching solution and analytical perturbation solution, as well as an error analysis of these results.