Conditions for coalescence of the full wave solutions for rough surface EM scattering with perturbation and physical optics solutions in the low and high frequency limits-theory and experiment

A full wave solution based on the complete expansion of the fields and the imposition of exact boundary conditions was developed to investigate propagation in irregular stratified media. On applying this approach to scattering and depolarization by two dimensionally rough surfaces separating two media with arbitrary (complex) permittivity and permeability, it was shown that closed-form expressions for the surface element scattering coefficients depend on the polarizations and directions of the incident and scattered waves, the relative complex permittivity and permeability of the media, and the direction of the normal to the two-dimensionally rough surface. It was also shown that the full-wave results satisfied the duality, reciprocity, and realizability relationships in electromagnetic theory and that they were invariant to coordinate transformations.<>