Numerical studies of the transmission of light through a two-dimensional randomly rough interface

To understand and predict diffuse scattering of electromagnetic waves through randomly rough surfaces is a relevant problem in many branches of science, engineering, military and medicine. In the current work we obtain nonperturbative solutions of the reduced Rayleigh equation for the transmission amplitudes when p- or s-polarized light is incident on a two-dimensional randomly rough interface between vacuum and an absorptionless dielectric. Not limited by one-dimensional interfaces, we obtain the full angular dependence of the total scattered intensity and also investigate cross-polarized scattering. For light transmitted into a denser medium we observe effects related to total internal reflection, namely Yoneda peaks. This phenomenon, together with Brewster scattering angles, are thoroughly investigated and analyzed based on comparisons with small amplitude perturbation theory.