We present rigorous, nonperturbative, purely numerical solutions of the Rayleigh equations for the scattering of p- and s-polarized light from a two-dimensional randomly rough perfectly conducting surface. The solutions are used to calculate the reflectivity of the surface, the mean differential reflection coefficients, and the full angular distribution of the intensity of the scattered field. These results are compared with previously published rigorous numerical solutions of the Stratton-Chu equations, and very good agreement is found.

We calculate all the elements of the Mueller matrix for light scattering from a two-dimensional randomly rough lossy metal surface. The calculations are carried out for arbitrary angles of incidence by the use of nonperturbative numerical solutions of the reduced Rayleigh equations. We foresee that the ability to model polarization effects in light scattering from surfaces will enable better interpretation of experimental data and allow for the design of surfaces which possess useful polarization effects. © 2012 American Physical Society.

The transmission of polarized light through a two-dimensional randomly rough interface between two dielectric media has been much less studied, by any approach, than the reflection of light from such an interface. We have derived a reduced Rayleigh equation for the transmission amplitudes when p- or s-polarized light is incident on this type of interface, and have obtained rigorous, purely numerical, nonperturbative solutions of it. The solutions are used to calculate the transmissivity and transmittance of the interface, the mean differential transmission coefficient, and the full angular distribution of the intensity of the transmitted light. These results are obtained for both the case where the medium of incidence is the optically less dense medium and in the case where it is the optically more dense medium. Optical analogs of Yoneda peaks observed in the scattering of x rays from metallic and nonmetallic surfaces are present in the results obtained in the former case. For p-polarized incident light we observe Brewster scattering angles, angles at which the diffuse transmitted intensity is zero in a single-scattering approximation, which depend on the angle of incidence in contrast to the Brewster angle for flat-surface reflection.