Numerical and experimental studies of the scattering of light from a two-dimensional randomly rough interface between two dielectric media

Calculations of the scattering of light in both reflection from, and transmission through, two-dimensional randomly rough surfaces are challenging, and are still often carried out by means of small-amplitude perturbation theory, the Kirchhoff approximation, or similar. How- ever, accurate approaches to the solution of such problems are needed in a variety of contexts, and searches for such approaches, and their verification through experiments, are an active area of re- search in computational electrodynamics. In this talk we present the first experimental results for the scattering of p- and s-polarized light from a dielectric structure with a two-dimensional randomly rough interface that can display effects associated with total internal reflection. The experimental results are supported by the results of rigorous, purely numerical, nonperturbative solutions of the reduced Rayleigh equation for scattering from this film structure, which also provides insight into the reflectivity and reflectance of the system. The illuminated interface is planar, while the back interface is a two-dimensional randomly rough interface. We consider only the case in which the medium of incidence is optically more dense than the substrate, in which case effects due to the presence of a critical angle for total internal reflection occur. In particular, we show the existence of “Yoneda peaks” in the angular dependence of the mean differential reflection coefficient, which have only briefly been investigated in past publications. These are sharp asymmetric peaks occurring at the critical angle for total internal reflection, for a fixed angle of incidence, for either p- or s-polarization of the incident light. These peaks were first observed experimentally in the scattering of x-rays incident from air on a metal surface. Until now they have not been observed in optical experiments. Finally, we also find that even a small degree of roughness significantly depresses the reflection of p- and s-polarized light for scattering angles greater than the critical angle for total internal reflection. When the computational results are compared with experimental data for the in-plane mean differential reflection coefficient, good agreement between theory and experiment is found. We hope and believe that the presentation of these results will stimulate and motivate further com- putational and experimental studies of similar scattering systems.