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

TL;DR

This paper presents a numerical study of light transmission through a two-dimensional randomly rough interface, deriving a new equation and analyzing transmission properties including angular distribution and special scattering phenomena.

Contribution

Derived a reduced Rayleigh equation for transmission amplitudes and provided rigorous numerical solutions for light transmission through rough interfaces.

Findings

Optical analogues of Yoneda peaks are observed.

Brewster scattering angles depend on the incidence angle.

Calculated transmissivity and angular distribution of transmitted light.

Abstract

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 analogues of Yoneda peaks observed in the scattering of x-rays from metal 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.