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

TL;DR

This paper presents a comprehensive numerical analysis of polarized light scattering from a two-dimensional randomly rough dielectric interface, deriving a general reduced Rayleigh equation and exploring optical phenomena like Yoneda peaks and Brewster angles.

Contribution

It introduces a nonperturbative numerical solution to the reduced Rayleigh equation for arbitrary dielectric functions, enabling detailed analysis of scattering properties.

Findings

Identification of Yoneda peaks in scattering from rough dielectric interfaces.

Dependence of Brewster scattering angles on incidence angle and medium properties.

High accuracy unitarity compliance in numerical results.

Abstract

The scattering of polarized light incident from one dielectric medium on its two-dimensional randomly rough interface with a second dielectric medium is studied. A reduced Rayleigh equation for the scattering amplitudes is derived for the case where p- or s-polarized light is incident on this interface, with no assumptions being made regarding the dielectric functions of the media. Rigorous, purely numerical, nonperturbative solutions of this equation are obtained. They are used to calculate the reflectivity and reflectance of the interface, the mean differential reflection coefficient, and the full angular distribution of the intensity of the scattered 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 the Yoneda peaks observed in the scattering of x-rays from metal surfaces are present in the results obtained in the latter case. Brewster scattering angles for diffuse scattering are investigated, reminiscent of the Brewster angle for flat-interface reflection, but strongly dependent on the angle of incidence. When the contribution from the transmitted field is added to that from the scattered field it is found that the results of these calculations satisfy unitarity with an error smaller than $10^{-4}$.