Numerical simulations of scattering of light from two-dimensional surfaces using the Reduced Rayleigh Equation

TL;DR

This paper introduces a numerical formalism for solving the reduced Rayleigh equation to analyze light scattering from two-dimensional rough surfaces, providing accurate results validated by energy conservation checks.

Contribution

A non-perturbative, purely numerical method for solving the reduced Rayleigh equation applied to complex surface scattering problems.

Findings

Reliable results within the Rayleigh hypothesis validity

Energy conservation verified to within 0.03% for metal surfaces

Effective for Gaussian and cylindrical power spectra

Abstract

A formalism is introduced for the non-perturbative, purely numerical, solution of the reduced Rayleigh equation for the scattering of light from two-dimensional penetrable rough surfaces. As an example, we apply this formalism to study the scattering of p- or s-polarized light from two- dimensional dielectric or metallic randomly rough surfaces by calculating the full angular distribution of the co- and cross-polarized intensity of the scattered light. In particular, we present calculations of the mean differential reflection coefficient for glass and silver surfaces characterized by (isotropic or anisotropic) Gaussian and cylindrical power spectra. The proposed method is found, within the validity of the Rayleigh hypothesis, to give reliable results. For a non-absorbing metal surface the conservation of energy was explicitly checked, and found to be satisfied to within 0.03%, or better, for the parameters assumed. This testifies to the accuracy of the approach and a satisfactory discretization.