The scattering of a scalar beam from isotropic and anisotropic two-dimensional randomly rough Dirichlet or Neumann surfaces: The full angular intensity distributions

TL;DR

This paper investigates how scalar Gaussian beams scatter from two-dimensional rough surfaces with isotropic or anisotropic properties, providing detailed angular intensity distributions and analyzing the effects of surface anisotropy on scattering patterns.

Contribution

It introduces a nonperturbative computer simulation method to compute full angular scattering distributions from rough surfaces with anisotropic properties.

Findings

Reflectivities vary with incident angle and surface type.

Anisotropy significantly affects scattering symmetry and intensity.

Small anisotropy levels can cause notable changes in scattering patterns.

Abstract

By the use of Green's second integral identity we determine the field scattered from a two-dimensional randomly rough isotropic or anisotropic Dirichlet or Neumann surface when it is illuminated by a scalar Gaussian beam. The integral equations for the scattering amplitudes are solved nonperturbatively by a rigorous computer simulation approach. The results of these calculations are used to calculate the full angular distribution of the mean differential reflection coefficient. For isotropic surfaces, the results of the present calculations for in-plane scattering are compared with those of earlier studies of this problem. The reflectivities of Dirichlet and Neumann surfaces are calculated as functions of the polar angle of incidence, and the reflectiveties for the two kinds of surfaces of similar roughness parameters are found to be different. For an increasing level of surface anisotropy, we study how the angular intensity distributions of the scattered waves are affected by this level. We find that even small to moderate levels of surface anisotropy can significantly alter the symmetry, shape, and amplitude of the scattered intensity distributions when Gaussian beams are incident on the anisotropic surfaces from different azimuthal angles of incidence.