Wave scattering from self-affine surfaces

TL;DR

This paper derives an exact analytical expression for electromagnetic wave scattering from self-affine surfaces using Levy distributions, revealing detailed scattering characteristics based on surface roughness and wave parameters.

Contribution

It introduces a novel exact formulation of wave scattering from self-affine surfaces using Levy distributions within the Kirchhoff approximation.

Findings

Scattering cross section expressed as a Levy distribution function.

Analysis of the specular peak's amplitude, width, and position.

Power-law decay of scattering cross section with angle.

Abstract

Electromagnetic wave scattering from a perfectly reflecting self-affine surface is considered. Within the framework of the Kirchhoff approximation, we show that the scattering cross section can be exactly written as a function of the scattering angle via a centered symmetric Levy distribution for general roughness amplitude, Hurst exponent and wavelength of the incident wave. The amplitude of the specular peak, its width and its position are discussed as well as the power law decrease (with scattering angle) of the scattering cross section.