Electromagnetic wave scattering from conducting self-affine surfaces : An analytic and numerical study

TL;DR

This paper presents an analytical and numerical study of electromagnetic wave scattering from conducting self-affine surfaces, highlighting the role of surface slope and roughness parameters in the scattering process.

Contribution

It derives an analytical expression for wave scattering from self-affine surfaces and validates it with numerical simulations across various roughness levels.

Findings

Analytical expression accurately predicts scattering behavior.

Surface slope over one wavelength controls scattering.

Results hold for surfaces with small electrical resistivity.

Abstract

We derive an analytical expression for the scattering of a scalar wave from a perfectly conducting self-affine one dimensional surface in the framework of the Kirchhoff approximation. We show that most of the results can be recovered via a scaling analysis. We identify the typical slope taken over one wavelength as the relevant parameter controlling the scattering process. We compare our predictions with direct numerical simulations performed on surfaces of varying roughness parameters and confirm the broad range of applicability of our description up to very large roughness. Finally we check that a non zero electrical resistivity provided small does not invalidate our results.