The Scattering of Electromagnetic Waves from Two-Dimensional Randomly Rough Penetrable Surfaces

TL;DR

This paper presents a numerical simulation method for electromagnetic wave scattering from two-dimensional randomly rough penetrable surfaces, accurately calculating the scattered field distribution and verifying energy conservation.

Contribution

It introduces an efficient numerical approach using Muller equations and impedance boundary conditions for 2D rough surfaces, ensuring high accuracy in scattering simulations.

Findings

Energy conservation is well-satisfied in non-absorbing cases (${\mathcal U}>0.995$).

The method accurately computes the full angular intensity distribution of scattered fields.

Numerical treatment of matrix elements is crucial for simulation accuracy.

Abstract

An accurate and efficient numerical simulation approach to electromagnetic wave scattering from two-dimensional, randomly rough, penetrable surfaces is presented. The use of the M\"uller equations and an impedance boundary condition for a two-dimensional rough surface yields a pair of coupled two-dimensional integral equations for the sources on the surface in terms of which the scattered field is expressed through the Franz formulas. By this approach, we calculate the full angular intensity distribution of the scattered field that is due to a finite incident beam of $p$-polarized light. We specifically check the energy conservation (unitarity) of our simulations (for the non-absorbing case). Only after a detailed numerical treatment of {\em both} diagonal and close-to-diagonal matrix elements is the unitarity condition found to be well-satisfied for the non-absorbing case (${\mathcal U}>0.995$), a result that testifies to the accuracy of our approach.