Polarization effects for electromagnetic wave propagation in random media

TL;DR

This paper investigates how electromagnetic waves lose coherence and polarization due to scattering in random media, using stochastic differential equations and asymptotic analysis to quantify energy exchange and wave behavior over long distances.

Contribution

It provides a detailed asymptotic analysis of electromagnetic wave propagation in random media, including polarization effects and energy transfer between modes, using stochastic differential equations and transport equations.

Findings

Quantifies scattering mean free paths for wave amplitude decay.

Analyzes energy exchange and polarization loss between modes.

Derives transport equations with polarization for wave energy density.

Abstract

We study Maxwell's equations in random media with small fluctuations of the electric permittivity. We consider a setup where the waves propagate toward a preferred direction, called range. We decompose the electromagnetic wave field in transverse electric and transverse magnetic plane waves, called modes, with random amplitudes that model cumulative scattering effects in the medium. Their evolution in range is described by a coupled system of stochastic differential equations driven by the random fluctuations of the electric permittivity. We analyze the solution of this system with the Markov limit theorem and obtain a detailed asymptotic characterization of the electromagnetic wave field in the long range limit. In particular, we quantify the loss of coherence of the waves due to scattering by calculating the range scales (scattering mean free paths) on which the mean amplitudes of the modes decay. We also quantify the energy exchange between the modes, and consequently the loss of polarization induced by scattering, by analyzing the Wigner transform (energy density) of the electromagnetic wave field. This analysis involves the derivation of transport equations with polarization. We study in detail these equations and connect the results with the existing literature in radiative transport and paraxial wave propagation.