Stochastic description of geometric phase for polarized waves in random media

TL;DR

This paper develops a stochastic framework using compound Poisson processes on SO(3) to describe the polarization behavior of waves in random media, enabling estimation of scattering properties from polarization data.

Contribution

It introduces a novel stochastic model for polarized wave scattering and an algorithm for inverse problem solving based solely on polarization measurements.

Findings

Generalizes previous multiple scattering theories

Provides a method for estimating medium properties from polarization

Applicable to thin layers and fluctuating media

Abstract

We present a stochastic description of multiple scattering of polarized waves in the regime of forward scattering. In this regime, if the source is polarized, polarization survives along a few transport mean free paths, making it possible to measure an outgoing polarization distribution. We solve the direct problem using compound Poisson processes on the rotation group SO(3) and non-commutative harmonic analysis. The obtained solution generalizes previous works in multiple scattering theory and is used to design an algorithm solving the inverse problem of estimating the scattering properties of the medium from the observations. This technique applies to thin disordered layers, spatially fluctuating media and multiple scattering systems and is based on the polarization but not on the signal amplitude. We suggest that it can be used as a non invasive testing method.