Higher Order Statistsics of Stokes Parameters in a Random Birefringent Medium

TL;DR

This paper introduces a novel model for analyzing the propagation of polarized light in random birefringent media using higher order statistics of Stokes parameters, providing analytical tools for detailed characterization.

Contribution

The paper develops a new model based on higher order statistics and group representations, enabling detailed analytical descriptions of polarization evolution in random media.

Findings

Analytical expressions for probability densities of Mueller matrix and Stokes vector.

Exact evolution equations for degree of polarization.

Extension of polarization concepts to higher order statistics.

Abstract

We present a new model for the propagation of polarized light in a random birefringent medium. This model is based on a decomposition of the higher order statistics of the reduced Stokes parameters along the irreducible representations of the rotation group. We show how this model allows a detailed description of the propagation, giving analytical expressions for the probability densities of the Mueller matrix and the Stokes vector throughout the propagation. It also allows an exact description of the evolution of averaged quantities, such as the degree of polarization. We will also discuss how this model allows a generalization of the concepts of reduced Stokes parameters and degree of polarization to higher order statistics. We give some notes on how it can be extended to more general random media.