Polarized Light in Random Media: A Formalism Based on Non Commutative Harmonic Analysis

This is a note containing the most recent results we have arrived at in our work on polarized light in random media. After an introduction fixing the problem we are dealing with, we start by pointing out the connection between the Poincaré sphere formalism and noncommutative harmonic analysis. This leads us to the main equations of our formalism. We use these equation to generalize the notions of Stokes vector, degree of polarization (DOP) and Mueller matrix to higher order statistics of the electric field. We also use them to give a formalism for the propagation of a state of polarisation (SOP) in a random medium. We show how a more detailed description of this propagation is then made possible.