A complete characterization of pre-Mueller and Mueller matrices in polarization optics

Abstract

The Mueller-Stokes formalism that governs conventional polarization optics is formulated for plane waves, and thus the only qualification one could require of a 4×4 real matrix M in order that it qualify to be the Mueller matrix of some physical system would be that M map Ω^(pol), the positive solid light cone of Stokes vectors, into itself. In view of growing current interest in the characterization of partially coherent partially polarized electromagnetic beams, there is a need to extend this formalism to such beams wherein the polarization and spatial dependence are generically inseparably intertwined. This inseparability brings in additional constraints that a pre-Mueller matrix M mapping Ω^(pol) into itself needs to meet in order to be an acceptable physical Mueller matrix. These additional constraints are motivated and fully characterized.