Non-quantum entanglement and a complete characterization of pre-Mueller and Mueller matrices in polarization optics

TL;DR

This paper extends the Mueller-Stokes formalism to partially coherent, entangled electromagnetic beams, identifying additional constraints for physical Mueller matrices beyond classical criteria.

Contribution

It introduces a complete characterization of pre-Mueller and Mueller matrices considering non-quantum entanglement in polarization optics.

Findings

Additional constraints for physical Mueller matrices are fully characterized.

Non-quantum entanglement affects the criteria for Mueller matrix validity.

The formalism now applies to partially coherent, entangled beams.

Abstract

The Mueller-Stokes formalism which governs conventional polarization optics is formulated for plane waves, and thus the only qualification one could demand of a $4\times 4$ real matrix $M$ in order that it qualifies to be the Mueller matrix of some physical system is that $M$ should map $\Omega^{({\rm pol})}$, the positive cone of Stokes vectors, into itself. In view of growing current interest in the characterization of partially coherent partially polarized electromagnetic beams, there is need to extend this formalism to such beams wherein the polarization and spatial dependence are generically inseparably intertwined. This inseparability or non-quantum entanglement brings in additional constraints that a pre-Mueller matrix $M$ mapping $\Omega^{({\rm pol})}$ into itself needs to meet in order that it is an acceptable physical Mueller matrix. These additional constraints are motivated and fully characterized.