Electromagnetic polarization matrix and its physical interpretation

TL;DR

This paper introduces a comprehensive 6x6 electromagnetic polarization matrix that unifies electric and magnetic field properties, providing new insights into their coupled polarization states and physical interpretations.

Contribution

It presents a novel 6x6 matrix formalism that generalizes the electric polarization matrix by including magnetic contributions and their correlations, bridging classical and quantum-like descriptions.

Findings

The matrix captures electric-magnetic cross-correlations.

Application to orthogonal plane waves illustrates the need for a combined representation.

Provides physically meaningful quantities like energy fluxes and coupling indices.

Abstract

Despite the intrinsic coupling between electric and magnetic fields in random stationary light, their polarization properties are not mutually determined. A complete second-order description thus necessitates a joint electromagnetic treatment. The 6x6 electromagnetic polarization matrix introduced here generalizes the conventional electric 3x3 matrix by incorporating both electric and magnetic contributions together with their mutual correlations. It consists of diagonal 3x3 blocks, representing the electric and magnetic polarization matrices, and off-diagonal 3x3 blocks that encode the full structure of electric-magnetic cross-correlations. The information contained in this matrix can be interpreted through physically meaningful quantities such as active and reactive energy fluxes, in-phase and quadrature alignment matrices, and global indices describing electric-magnetic coupling. The formalism is applied to a field composed of two orthogonally propagating plane waves sharing a common linear electric polarization (a simple yet physically realizable configuration) that demonstrates the need for a general combined electric-magnetic representation even in free space. This approach provides a comprehensive and unified framework for characterizing electromagnetic polarization beyond the electric-field description alone, bridging classical statistical optics with quantum-like density-matrix interpretations.