Three-dimensional coherence matrix and degree of polarization

TL;DR

This paper investigates the properties of three-dimensional partially polarized light fields, clarifies the definition of unpolarized light in 3D, and shows that only six Stokes parameters are needed to describe the coherence matrix, which can be measured in-plane.

Contribution

It introduces a consistent definition of unpolarized light in three dimensions and demonstrates that six Stokes parameters suffice to describe the coherence matrix, simplifying measurements.

Findings

No unambiguous correspondence between 3D field and coherence matrix

Unpolarized light should be treated as equiprobable polarizations in 3D

Six Stokes parameters are sufficient for describing the coherence matrix

Abstract

Inspecting three-dimensional partially polarized light fields we show that there is no unambiguous correspondence between the three-dimensional field and coherence matrix (or light beam tensor). Therefore, it is needed to clarify the definition of unpolarized light. We believe that unpolarized field should be treated as light of equiprobable polarizations similar to the case of two-dimensional light. Then degree of polarization bridges two definitions of the three-dimensional degrees of polarization known in literature. We reveal that only 6 Stokes parameters are sufficient to describe the coherence matrix. All these parameters can be retrieved from the in-plane measurements of two-dimensional coherence matrices.