Interpretation of the coherency matrix for three-dimensional polarization states

TL;DR

This paper analyzes the 3D coherency matrix for polarization states, classifying and interpreting it physically, revealing new insights into the properties and limitations of 3D polarization representations.

Contribution

It introduces a comprehensive parameterization and physical interpretation framework for 3D coherency matrices, including classifications and insights into their propagation and decomposition properties.

Findings

Certain 3D mixed states cannot be decomposed into simpler components.

Coherency matrices do not always indicate a well-defined propagation direction.

The 2D polarization model is a special case within the 3D framework.

Abstract

From an appropriate parameterization of the three-dimensional (3D) coherency matrix R, that characterizes the second-order, classical states of polarization, the coherency matrices are classified and interpreted in terms of incoherent decompositions. The relevant physical quantities derived from R, as the intensity, the degree of polarimetric purity, the indices of polarimetric purity, the angular momentum, the degree of directionality and the degree of linear polarization are identified and interpreted on the light of the case study performed. The information provided by R about the direction of propagation is clarified and it is found that coherency matrices with, does not always represent states with a well-defined direction of propagation. Moreover, it is demonstrated the existence of 3D mixed states that cannot be decomposed into a superposition of a pure state, a 2D unpolarized state, and a 3D unpolarized state. Appropriate representation and interpretation for all the different types of 3D coherency matrices is provided through physical consistent criteria. Under the approach proposed, the conventional two-dimensional model arises naturally.