Geometric approach of degree of polarization in 3D polarimetry

TL;DR

This paper introduces a geometric method to quantify the degree of polarization in 3D electromagnetic fields, using a spherical shell model and coherency matrix decomposition for intuitive visualization.

Contribution

It presents a novel geometric framework for 3D polarization analysis based on coherency matrix decomposition and a spherical shell model, enhancing interpretability of polarimetric data.

Findings

Defined a spherical shell model for 3D polarization

Established a relationship between parameters and DoP

Demonstrated applicability through examples

Abstract

The geometric approach presented in this paper concerns the degree of polarization (DoP) of a random 3D statistical electromagnetic field. We use that a 3*3 coherency matrix can always be decomposed into an incoherent superposition of three specific coherency matrices, to construct the first orthant of a spherical shell(0<x,y,z<1,sqrt(3)/3<r<1) . For a random 3D statistical electromagnetic field, the polarimetric result of the can be expressed in terms of a point located in the first orthant of this spherical shell physically. Furthermore, based on the intrinsic relationship between the defined parameters (DoP3D_P,DoP3D_PP) and DoP, a spatially quadric surface is obtained to quantify the values of DoP the for all physically reachable points contained in the first orthant of this spherical shell. Within this geometric approach, two examples are cited to demonstrate the applicability of 3D polarimetry to intuitively display the polarimetric result of a random 3D statistical electromagnetic field.