A unified matrix representation for spin and orbital angular momentum in partially coherent beams

TL;DR

This paper introduces a unified matrix framework to describe the combined properties of spin and orbital angular momentum in partially coherent light beams, enabling comprehensive analysis of their coherence and angular momentum states.

Contribution

It presents a novel Coherence-OAM matrix and a unifying Coherence-SAM-OAM matrix for analyzing beams with arbitrary coherence, spin, and orbital angular momentum.

Findings

The Coherence-OAM matrix characterizes the spatial coherence and OAM simultaneously.

The Coherence-SAM-OAM matrix unifies the treatment of spin and orbital angular momentum in partially coherent beams.

The framework generalizes existing polarization and coherence matrices to include orbital angular momentum.

Abstract

A matrix representation is introduced for stationary beam-like light fields that allows for simultaneous treatment of the orbital angular momentum (OAM) and the second-order state of spatial coherence. This Coherence-OAM matrix is a counterpart of the 2 x 2 beam Coherence-polarization matrix in a Cartesian polarization basis or Coherence-spin angular momentum (SAM) matrix in a circular polarization basis. The general properties of the Coherence-OAM matrix are discussed and then the Coherence-SAM-OAM matrix is introduced as a unifying entity for treating beams with any coherence, spin and orbital angular momentum states.