Total Angular Momentum Coherent State Fields

TL;DR

This paper introduces a symmetry-based framework for controlling structured light fields by combining spin and orbital angular momentum, enabling continuous and precise manipulation of polarization and spatial structure.

Contribution

It develops a novel approach using the shared su(2) Lie algebra to construct total angular momentum fields as superpositions of polarization and Laguerre-Gaussian beams.

Findings

Unified control of polarization and spatial structure via a single parameter

Construction of su(2) coherent states for total angular momentum fields

Continuous, symmetry-preserving tuning of structured light fields

Abstract

Structured light fields exploit spin and orbital angular momentum for precision manipulation, advanced imaging, and high-capacity communication. Orbital angular momentum coherent state beams interpolate between Hermite- and Laguerre-Gaussian beams, enabling continuous spatial control. We introduce a symmetry-based framework for joint control of polarization and spatial structure under the shared \$su(2)\$ Lie algebra of spin and orbital angular momentum. Within this structure, we construct total angular momentum fields as superpositions of circular polarization and Laguerre-Gaussian beams, and define their \$su(2)\$ coherent states within fixed-angular-momentum subspaces. A single complex parameter controls both polarization and spatial degrees of freedom, enabling continuous, symmetry-preserving tuning.