Majorana constellations for optical scalar beams and vector fields

TL;DR

This paper applies Majorana stellar representation to optical beams and fields, revealing geometric structures and symmetries that aid in visualizing and characterizing complex light configurations for advanced optical applications.

Contribution

It introduces a novel application of Majorana constellation visualization to scalar and vector optical beams, including new insights into their symmetry properties and quantum analogues.

Findings

Scalar beam constellations at poles for Laguerre-Gaussian beams

Vector fields exhibit circular polarization representations

Constellations for Hermite-Gaussian beams on the equator

Abstract

We explore Majorana stellar representation on the Riemann sphere for optical scalar beams and vector fields, leveraging the spin and orbital angular momentum of light. For scalar beams, the star constellations for the Laguerre-Gaussian beam basis reside at the poles of the sphere. For vector fields, these constellations represent well-defined circular polarization. The underlying $su(2)$ symmetry of angular momenta enables populating the sphere through generalized unitary rotations of the basis elements, resulting in optical analogues of Bloch and generalized $su(2)$ coherent states for both scalar beams and vector fields. Constellations for scalar Hermite-Gaussian beams and vector Hermite-Gaussian partial Poincar\'e fields, restricted to linear polarization, occupy the equator of the sphere as a result of these rotations. Additionally, we investigate scalar and vector analogues of cat codes and kings of quantumness, providing insights into the visualization and characterization of complex optical beams and fields with potential applications in optical communications.