# Generalized Gaussian beams in terms of Jones vectors

## TL;DR

This paper introduces a novel operator formalism linking generalized Gaussian beams with Jones vectors, revealing their relation to elliptical ray families and Majorana constellations, and offering computational improvements.

## Contribution

It develops a new formula based on SU(2) group theory that describes generalized Hermite-Laguerre Gaussian modes using Jones vectors, connecting polarization and structured beams.

## Key findings

- Provides a new SU(2)-based formula for Gaussian beams
- Establishes links between beams, ray families, and Majorana constellations
- Offers computational advantages over existing methods

## Abstract

Based on the operator formalism that arises from the underlying SU(2) group structure, a formula is derived that provides a description of the generalized Hermite-Laguerre Gauss modes in terms of a Jones vector, traditionally used to describe polarization. This identity highlights the relation between these generalized Gaussian beams, the elliptical ray families, and the Majorana constellations used to represent structured-Gaussian beams. Moreover, it provides a computational advantage over the standard formula in terms of Wigner $d$ functions.