Generalized Gaussian beams in terms of Jones vectors

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.

References in corpus (6)

• Electromagnetic Angular Momentum
• Electromagnetic Force and Momentum
• A ray-optical Poincaré sphere for structured Gaussian beams
• Swings and roundabouts: Optical Poincaré spheres for polarization and Gaussian beams
• Canonical representation of spherical functions: Sylvester's theorem, Maxwell's multipoles and Majorana's sphere
• Measuring geometric phase without interferometry

Cited by in corpus (11)

• Geometric phases in 2D and 3D polarized fields: geometrical, dynamical, and topological aspects
• Geometric descriptions for the polarization for nonparaxial optical fields: a tutorial
• Modal Majorana sphere and hidden symmetries of structured-Gaussian beams
• Observation of Anomalous Orbital Angular Momentum Conservation in Parametric Nonlinearity
• Structured Light Modal Interface via Liquid-Crystal Planar Optics
• Exactly solvable model behind Bose-Hubbard dimers, Ince-Gauss beams, and aberrated optical cavities
• Hydrodynamics Explanation for the Splitting of Higher-charge Optical Vortices
• Ray and caustic structure of Ince-Gauss beams
• Single-shot, full characterization of the spatial wavefunction of light fields via Stokes tomography
• Propagation-invariant high-dimensional orbital angular momentum states
• Tilted Poincaré Sphere Geodesics