title: Swings and roundabouts: optical Poincaré spheres for polarization and Gaussian beams.
abstract: The connection between Poincaré spheres for polarization and Gaussian beams is explored, focusing on the interpretation of elliptic polarization in terms of the isotropic two-dimensional harmonic oscillator in Hamiltonian mechanics, its canonical quantization and semiclassical interpretation. This leads to the interpretation of structured Gaussian modes, the Hermite-Gaussian, Laguerre-Gaussian and generalized Hermite-Laguerre-Gaussian modes as eigenfunctions of operators corresponding to the classical constants of motion of the two-dimensional oscillator, which acquire an extra significance as families of classical ellipses upon semiclassical quantization.This article is part of the themed issue 'Optical orbital angular momentum'.
authors.affiliation: H H Wills Physics Laboratory, University of Bristol, Bristol BS8 1TL, UK mark.dennis@bristol.ac.uk.
authors.forename: M R
authors.identifier: http://orcid.org/0000-0003-1147-1804
authors.initials: MR
authors.lastname: Dennis
authors.affiliation: The Institute of Optics, University of Rochester, Rochester, NY 14627, USA.
authors.forename: M A
authors.initials: MA
authors.lastname: Alonso
keywords: Hermite–Gaussian; Laguerre–Gaussian; harmonic oscillator