Swings and roundabouts: optical Poincaré spheres for polarization and Gaussian beams

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Colleges, School and Institutes


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.

Bibliographic note

arXiv: 1611.10245


Original languageEnglish
Article number20150441
JournalRoyal Society of London. Philosophical Transactions A. Mathematical, Physical and Engineering Sciences
Issue number2087
Early online date9 Jan 2017
Publication statusPublished - 28 Feb 2017