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

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 l...

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Bibliographic Details
Published in:Philosophical transactions of the Royal Society of London. Series A: Mathematical, physical, and engineering sciences physical, and engineering sciences, 2017-02, Vol.375 (2087), p.20150441-20150441
Main Authors: Dennis, M. R., Alonso, M. A.
Format: Article
Language:English
Subjects:
Angular momentum
Beams (radiation)
Eigenvectors
Gaussian beams (optics)
Harmonic Oscillator
Hermite-Gaussian
Laguerre-Gaussian
Measurement
Oscillators
Polarization
Roundabouts
Three dimensional motion
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Summary: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’.
ISSN:1364-503X
1471-2962
DOI:10.1098/rsta.2015.0441