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arXiv · 1611.10245

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

Mark R Dennis·Miguel A Alonso
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Abstract

The connection between Poincaré spheres for polariz-ation and Gaussian beams is explored, focusing on the interpretation of elliptic polarization in terms of the isotropic 2-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 2-dimensional oscillator, which acquire an extra significance as families of classical ellipses upon semiclassical quantization.

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Mark R Dennis, Miguel A Alonso. 2016-11-30. Swings and roundabouts: Optical Poincaré spheres for polarization and Gaussian beams. https://doi.org/10.1098/rsta.2015.0441

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