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

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.

22 pages, 6 figures

References in corpus (1)

• Rows of optical vortices from elliptically perturbing a high-order beam

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