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’.
One contribution of 14 to a theme issue ‘Optical orbital angular momentum’.
- Accepted September 6, 2016.
- © 2017 The Author(s)
Published by the Royal Society. All rights reserved.