  The connection between Poincar\'e 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.
