Semiclassical quantization of the mixed-flux AdS3 giant magnon

We obtain explicit formulas for the eight bosonic and eight fermionic fluctuations around the mixed-flux generalization of the Hofman-Maldacena giant magnon on AdS3×S3×T4 and AdS3×S3×S3×S1. As a check of our results, we confirm that the semiclassical quantization of these fluctuations leads to a vanishing one-loop correction to the magnon energy, as expected from symmetry based arguments.

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 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’.