Generalized Gaussian beams in terms of Jones vectors

R. Gutiérrez-Cuevas (1) , R Dennis (2, 3) , Miguel Alonso (4, 5, 6, 7, 8)

1 The Institute of Optics, University of Rochester
2 University of Birmingham [Birmingham]
3 University of Bristol [Bristol]
4 MOSAIC - MOSAIC
5 AMU - Aix Marseille Université
6 FRESNEL - Institut FRESNEL
7 ECM - École Centrale de Marseille
8 University of Rochester [USA]

Based on the operator formalism that arises from the underlying SU(2) group structure, a formula is derived that provides a description of the generalized Hermite-Laguerre Gauss modes in terms of a Jones vector, traditionally used to describe polarization. This identity highlights the relation between these generalized Gaussian beams, the elliptical ray families, and the Majorana constellations used to represent structured-Gaussian beams. Moreover, it provides a computational advantage over the standard formula in terms of Wigner d functions.

Domaines: Optique [physics.optics]; Physique mathématique [math-ph]

R. Gutiérrez-Cuevas, R Dennis, Miguel Alonso. Generalized Gaussian beams in terms of Jones vectors. Journal of Optics, 2019, 21 (8), pp.084001. ⟨10.1088/2040-8986/ab2c52⟩. ⟨hal-02196272⟩