Ray and caustic structure of Ince-Gauss beams

R Gutiérrez-Cuevas (1, 2, 3) , M R Dennis (4, 5) , Miguel Alonso (6, 7, 3, 8, 9, 10)

1 IL - Institut Langevin - Ondes et Images (UMR7587)
2 ESPCI Paris - Ecole Superieure de Physique et de Chimie Industrielles de la Ville de Paris
3 AMU - Aix Marseille Université
4 University of Birmingham [Birmingham]
5 University of Bristol [Bristol]
6 University of Rochester [USA]
7 CNRS - Centre National de la Recherche Scientifique
8 FRESNEL - Institut FRESNEL
9 ECM - École Centrale de Marseille
10 MOSAIC - MOSAIC

The Ince-Gauss beams, separable in elliptic coordinates, are studied through a ray-optical approach. Their ray structure can be represented over a Poincaré sphere by generalized Viviani curves (intersections of a cylinder and a sphere). This representation shows two topologically different regimes, in which the curve is composed of one or two loops. The overall beam shape is described by the ray caustics that delimit the beams' bright regions. These caustics are inferred from the generalized Viviani curve through a geometric procedure that reveals connections with other physical systems and geometrical constructions. Depending on the regime, the caustics are composed either of two confocal ellipses or of segments of an ellipse and a hyperbola that are confocal. The weighting of the rays is shown to follow the two-mode meanfield Gross-Pitaevskii equations, which can be mapped to the equation of a simple pendulum. Finally, it is shown that the wave field can be accurately estimated from the ray description.

Keywords: structured light Ince-Gauss beams caustics Bose-Hubbard model ray optics pendulum; structured light; Ince-Gauss beams; caustics; Bose-Hubbard model; ray optics; pendulum

Domains: Optics [physics.optics]

R Gutiérrez-Cuevas, M R Dennis, Miguel Alonso. Ray and caustic structure of Ince-Gauss beams. New Journal of Physics, 2024, 26, ⟨10.1088/1367-2630/ad17dc⟩. ⟨hal-04440282⟩