paper

A ray-optical Poincaré sphere for structured Gaussian beams

arXiv:1612.06824 · doi:10.1364/OPTICA.4.000476

Abstract

A general family of structured Gaussian beams naturally emerges from a consideration of families of rays. These ray families, with the property that their transverse profile is invariant upon propagation (except for cycling of the rays and a global rescaling), have two parameters, the first giving a position on an ellipse naturally represented by a point on the Poincaré sphere (familiar from polarization optics), and the other determining the position of a curve traced out on this Poincaré sphere. This construction naturally accounts for the familiar families of Gaussian beams, including Hermite-Gauss, Laguerre-Gauss and Generalized Hermite-Laguerre-Gauss beams, but is far more general. The conformal mapping between a projection of the Poincaré sphere and the physical space of the transverse plane of a Gaussian beam naturally involves caustics. In addition to providing new insight into the physics of propagating Gaussian beams, the ray-based approach allows effective approximation of the propagating amplitude without explicit diffraction calculations.

Main article 12 pages 10 figures; supplementary material (appendices) 7 pages, 3 figures

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