Ray-optical Poincaré sphere for structured Gaussian beams

• DOI: 10.1364/optica.4.000476
• Publication Date: 2017-04-19T15:57:52Z
• Authors: Miguel A. Alonso; Mark R. Dennis
• Keywords: Stereographic projection; Ellipse; Laguerre polynomials

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