Analytic treatment of nonparaxial full-Poincaré fields: singularity structure and trapping properties

An analytic extension to the nonparaxial regime of the full-Poincaré (FP) beams is presented. Instead of the stereographic mapping used in the paraxial case, these FP fields are defined in terms of a mapping from the polarization Poincaré sphere onto the sphere of plane-wave directions. It is shown that multipolar fields with complex arguments can be used to implement this mapping and provide closed-form expressions. The three-dimensional polarization singularities of the resulting fields are studied with the help of auxiliary fields presenting vortices at points where the polarization is circular or linear. Finally, the Mie scattering and trapping properties of the FP fields are studied, both of which are greatly simplified by the choice of fields.