The spirality of beams defined on the Poincare sphere

This research examines spirality characteristics in Poincaré beams under tight focusing conditions through the Richards-Wolf vector diffraction framework. Key findings reveal that spirality in such beams exhibits radial symmetry and remains invariant to azimuthal variations across the beam cross-section. The spirality magnitude peaks at polar angles Θ = 0 or π (associated with circularly polarized optical vortices) and vanishes entirely at Θ = π/2 (corresponding to cylindrical vector beams). Notably, non-zero spirality values persist along the optical axis for beam orders n = 0, 1, and 2. A direct proportionality is observed between the beam's intensity profile and its spirality distribution when Θ = 0, differing only by a scaling factor. These results highlight the unique interplay between polarization geometry and focused-field properties in structured light systems.