Hybrid order Poincaré spheres for Stokes singularities

Hybrid order Poincaré spheres to represent more general Stokes singularities are presented. Polarization singularities form a subset of Stokes singularities, and therefore induction of these spheres brings completeness. The conventional understanding of Poincaré beams as hybrid order Poincaré sphere beams is also expanded to include more beams. Construction and salient properties of these spheres are explained with illustrations to show their ability to represent more exotic Poincaré beams that have zero total helicity irrespective of their size. Pancharatnam–Berry geometric phase formulation using these new spheres is also possible.