Full Poincaré beam delineation based on the Stokes vortex ring

Abstract

Axial and lateral polarization gradients in optical beams that can be created by counter/co-propagating fields have many applications including atom optics and optical lattices. One such beam studied in recent years is a Poincaré beam with interesting topological polarization structures such as Möbius strips, lemon, monstar, and star singularities. Though topological constructs such as linear and circular-basis hybrid-order Poincaré spheres are used to represent these beams as points on these spheres, there is no study on the spatial extent of these beams to qualify them as full Poincaré beams. In this article, we adopt the Stokes vortex ring approach to characterize Poincaré beams and their spatial extent. This ring separates the polarization states present in the beam into two parts that can be mapped onto two hemispherical regions on the fundamental Poincaré sphere. In general, a Poincaré beam containing C-points with its neighborhood of all sizes are treated on equal footing. Experimental and theoretical results are also presented to show that in finite-sized beams, the Stokes vortex ring can be tuned wisely to realize full Poincaré beams.