Helicity Density of Tightly Focused Hybridly Polarized Beam

In this paper, using the Richards-Wolf formalism, we investigate the helicity of hybrid vector vortex beams, which represent beams with various combinations of topological charges (vortex orders) and polarization orders. It is shown that the helicity in such beams is centrally asymmetric. It was shown that when focusing an optical vortex with hybrid polarization, both the intensity and the helicity density do not exhibit radial symmetry, but have central symmetry. Unlike non-vortex beams with hybrid polarization, an asymmetry in the zones with negative and positive helicity density values is observed. For example, for a beam with a unit polarization order and a unit topological charge, the maximum positive helicity density values are approximately half the absolute value of the minimum negative values. Such an asymmetry in the helicity density zones has not been previously observed in beams.