Helicity density of higher-order Poincaré beams in tight focus

Abstract

Helicity of higher-order Poincaré beams was investigated from the point of view of the Richards-Wolf formalism, which takes into account vector effects in the focal spots of lenses with large numerical aperture. It was shown that the helicity density for Poincaré beams always has radial symmetry and does not depend on the azimuthal angle of the beam section. The absolute value of helicity density is maximum when the polar angle of the beam is zero or π (optical vortex with circular polarization). Helicity is absent when the polar angle is π/2 (cylindrical vector beam). Non-zero values of helicity density on the optical axis are observed for beam orders 0, 1, and 2. If the polar angle of the beam is zero, the intensity of Poincaré beams coincides with the helicity density up to a factor.