Generation of optical chirality by the tightly focused higher-order Poincaré sphere vector vortex beams

We derive the analytical expressions of the electric and magnetic field vectors as well as optical chirality density of tightly focused higher-order Poincaré sphere (HOPS) vector vortex beams based on the Richards-Wolf vector diffraction theory. The optical chirality density induced by the tightly focused HOPS vector vortex beams is systematically explored, and its roles with respect to ellipticity, handedness, orientation, polarization topological charge (PTC), and vortex topological charge (VTC) are deeply revealed. The research results show that apart from the orientation of the polarization ellipse, other parameters of the input vortex beams have a significant influence on the optical chirality density of the tightly focused fields. It is noteworthy that because of the introduction of vortex phase, the optical chirality density of linearly polarized light before being focused carrying no spin angular momentum (SAM) is no longer zero. The change of the sign of VTC and PTC has an important effect on the sign of optical chirality density of the tightly focused fields, whereas its spatial distribution and magnitude mainly arises from the change of the value of VTC and PTC. Furthermore, for the non-linearly polarized input beam, due to the interplay of the orbital angular momentum (OAM) and SAM, the sign and value of VTC and ellipticity have an important influence not only on the sign, but also on the spatial distribution and magnitude of the optical chirality density. These research results may provide new insights into the chiral light–matter​ interactions and find potential applications in chiral particle trapping, manipulation, and so on.