Optical spin and orbital Hall effects at the tight focus of the superposition of two coaxial cylindrical vector beams with different-parity numbers

Abstract

We study properties of a light field at the tight focus of the superposition of two different-order cylindrical vector beams (CVBs). In the source plane, this superposition has a polarization singularity index amounting to the half-sum of the numbers of two constituent CVBs, while having neither spin angular momentum (SAM) nor transverse energy flow. We show that if the constituent CVBs have different-parity numbers, in the focal plane there occur areas that have opposite-sign longitudinal SAM projections, alongside areas of opposite-handed energy flows rotating on closed paths (clockwise and anticlockwise). The observed phenomena indicate that longitudinal optical spin/orbital Hall effects occur in the focal plane. It is found that if the two constituent CVBs have the same-parity numbers, in the focal plane the light field is inhomogeneously linearly polarized and the energy flow (Umov-Poytning vector) has just a longitudinal component. It is also shown that in the focal plane, the intensity of the on-axis superposition of two opposite-parity CVBs is defined by the sum of the constituent beams’ intensities, as though the two beams would be orthogonally polarized. Meanwhile, in the source plane, the beams under study are not orthogonally polarized and the relation for the intensity contains an interference term.