Polarization Möbius strip at the tight focus of a generalized Poincaré beam

Abstract

Based on the Richards-Wolf formalism, we investigate tight focusing of a generalized Poincaré beam. Analytical expressions are derived for all components of the electric field strength vector in the focal plane. For superposition of a right-handed circularly polarized plane wave with a left-handed circularly polarized optical vortex with topological charge –1, we obtain expressions for the intensity distribution and the longitudinal component of the spin angular momentum vector at the tight focus. We demonstrate both theoretically and numerically that the initial beam has topological charge –1/2 and, in the center of the focal plane, there is a C-point (a point with circular polarization which makes a C-line along the optical axis) with the singularity index of –1/2 (star), whereas the vector of major axis of the polarization ellipse makes along a certain-radius circle around the optical axis a single-side polarization Möbius stripe of the order –3/2, which has three half-turnovers and one stitching, where two opposite major axis vectors of the polarization ellipse meet.