Tunable spatial and angular spin splitting of reflected vortex-beam off hyperbolic metasurface

Abstract

This paper investigated the spin splitting of the reflected beam with a vortex beam irradiating on a hyperbolic metasurface. This metasurface structure is the periodically rectangular-groove array on the surface of a hyperbolic crystal with the optical axis normal to its surface, where the array is a sub-wavelength biaxially hyperbolic grating with its periodical direction situated in the surface plane. Based on the hexagonal nitride boron crystal, we theoretically and numerically analyzed the spatial and angular spin splittings of the reflected beam, containing those produced by the transverse and longitudinal shifts. We found that the spatial shifts or spin splitting can be obtained in the first-order approximation of beam deflection, but the angular shifts can be described in the second-order approximation so that it enormously varies with the beam waist. Due to the hyperbolic anisotropy of the metasurface and the intrinsic orbital angular momentum in the incident beam, the expressions of spatial and angular shifts are effectively modified, and a unique double reflection effect occurs on the surface. Near certain reflective intensity distribution singularities, extremely asymmetrical spin splitting can be observed. These shifts and spin splitting can be tuned by varying the orientation of the incident plane and the angle of incidence.