Spin splitting of vortex beams on the surface of natural biaxial hyperbolic materials

We investigated the spin splitting of vortex beam on the surface of biaxial natural hyperbolic materials (NHMs) rotated by an angle with respect to the incident plane. An obvious asymmetry of spatial shifts produced by the left-handed circularly (LCP) component and right-handed circularly polarized (RCP) component is exhibited. We derived the analytical expression for in- and out-of-plane spatial shifts for each spin component of the vortex beam. The orientation angle of the optical axis plays a key role in the spin splitting between the two spin components, which can be reflected in the simple expressions for spatial shifts without the rotation angle. Based on an α-MoO₃ biaxial NHM, the spatial shifts of the two spin components with the topological charge were investigated. As the topological charge increases, the spatial shifts also increase; in addition, a tiny spatial shift close to zero can be obtained if we control the incident frequency or the polarization of the reflected beams. It can also be concluded that the maximum of the spin splitting results from the LCP component at p-incidence and the RCP component at s-incidence in the RB-II hyperbolic frequency band. The effect of the incident angle and the thickness of the α-MoO₃ film on spin splitting is also considered. These results can be used for manipulating infrared radiation and optical detection.