Spin-orbit interaction of light: When twisted light meets twisted metasurfaces

Singular optics and metamaterials are both fascinating branches of modern optics. While the twist of vortex beams in phase and polarization leads to singularities, the twist of metasurfaces also leads to extraordinary properties in both optics and electronics. Here we present the spin-orbit interaction of a vortex beam reflected on twisted few-layer hyperbolic metasurfaces. As a result, the spatial Imbert-Fedorov (IF) shift and photonic spin Hall effect (PSHE) shift are investigated. We find that the spatial IF shift versus twist angle is symmetrical about the $l=0$ shift and it is symmetrical about the origin for opposite twist angle with opposite topological charge. In addition, the PSHE shift versus twist angle is also symmetrical about the $l=0$ shift. The shifts are enhanced with increasing topological charge and show a pretty different dependence on the twist angle when the incident beam is in different polarization state. These findings provide a different perspective for further investigations of twisted light and twisted metasurfaces.