Control of optical spin Hall shift in phase-discontinuity metasurface by weak value measurement post-selection

Spin Hall effect of light is a spin-dependent transverse shift of optical beam propagating along a curved trajectory, where the refractive index gradient plays a role of the electric field in spin Hall effect of solid-state systems. In order to observe optical spin Hall shift in a refraction taking place at air-glass interface, an amplification technique was necessary such as quantum weak measurement. In phase-discontinuity metasurface (PMS) a rapid phase-change along metasurface takes place over subwavelength distance, which leads to a large refractive index gradient for refraction beam enabling a direct detection of optical spin Hall shift without amplification. Here, we identify that the relative optical spin Hall shift depends on incidence angle at PMS, and demonstrate a control of optical spin Hall shift by constructing weak value measurement with a variable phase retardance in the post-selection. Capability of optical spin Hall shift control permits a tunable precision metrology applicable to nanoscale photonics such as angular momentum transfer and sensing.