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

Optical spin Hall (OSH) shift has been observed by weak measurement amplification in a refraction beam passing through air-glass interface, the refractive index gradient $\vec{\nabla} n$ being normal to the interface. Phase-discontinuity metasurface (PMS) possesses $\vec{\nabla} n$ tangential to the metasurface, and depending on the incidence angle either positive or negative refraction takes place satisfying the generalized Snell's law. Rapid phase-change over subwavelength distance at PMS leads to a large $\vec{\nabla} n$, enabling a direct observation of OSH shift. Here, we identify that the relative OSH shift between optical beams with spins $\pm 1$ depends on incidence and refraction angles at PMS, and construct a measurement of OSH effect with a variable phase retardance in the post-selection to demonstrate a control of transverse shift. and demonstrate a control of OSH shift by constructing a weak value measurement with a variable phase retardance in the post-selection. Capability of OSH shift control permits a tunable precision metrology applicable to nanoscale photonics such as angular momentum transfer and sensing.