Symmetry-Breaking Controlled Photonic Spin Hall Effect Induced by Spatially Offset Pancharatnam–Berry Phase Elements

A generalized mathematical model is established to describe the symmetry-broken photonic spin Hall effect (PSHE) induced by spatially offset Pancharatnam–Berry phase elements (PBPEs). This model qualitatively explains the spin-dependent separation of light beams in rotationally symmetric systems with offset PBPEs. Significantly, formalism yields a Bessel-type eigenmode solution, which supports the PSHE with constant spin separation maintained over extended propagation distances. Quantitative validation of this propagate-invariant PSHE over 30 cm propagation is achieved through a liquid crystal PBPE, and the dynamic control over the magnitude and direction of the spin separation is demonstrated, which can be extended to cylindrical vector beams. Finally, directionally adjustable edge detection of optical images is demonstrated by exploiting the spin-dependent phase shift. The results enable on-demand spin-separation manipulation with a new degree of freedom and are expected to provide new insights into spin optics.