Quadratic spin Hall effect of light due to phase change

The spin Hall effect (SHE) of light has brought important applications, but the involved spin states only split in one direction. Here we employ an accurate three-dimensional model of light to show that the SHE generally exhibits quadratic spin splitting, i.e., both vertical and horizontal splitting, in the presence of a fast phase change of reflection. Further, we disclose that the two splittings are actually different from each other, and that they originate from the vertical and horizontal spin momentum flows, respectively, owing to the spatial gradient of polarization in the individual direction. Finally, it is found that by tuning the incident angle and polarization of light, one can manipulate the quadratic SHE so as to realize a variety of spin splittings, such as unbalanced quadratic splitting and off-center splitting of spin states.