Spin Hall effect of light under arbitrarily polarized and unpolarized light

The spin Hall effect of light (SHEL), which refers to a spin-dependent and transverse splitting at refraction and reflection phenomena, inherently depends on the polarization states of the incidence. Most of the previous research have focused on a horizontally or vertically polarized incidence, in which the analytic formula of the shift is well-formulated and SHEL appears symmetrically in both shift and intensity. However, the SHEL under an arbitrarily polarized or unpolarized incidence has remained largely unexplored. Whereas the SHEL under other polarization is sensitive to incident polarization and is asymmetrical, here we demonstrate that the SHEL is independent of the incident polarization and is symmetrical in shift if Fresnel coefficients of the two linear polarization are the same. The independence of the shift with respect to the incident polarization is proved both analytically and numerically. Moreover, we prove that under an unpolarized incidence composed of a large number of completely random polarization states, the reflected beam is split in half into two circularly polarized components that undergo the same amount of splitting but in opposite directions. This result means that under unpolarized incidence, the SHEL occurs exactly the same as under horizontally or vertically polarized incidence. We believe that the incident-polarization-independent SHEL can broaden the applicability of the SHEL to cover optical systems in which polarization is ill-defined.