  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.
