  An inhomogeneous anisotropic medium with specific structure geometry can
apply the tunable spin-dependent geometrical phase to the light passing through
the medium, and thus can be used to steer the spin-dependent splitting (SDS) of
light. In this paper, we exemplify this inference by the q plate, an
inhomogeneous anisotropic medium. It is demonstrated that when a linearly
polarized light beam normally passes through a q plate, k-space SDS first
occurs, and then the real-space SDS in the far-field focal plane of a
converging lens is distinguishable. Interestingly, the SDS, described by the
normalized Stokes parameter S3 shows a multilobe and rotatable splitting
pattern with rotational symmetry. Further, by tailoring the structure geometry
of the q plate and/or the incident polarization angle of light, the lobe number
and the rotation angle both are tunable. Our result suggests that the q plate
can serve as a potential device for manipulating the photon spin states and
enable applications such as in nano-optics and quantum information.
