  A spin current has novel linear and second-order nonlinear optical effects
due to its symmetry properties. With the symmetry analysis and the eight-band
microscopic calculation we have systematically investigated the interaction
between a spin current and a polarized light beam (or the "photon spin
current") in direct-gap semiconductors. This interaction is rooted in the
intrinsic spin-orbit coupling in valence bands and does not rely on the Rashba
or Dresselhaus effect. The light-spin current interaction results in an optical
birefringence effect of the spin current. The symmetry analysis indicates that
in a semiconductor with inversion symmetry, the linear birefringence effect
vanishes and only the circular birefringence effect exists. The circular
birefringence effect is similar to the Faraday rotation in magneto-optics but
involves no net magnetization nor breaking the time-reversal symmetry.
Moreover, a spin current can induce the second-order nonlinear optical
processes due to the inversion-symmetry breaking. These findings form a basis
of measuring a pure spin current where and when it flows with the standard
optical spectroscopy, which may provide a toolbox to explore a wealth of
physics connecting the spintronics and photonics.
