  We propose an optical counterpart of the quantum spin Hall (QSH) effect in a
two-dimensional photonic crystal composed of a gyrotropic medium exhibiting
both gyroelectric and gyromagnetic properties simultaneously. Such QSH effect
shows unidirectional polarization-dependent transportation of photonic
topological edged states, which is robust against certain disorders and
impurities. More importantly, we find that such unique property is not
protected by conventional time-reversal symmetry of photons obeying the Bosonic
statistics but rather by the same symmetry, as electron's time-reversal
symmetry. Based on the tight-binding approximation approach, we construct an
effective Hamiltonian for this photonic structure, which is shown to have a
similar form to that of an electronic QSH system. Furthermore, the invariant of
such model is calculated in order to unify its topological non-trivial
character. Our finding provides a viable way to exploit the optical topological
property, and also can be leveraged to develop a photonic platform to mimic the
spin properties of electrons.
