The spin-orbit interaction and the spin-spin interaction of photons in an inhomogeneous medium

By means of the optical metric, we investigate the propagation of a polarized light in an inhomogeneous medium in this paper. We find that the evolution of photons is affected by the spin-spin interaction of photons, besides the spin-orbit interaction. Due to the spin-spin interaction, there is a small deflection of the ray trajectory of the polarized light along the direction of the inhomogeneity gradient of the medium. It is different from the transverse deflection described by the spin Hall effect of photons.