Spin-orbit interaction of a photon in an inhomogeneous medium

As light propagates in an optically inhomogeneous medium, bending and twisting of the beam cause the rotation of the polarization plane. This is the well-known Rytov-Vladimirsky effect or Berry phase. Considering this effect as the result of an interaction between the spin of the photon (polarization) and its orbital motion, one can expect the reverse effect. In fact, the additional angular shift of a trajectory of the circularly polarized beam (CPB) was recently studied for the particular case of an optical fiber. In this paper the spin-orbit interaction Hamiltonian is obtained both in geometrical optics and in wave optics. We have calculated also the effect of the transverse shift of CPB under refraction on the boundary of two media. The expressions for the angular shift of a trajectory of CPB in optical fibers with two types of refractive-index profiles have been obtained. Geometrical optics expressions can be applied for the typical waveguides only at lengths less than 0.05 cm. However, using the geometric optical picture we can successfully describe statistical properties of speckle patterns of laser radiation as it propagates at a considerable distance.