Topological spin transport of photons: Magnetic monopole gauge field in Maxwell's equations and polarization splitting of rays in periodically inhomogeneous media

Topological spin transport of electromagnetic waves (photons) in stationary smoothly inhomogeneous isotropic medium is studied. By diagonalizing the photon kinetic energy in Maxwell equations, we derive the non-Abelian pure gauge potential in the momentum space, which in adiabatic approximation for transverse waves takes the form of two U(1) Abelian potentials corresponding to magnetic monopole-type fields. These fields act on circularly polarized waves resulting in the topological spin transport of photons. We deduce general semiclassical (geometrical optics) ray equations that take into account a Lorentz-type force of the magnetic-monopole-like gauge field. Detailed analysis of rays in three-dimensional medium with two-dimensional periodic inhomogeneity is presented. It is shown that rays located initially in the inhomogeneity plane experience topological deflections or splitting that move them out from this plane. The dependence of the rays' deflection on the parameters of the medium and on the direction of propagation is studied.