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

摘要

Topological spin transport of electromagnetic waves (photons) in stationarysmoothly inhomogeneous isotropic medium is studied. By diagonalizing photonkinetic energy in Maxwell equations we derive the non-Abelian pure gaugepotential in the momentum space, which in adiabatic approximation fortransverse waves takes the form of two Abelian U(1) potentials corresponding tomagnetic monopole-type fields. These fields act on circularly polarized wavesresulting in the topological spin transport of photons. We deduce generalsemiclassical (geometrical optics) ray equations that take into account aLorentz-type force of the magnetic-monopole-like gauge field. Detailed analysisof rays in 3D medium with 2D periodic inhomogeneity is presented. It is shownthat rays located initially in the inhomogeneity plane experience topologicaldeflections or splitting that move them out from this plane. The dependence ofthe rays' deflection on the parameters of the medium and on the direction ofpropagation is studied.