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The spin-orbit interaction of light is a crucial concept for understandingthe electromagnetic properties of a material and realizing the spin-controlledmanipulation of optical fields. Achieving these goals requires a completedescription of spin-dependent optical phenomena in the context of vector-wavemechanics. We develop an extended Dirac theory for optical fields in genericmedia, which was found to be akin to a non-Hermitian chiral-extension ofmassive fermions with anomalous magnetic momenta moving in an externalpseudo-magnetic field. This similarity allows us to investigate the opticalbehaviors of a material by effective field theory methods and can find wideapplications in metamaterials, photonic topological insulators, etc. Wedemonstrate this method by studying the spin-orbit interaction of structuredlight in a spin-degenerate medium and inhomogeneous isotropic medium, whichleads to both spin-orbital-Hall effects and spin-to-orbital angular momentumconversion. Of importance, our approach provides simple and clear physicalinsight into the spin-orbit interaction of light in generic media, and couldpotentially bridge our understanding of topological insulators betweenelectronic and photonic systems.

Four-Vector Optical Dirac Equation and Spin-Orbit Interaction of Structured Light