The spin-orbit interaction of light is a crucial concept for understanding
    the electromagnetic properties of a material and realizing the spin-controlled
    manipulation of optical fields. Achieving these goals requires a complete
    description of spin-dependent optical phenomena in the context of vector-wave
    mechanics. We develop an extended Dirac theory for optical fields in generic
    media, which was found to be akin to a non-Hermitian chiral-extension of
    massive fermions with anomalous magnetic momenta moving in an external
    pseudo-magnetic field. This similarity allows us to investigate the optical
    behaviors of a material by effective field theory methods and can find wide
    applications in metamaterials, photonic topological insulators, etc. We
    demonstrate this method by studying the spin-orbit interaction of structured
    light in a spin-degenerate medium and inhomogeneous isotropic medium, which
    leads to both spin-orbital-Hall effects and spin-to-orbital angular momentum
    conversion. Of importance, our approach provides simple and clear physical
    insight into the spin-orbit interaction of light in generic media, and could
    potentially bridge our understanding of topological insulators between
    electronic and photonic systems.

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