  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.
