Photons in Media: A Second-Quantization Scheme Based on a Dirac-like Equation

Abstract

We develop a second-quantization framework for photons based on the optical Dirac equation of source-free Maxwell theory in generic media. In this formulation, the electromagnetic field is recast as a four-component spinor-like wave function that admits both positive-energy and negative-energy solutions, which are naturally interpreted as photon and antiphoton states. By expanding the field in terms of single-photon eigenmodes, we construct a consistent quantization scheme in which the photon field operators obey bosonic commutation relations, in close analogy with the Dirac quantization of electrons. In structured media, the optical Dirac equation acquires effective mass and coupling terms induced by the dielectric tensor, analogous to an electronic Dirac-type structure. This allows photon propagation in media to be interpreted in terms of boosted spinor states and provides a unified description of vacuum and medium-modified dispersion relations. The framework further reveals a natural quantum-mechanical origin of transverse spin in structured electromagnetic fields, including evanescent waves, where spin components perpendicular to the propagation direction emerge from the underlying helicity structure. In the context of optical Dirac theory, this work presents a quantum field-theoretic description of photons in both vacuum and media, offering a new perspective on photon quantization, spin-orbit interaction, and light-matter coupling in structured optical systems.