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

TL;DR

This paper introduces a novel four-vector optical Dirac equation framework to analyze the spin-orbit interaction of structured light, revealing new effects and providing deeper physical insights into light-matter interactions in complex media.

Contribution

It develops an extended Dirac theory for optical fields in media, enabling effective field theory analysis of spin-dependent phenomena and bridging understanding between electronic and photonic topological systems.

Findings

Demonstrates spin-orbit Hall effects in structured light

Shows spin-to-orbital angular momentum conversion

Provides a unified physical insight into light's spin-orbit interaction

Abstract

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.