Exact Helicity-Orbital Coupled Dynamics in Chiral Media: An Optical Dirac Framework for Photonic Rabi Oscillations

Abstract

We demonstrate that light propagation in reciprocal chiral photonic media admits a unified description in terms of an emergent Dirac structure in helicity space. Starting from Maxwell's equations, we reformulate the electromagnetic field as a four-component spinor governed by an effective non-Hermitian optical Dirac equation. In this representation, the magnetoelectric response of the chiral medium appears as a helicity-dependent background that modifies the spectrum and eigenmodes, while the breaking of the spin-degenerate condition generates the intrinsic spin-orbit coupling between helicity and orbital degrees of freedom. After projection onto the positive-frequency sector, the theory reduces to an exact two-level helicity-orbital model. This model is found to have an analytical solution and describes coherent Rabi-like oscillations between spin-orbit-coupled vector modes. Chirality controls the helicity splitting and detuning, whereas the electromagnetic mismatch of the medium determines the coupling strength responsible for oscillatory spin-orbit conversion. The resulting dynamics is constrained by exact conservation of the total angular momentum, leading to reversible conversion between spin and orbital angular momentum with well-defined selection rules. Our work establishes an optical Dirac framework for structured light in chiral media, and provides experimentally accessible predictions for chirality-controlled oscillations, polarization dynamics, and orbital angular momentum conversion in structured optical fields.