Axion-Photon Mixing in 3D: Classical Equations and Geometric Optics

Light particle-photon mixing in magnetised plasmas plays a vital role in constraining the existence of new physics, especially axions, dark photons, and ultra-high-frequency gravitational waves. Recently, we derived an expression for the resonant conversion of axions to photons in inhomogeneous media using kinetic theory to derive photon transport equations. In this work, we show how the same expression for the conversion probability can be obtained from the classical wave equations of axion-electrodynamics by deriving an equivalent transport equation along the photon worldline. This result provides further corroboration of this expression for the resonant production of photons from light particles, which has also recently been supported by independent numerical simulations of full axion-electrodynamics. In addition, this new approach provides a more general expression that accounts for mixing away from resonance, which is integrated along the whole worldline of the photon in a way that naturally incorporates a curved photon trajectory relevant to refractive media where the photon and light-particle worldlines differ.