Time-domain properties of electromagnetic signals in a dynamical axion background

Electromagnetic waves in a dynamical axion background exhibit superluminal group velocities at high frequencies and instabilities at low frequencies, altering how photons propagate through space. Local disturbances propagate causally, but unlike in ordinary Maxwell theory, propagation occurs inside as well as on the lightcone. For the unstable modes, the energy density in the electromagnetic field grows exponentially along timelike displacements. In this paper we derive retarded Green functions in axion electrodynamics in various limits and study the time-domain properties of propagating signals.