  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.
