We consider two semi-infinite magnetoelectric media with constant dielectric permittivity separated by a planar interface, whose electromagnetic response is described by non-dynamical axion electrodynamics and investigate the radiation of a point-like electric dipole located perpendicularly to the interface. We start from the exact Greens function for the electromagnetic potential, whose far-field approximation is obtained using a modified steepest descent approximation. This procedure yields the standard spherical waves as well as axially symmetric cylindrical superficial waves, which nevertheless are restricted to a region very close to the interface. We compute the angular distribution of the radiation and the total radiated power finding different interference patterns, depending on the relative position dipole-observer, and polarization mixing effects which are all absent in the standard dipole radiation. They are a manifestation of the magnetoelectric effect induced by axion electrodynamics. We illustrate our findings with some numerical estimations employing realistic media as well as some hypothetical choices in order to illuminate the effects of the magnetoelectric coupling which is usually very small.
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