  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 Green's 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.
