  We study how transition radiation is modified by the presence of a generic
magnetoelectric medium with a special focus on topological insulators. To this
end, we use the Green's function for the electromagnetic field in presence of a
plane interface between two topological insulators with different topological
parameters, permittivities and permeabilities. We employ the far-field
approximation together with the steepest descent method to obtain approximate
analytical expressions for the electromagnetic field. Through this method we
find that the electric field is a superposition of spherical waves and lateral
waves. Contributions of both kind can be attributed to a purely topological
origin. After computing the angular distribution of the radiation, we find that
in a region far from the interface the main contribution to the radiation comes
from the spherical waves. We present typical radiation patterns for the
topological insulator TlBiSe$_2$ and the magnetoelectric TbPO$_4$. In the
ultra-relativistic case, the additional contributions from the magnetoelectric
coupling appreciably enhance the global maximum of the angular distribution. We
also present an analytic expression for the frequency distribution of the
radiation for this case. We find that in the limit where the permittivities are
equal there still exists transition radiation of the order of the square of the
topological parameter with a pure topological origin.
