Reversed electromagnetic Vavilov-Cerenkov radiation in naturally existing magnetoelectric media

We consider two semi-infinite magnetoelectric media separated by a planar interface whose electromagnetic response is described by axion electrodynamics. The time-dependent Green's function characterizing this geometry is obtained by a method that can be directly generalized to cylindrical and spherical configurations of two magnetoelectrics separated by an interface. We establish the far-field approximation of Green's function and apply these results to the case of a charged particle moving from one medium to the other at a high constant velocity perpendicular to the interface. From the resulting angular distribution of the radiated energy per unit frequency, we provide theoretical evidence for the emergence of reversed Vavilov-Cerenkov radiation in naturally existing magnetoelectric media. In the case where one of the magnetoelectrics is a 3D topological insulator, TlBiSe2, for example, located in front of a regular insulator, we estimate that an average forward Vavilov-Cerenkov radiation with frequency similar to 2.5 eV (similar to 500 nm) will produce a highly suppressed reversed Vavilov-Cerenkov radiation, which can be characterized by an effective frequency in the range of similar to(4 x 10(-3) - 0.5) meV. However, this value compares favorably with recent measurements in left-handed metamaterials yielding reversed Vavilov-Cerenkov radiation with frequencies of the order of (1.2-3.9) x 10(-2) meV.