Reversed electromagnetic Vavilov-Čerenkov radiation in naturally existing magnetoelectric media

Abstract

We consider two semi-infinite magnetoelecteric 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 which can be directly generalized to cylindrical and spherical configurations of two magnetoelectrics separated by an interface. We establish the far-field approximation of the 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-Čerenkov radiation in naturally existing magnetoelectric media. In the case where one of the magnetolectrics is a 3D topological insulator, ${\mathrm{TlBiSe}}_2$ for example, located in front of a regular insulator, we estimate that an average forward Vavilov-Čerenkov radiation with frequency $\sim 2.5\mathrm{eV}$ ($\sim 500\mathrm{nm}$) will produce a highly suppressed reversed Vavilov-Čerenkov radiation which can be characterized by an effective frequency in the range of $\sim (4\times 10^{-3}-0.5)\mathrm{meV}$. However, this value compares favorably with recent measurements in left-handed metamaterials yielding reversed Vavilov-Čerenkov radiation with frequencies of the order of $(1.2-3.9)\times 10^{-2}\mathrm{meV}$.

arXiv comment18 pages, 7 figures, typos corrected, match published version

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