Electromagnetic Radiation in chiral matter: the Cherenkov case

Starting from the modified Maxwell equations in Carroll-Field-Jackiw electrodynamics we study the electromagnetic radiation in a chiral medium characterized by an axion coupling $\theta(x)=b_\mu x^\mu$, with $b_\mu= (0,\mathbf{b})$, which gives rise to the magnetoelectric effect. Employing the stationary phase approximation we construct the Green's matrix in the radiation zone which allows the calculation of the corresponding electromagnetic potentials and fields for arbitrary sources. We obtain a general expression for the angular distribution of the radiated energy per unit frequency. As an application we consider a charge moving at constant velocity parallel to $\mathbf{b}$ in the medium and discuss the resulting Cherenkov radiation. We recover the vacuum Cherenkov radiation. For the case of a material with refraction index $n > 1$ we find that zero, one or two Cherenkov cones can appear. The spectral distribution of the radiation together with the comparison of the radiation output of each cone are presented, as well as some angular plots showing the appearance of the cones.