Polarized electromagnetic radiation by chiral media with time-dependent chiral chemical potential

We investigate photon production from media characterized by a time-dependent chiral chemical potential $\mu_5(t)$. We first consider the chiral anomaly as a small perturbation and show that $\mu_5\to 2\gamma$ process generates non-polarized radiation, as the probabilities of producing right and left-handed photons are equal. In chiral semimetal with a vanishing chiral chemical potential but a finite separation of Weyl nodes, ${\bf \Delta}(t)$, the photon production vanishes at the leading order of perturbation theory. We then employ the method of Bogolyubov transformation to obtain the photon spectrum that sums up all powers of $\mu_5$. Employing the exactly solvable model $\mu_5(t) \propto A+B\tanh(t/\tau)$, we demonstrate that the spectrum exhibits strong circular polarization, whose direction is determined by the sign of $\mu_5$. The spectrum contains resonances associated with the instability of the electromagnetic field in chiral media. We discuss potential phenomenological applications of these findings.