A Theory of Stimulated and Spontaneous Axion Scattering

We present a theory for the nonlinear, resonant excitation of dynamical axions due to counter-propagating electromagnetic waves in materials that break both $\mathcal{P}$ and $\mathcal{T}$ symmetries. We show that dynamical axions can mediate an exponential growth in the amplitude of the lower frequency (Stokes) beam, leading to effective transmittance and reflectance coefficients that exceed $1$. We also discuss spontaneous generation of the counter-propagating Stokes mode in the presence of only a single source owing to the resonant amplification of quantum or thermal fluctuations in the axion medium. Further, we show that the gain coefficient for amplification owing to dynamical axions can be orders of magnitude larger than that obtained in the related stimulated Brillouin scattering process, and is tunable using magnetic fields, making stimulated axion scattering promising for applications in optoelectronics.