Anderson self-localization of light in pair plasmas

Abstract

We demonstrate that in pair plasma weakly nonlinear electromagnetic waves, $a_0 \leq 1$, experience Anderson self-localization. The beat between the driver and a back-scattered wave creates charge-neutral, large random density fluctuations $\delta n/n_0 \gg 1$, and corresponding fluctuations of the dielectric permittivity $\epsilon$ (random plasma density grating). Propagating in quasi-1D, waves in a medium with spatially random self-created fluctuations of dielectric permeability experience localization. {In the linear regime, the instability can be classified as Induced Brillouin Scattering; it is described by the parameter $\rho _L = \left( a_0 { \omega_{p}/ }{\omega}\right)^{2/3} \leq 1 $, related to the Pierce parameter of Free Electron Lasers. In the cold case, the growth rate is $\Gamma \approx \rho _{L} \omega$ ($a_0 $ is laser nonlinearity parameter, $\omega_p$ is plasma frequency, $\omega$ is the laser frequency). } Anderson self-localization of light leads to (i) reflection of EM waves by the under-dense pair plasma; (ii) a wave already present inside the plasma separates into bright trapped pockets and dark regions. Mild initial thermal spread with $\Theta \equiv k_B T/(m_e c^2) \approx a_0^2$, restores wave propagation by suppressing the seeds of parametrically unstable density fluctuations. A circularly polarized driver produces linearly polarized structures, with position angle varying randomly between the bright pulses. Time-variability of the resulting density structures does not suppress localization due to remaining corrections (not white noise). We discuss possible applications to astrophysical Fast Radio Bursts.