Anderson self-localization of light in pair plasmas

We demonstrate that in pair plasma weakly nonlinear electromagnetic waves, $a_0\le 1$, experience Anderson self-localization. The beat between the driver and a back-scattered wave creates charge-neutral, large random density fluctuations $\delta n\mathrm{/}{n}_0\gg 1$, 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 ${\rho }_L={\left(a_0{\omega }_p\mathrm{/}\omega \right)}^{2\mathrm{/}3}\le 1$, related to the Pierce parameter of Free Electron Lasers. In the cold case, the growth rate is $\mathrm{\Gamma }\approx {\rho }_L\omega$ ($a_0$ 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 $\mathrm{\Theta }\equiv k_{B}T\mathrm{/}(m_e{c}^2)\approx a_0^2$, 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.