Description
The discovery of Fast Radio Bursts (FRBs) has been the most important breakthrough in radio astronomy since the discovery of pulsars. FRBs are capable of releasing a huge amount of energy in GHz waves (up to $10^{39}{\rm erg}$) in just a few milliseconds. FRB sources are most likely magnetars, i.e. neutron stars carrying a huge magnetic field. Due to the huge luminosity of FRBs, sufficiently close to the source electrons in the field of the FRB electromagnetic wave oscillate with ultra-relativistic velocities. At a distance of $10^{11}{\rm cm}$ from the neutron star, which corresponds to $10^5$ stellar radii, the FRB wave strength parameter is $a_0\sim 100$. The properties of the plasma that surrounds FRB sources are very different with respect to laboratory plasmas. The plasma is strongly magnetized (energy density of the background magnetic field $\gg$ particle rest mass energy density) and composed of electron-positron pairs. The frequency of the FRB electromagnetic wave can exceed the local plasma frequency by several orders of magnitudes. I will discuss the propagation of strong electromagnetic waves in such an environment. I will show that the escape of FRBs from the source puts non-trivial constraints on theoretical emission models of FRBs. Finally, I will discuss imprints of propagation effects on the observed temporal and spectral structure of FRBs.