Self-modulation of fast radio bursts

Fast radio bursts (FRBs) are extreme astrophysical phenomena entering the realm of non-linear optics, a field developed in laser physics. A classical non-linear effect is self-modulation. We examine the propagation of FRBs through the circumburst environment using the idealized setup of a monochromatic linearly polarized GHz wave propagating through a uniform plasma slab of density N at distance R from the source. We find that self-modulation occurs if the slab is located within a critical radius R_crit ∼ 10¹⁷(N/10² cm⁻³)(L/10⁴² erg s⁻¹) cm, where L is the isotropic equivalent of the FRB luminosity. Self-modulation breaks the burst into pancakes transverse to the radial direction. When R ≲ R_crit, the transverse size of the pancakes is smaller than the Fresnel scale. The pancakes are strongly diffracted as the burst exits the slab, and interference between the pancakes produces a frequency modulation of the observed intensity with a sub-GHz bandwidth. When R ∼ R_crit, the transverse size of the pancakes becomes comparable with the Fresnel scale, and the effect of diffraction is weaker. The observed intensity is modulated on a time-scale of 10 μm, which corresponds to the radial width of the pancakes. Our results suggest that self-modulation may cause the temporal and frequency structure observed in FRBs.