We study induced (stimulated) scattering of linearly polarized, strong electromagnetic waves in pair plasmas, which is crucial for understanding the propagation of fast radio bursts (FRBs). Magnetars are the most promising progenitors of FRBs, and FRBs propagate through the magnetar wind and successfully escape before being significantly scattered. We revisit the steady-state solution of linearly polarized electromagnetic waves in pair plasmas with arbitrary amplitude, and demonstrate that the nonlinearity is characterized by the nonlinearity parameter $a_0{\omega }_{pe}/{\omega }_0$ rather than the dimensionless amplitude $a_0$, where ${\omega }_{pe}$ is the electron plasma frequency and ${\omega }_0$ is the wave frequency in the frame in which the plasma is at rest when the wave fields vanish. We follow the time evolution of the steady-state solution for the linear regime $a_0{\omega }_{pe}/{\omega }_0\ll 1$ by performing one-dimensional particle-in-cell simulations, and show that the conventional linear analysis of induced scattering assuming $a_0\ll 1$ is applicable even for $a_0>1$ when the Lorentz boost due to the plasma motion in the incident wave is considered. The saturation level is controlled by $a_0{\omega }_0/{\omega }_{pe}$, which corresponds to the ratio of the wave energy to the plasma energy, and the incident wave is hardly scattered for $a_0{\omega }_0/{\omega }_{pe}\gg 1$. We discuss the application of our results to FRBs.

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• Electromagnetic radiation astronomy
• Laser-plasma interactions
• Transient & explosive astronomical phenomena
• Wave-wave, wave-particle interactions