Optimizing Laser Pulses for Narrowband Inverse Compton Sources in the High-Intensity Regime

Scattering of ultraintense short laser pulses off relativistic electrons allows one to generate a large number of X- or $\gamma$-ray photons with the expense of the spectral width---temporal pulsing of the laser inevitable leads to considerable spectral broadening. In this Letter, we describe a simple method to generate optimized laser pulses that compensate the nonlinear spectrum broadening, and can be thought of as a superposition of two oppositely linearly chirped pulses delayed with respect to each other. We develop a simple analytical model that allow us to predict the optimal parameters of such a two-pulse---the delay, amount of chirp and relative phase---for generation of a narrowband {\gamma}-ray spectrum. Our predictions are confirmed by numerical optimization and simulations including 3D effects.