Global phase and frequency comb structures in nonlinear Compton and Thomson scattering

The Compton and Thomson radiation spectra generated in collisions of an electron beam with a powerful laser beam are studied in the framework of quantum and classical electrodynamics, respectively. We show that there are frequency regimes where both radiation spectra are nearly identical, which for Compton scattering relates to the process which preserves the electron spin. Although the radiation spectra are nearly identical, the corresponding probability amplitudes exhibit different global phases. This has pronounced consequences, which we demonstrate by investigating temporal power distributions in both cases. We show that, contrary to Thomson scattering, it is not always possible to synthesize short laser pulses from Compton radiation. This happens when the global phase of the Compton amplitude varies in a nonlinear way with the frequency of emitted photons. We also demonstrate that, while the Compton process driven by a nonchirped laser pulse can generate chirped bursts of radiation, this is not the case for the Thomson process. In principle, both processes can lead to a generation of coherent frequency combs when single or multiple driving laser pulse collide with electrons. Once we synthesize these combs into short bursts of radiation, we can control them, for instance, by changing the time delay between the driving pulses.