Shape effects in nonlinear Thomson and Compton processes: the quest for MeV high-order harmonics

Spectra of Thomson and Compton radiation, emitted during electron scattering off an intense laser beam, are calculated using the frameworks of classical and strong-field quantum electrodynamics, respectively. Both approaches use a plane-wave-fronted pulse approximation regarding the driving laser beam. Within this approximation, a very good agreement between Thomson and Compton frequency distributions is observed provided that frequencies of the emitted radiation is relatively low. The dependence of frequency spectra on the laser pulse envelope is analyzed. This becomes important in the context of ultra-short pulse generation, as illustrated by numerical examples.