Spectral distributions of Thomson-scattered photons from high-intensity pulsed lasers

General formulas for the far-field spectral distribution of photons Thomson scattered by a single electron have been obtained. Effects due to the pulsed nature of the laser beam are explicitly allowed, simultaneously with intensity high enough that harmonic generation is possible. For realistic pulsed photon beams, the spectrum of backscattered radiation is considerably broadened because of changes in the longitudinal velocity of the electrons during the pulse. Such ponderomotive broadening is especially pronounced at higher harmonics, eventually leading to a continuous emission spectrum.