Focusing effects in laser-electron Thomson scattering

We study the effects of laser pulse focusing on the spectral properties of Thomson scattered radiation. Modeling the laser as a paraxial beam we find that, in all but the most extreme cases of focusing, the temporal envelope has a much bigger effect on the spectrum than the focusing itself. For the case of ultrashort pulses, where the paraxial model is no longer valid, we adopt a subcycle vector beam description of the field. It is found that the emission harmonics are blue shifted and broaden out in frequency space as the pulse becomes shorter. Additionally the carrier envelope phase becomes important, resulting in an angular asymmetry in the spectrum. We then use the same model to study the effects of focusing beyond the limit where the paraxial expansion is valid. It is found that fields focussed to subwavelength spot sizes produce spectra that are qualitatively similar to those from subcycle pulses due to the shortening of the pulse with focusing. Finally, we study high-intensity fields and find that, in general, the focusing makes negligible difference to the spectra in the regime of radiation reaction