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When an electron is scattered by a tightly-focused laser beam in vacuum, theintensity gradient is a critical factor to influence the electron dynamics, forexample, the electron energy exchange with the laser fields as have beenexplored before [P.X.Wang et al.,J. Appl. Phys. 91, 856 (2002]. In this paper,we have further investigated its influence upon the electron high-harmonicgeneration (HHG) by treating the spacial gradient of the laser intensity as aponderomotive potential. Based upon perturbative QED calculations, it has beenfound that the main effect of the intensity gradient is the broadening of theoriginally line HHG spectra. A one-to-one relationship can be built between thebeam width and the corresponding line width. Hence this finding may provides usa promising way to measure the beam width of intense lasers in experiments. Inaddition, for a laser pulse, we have also studied the different influences fromtransverse and longitudinal intensity gradients upon HHG.

Influence of the intensity gradient upon HHG from free electrons scattered by an intense laser beam