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

When an electron is scattered by a tightly focused laser beam in vacuum, the intensity gradient is a critical factor to influence the electron dynamics. In this paper, we have further investigated its influence upon the electron high-harmonic generation (HHG) by treating the spacial gradient of the laser intensity as a ponderomotive potential. Based upon perturbative quantum electrodynamics calculations, it has been found that the main effect of the intensity gradient is the broadening of the originally line HHG spectra. A one-to-one relationship can be built between the beam width and the corresponding line width. Hence, this finding may provide us a promising way to measure the beam width of intense lasers in experiments. In addition, for a laser pulse, we have also studied the different influences from transverse and longitudinal intensity gradients upon HHG.