Nonlinear Compton Scattering in a Pulsed Focused Laser Beam

We have calculated the radiation emitted from free electrons in an ultrashort pulsed laser focus. For low electron densities, where space charge is negligible, we find that ponderomotive forces limit the effective volume where the radiation is emitted to a region much smaller than the waist at the focus. For typical focal parameters, the emitting region is significantly smaller than the fundamental wavelength. Nonetheless, constructive inteference plays a significant role in the collective radiation spectrum. Phase mismatch becomes important only for the higher harmonics. These studies are intended as a prelude to experiments with high intensity ultrashort laser pulses.