A detailed analysis of the photon emission spectra of an electron scattered by a laser pulse containing only very few cycles of the carrying electromagnetic field is presented. The analysis is performed in the framework of strong-field quantum electrodynamics, with the laser field taken into account exactly in the calculations. We consider different emission regimes depending on the laser intensity, placing special emphasis on the regime of one-cycle beams and of high laser intensities, where the emission spectra depend nonperturbatively on the laser intensity. In this regime, we, in particular, present an accurate stationary phase analysis of the integrals that are shown to determine the computed emission spectra. The emission spectra show significant differences with respect to those in a long pulsed or monochromatic laser field:The emission lines obtained here are much broader, and more important, no dressing of the electron mass is observed.

The electromagnetic radiation emitted by an ultrarelativistic accelerated electron is extremely sensitive to the precise shape of the field driving the electron. We show that the angular distribution of the photons emitted by an electron via multiphoton Compton scattering off an intense (I>10(20)  W/cm(2)), few-cycle laser pulse provides a direct way of determining the carrier-envelope phase of the driving laser field. Our calculations take into account exactly the laser field, include relativistic and quantum effects and are in principle applicable to presently available and future foreseen ultrastrong laser facilities.

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A detailed analysis of the process of two-photon emission by an electron scattered from a high-intensity laser pulse is presented. The calculations are performed in the framework of strong-field QED and include exactly the presence of the laser field described as a plane wave. We investigate the full nonlinear quantum regime of interaction with a few-cycle pulse, where nonlinear effects in the laser field amplitude, photon recoil, and the short pulse duration substantially alter the emitted photon spectra as compared to those in previously studied regimes. We provide a semiclassical explanation for such differences, based on the possibility of assigning a trajectory to the electron in the laser field before and after each quantum photon emission. Our numerical results indicate the feasibility of investigating experimentally the full ultrarelativistic quantum regime of nonlinear double Compton scattering with available electron accelerator and laser technology.