Spectral analysis of the nonlinear relativistic Doppler shift in ultrahigh intensity Compton scattering

The relativistic dynamics of an electron subjected to the classical electromagnetic field of an ultrashort laser pulse is studied theoretically at arbitrary intensities. Frequency modulation effects associated with the nonlinear relativistic Doppler shift induced on the backscattered radiation are analyzed in detail. For circular polarization, an exact analytical expression for the full nonlinear spectrum is derived. For linear polarization, it is found that the scattering of coherent light by a single electron describing a well-behaved trajectory can yield anharmonic spectra when the laser ponderomotive force strongly modulates the electron close-quote s proper time. At ultrahigh intensities, these nonlinear relativistic spectra exhibit complex structures. In addition, the temporal laser pulse shapes best suited to generate narrow Compton backscattered spectral lines at ultrahigh intensities are discussed. copyright 1996 The American Physical Society