SPECTRAL-ANALYSIS OF THE NONLINEAR RELATIVISTIC DOPPLER-SHIFT IN ULTRAHIGH INTENSITY COMPTON-SCATTERING

The relativistic dynamics of an electron subjected to the classical el ectromagnetic field of an ultrashort laser pulse is studied theoretica lly at arbitrary intensities. Frequency modulation affects associated with the nonlinear relativistic Doppler shift induced an the backscatt ered radiation are analyzed in detail. For circular polarization, an e xact 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 yi eld anharmonic spectra when the laser ponderomative force strongly mod ulates the electron's proper time. At ultrahigh intensities, these non linear relativistic spectra exhibit complex structures. In addition, t he temporal laser pulse shapes best suited to generate narrow Compton backscattered spectral lines at ultrahigh intensities are discussed.