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Scattering of a few-cycle laser pulse by a plasma layer: the role of the carrier-envelope phase difference at relativistic intensities

The reflection and transmission of a few-cycle Ti:Sa laser pulse iminging on a thin plasma layer have been analysed on the basis of classical electrodynamics. An approximate analytic solution has been given for the coupled Maxwell-Lorentz equations describing the dynamics of the surface current and the composite radiation field. The nonlinearities stemming from the relativistics kinematics of free electrons lead to the appearance of higher-harmonics in the scattered spectra. In our analysis particular attention has been paid to the effect of the carrier-envelope phase difference of the incoming laser pulse. For the fourth harmonic peak we calculated almost 25 percent modulation. In general, the harmonic peaks are down-shifted due to presence of the intensity-dependent factors by an order of 15-65 percent in case of an incoming field of intensity we have discussed. The spectrum of the high-harmonics has a long tail where the heights of the peaks vary within one order of magnitude forming a quasi-continuum. By Fourier synthetising the field components of this plateau region attosecond pulses have been obtained.