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

Abstract

The reflection and transmission of a few-cycle femtosecond Ti:Sa laser pulse impinging on a thin plasma layer have been analysed on the basis of classical electrodynamics. The plasma electrons were represented by a surface current density along the layer. An approximate analytic solution has been given for the system of the coupled Maxwell-Lorentz equations describing the dynamics of the surface current and the composite radiation field. With the help of these solutions the Fourier components of the reflected radiation have been calculated. The nonlinearities stemming from the relativistic kinematics of the free electrons lead to the appearance of higher-order harmonics in the scattered spectra. We show that the fourth harmonic peak strongly depends on the carrier-envelope phase difference with a modulation being almost 25 percent. In general, the harmonic peaks are down-shifted due to the presence of the intensity-dependent factors by an order of 15-65 percent in case of an incoming field of intensity 2 × 1019 W/cm2. By Fourier synthetising the components from the plateau region of the higher-harmonic spectrum, attosecond pulses have been obtained.