Laser-driven ultra-thin foils used as relativistic mirrors

The generation of laser-driven dense relativistic electron layers from ultra- thin foils and their use for coherent Thomson backscattering is discussed, applying analytic theory and one-dimensional particle-in-cell simulation. The blow-out regime is explored in which all foil electrons are separated from ions by direct laser action. The electrons follow the light wave close to its leading front. Single electron solutions are applied to initial acceleration, phase switching, and second-stage boosting. Coherently reflected light shows Doppler-shifted spectra, chirped over several octaves. The Doppler shift is found prop gamma_x ² = 1/(1-beta_x ²) where beta_x is the electron velocity component in normal direction of the electron layer which is also the direction of the driving laser pulse. Due to transverse electron momentum py, the Doppler shift by 4gamma_x ² = 4gamma² / [1+(p_y ²/mc)²] ap 2gamma is significantly smaller than full shift of 4gamma². Methods to turn p_y rarr 0 and to recover the full Doppler shift are proposed and verified by 1D-PIC simulation. These methods open new ways to design intense single attosecond pulses. We also present an analytical formula for the reflectivity and improved results for foil acceleration, based on the analytical theory of Kulagin et al..