Nonlinear electrodynamics of the interaction of ultra-intense laser pulses with a thin foil

An analytical description of the interaction of laser light with a foil, described as a thin slab of overdense plasma, is presented together with the results of multidimensional particle in cell simulations. The matching conditions at the foil result in nonlinear boundary conditions for the wave equation. The conditions for relativistic transparency are given. The interaction with the foil leads to shaping of the laser pulse. In the case of oblique incidence of a relativistically intense pulse, nonlinear coupling modifies the pulse polarization and causes emission of high harmonics and generation of an electric current. Strong focalization of the reflected pulse, in particular in three-dimensional simulations, is observed for normal and oblique incidence due to the induced distortion of the foil surface.