Theory of Attosecond Pulses from Relativistic Surface Plasmas
  High harmonic generation by relativistically intense laser pulses from overdense plasma layers is surveyed. High harmonics are generated in form of (sub-)attosecond pulses when the plasma surface rebounds towards the observer with relativistic velocity. Different cases are considered. The "relativistically oscillating mirror" (ROM) model, describing the most typical case, is analyzed in detail. The resulting harmonic spectrum is usually a power law with the exponent -8/3 [baeva2006relativistic], but possible exceptions due to "higher order \gamma-spikes" are considered. It is shown that under certain conditions, ultra-dense electron nanobunches can be formed at plasma surface that emit coherent synchrotron radiation. The resulting spectrum is much flatter and leads to the formation of a giant attosecond pulse in the reflected radiation. The harmonics radiation is also considered in time domain, where they form a train of attosecond pulses. It is characterized and a possibility to select a single attosecond pulse via polarization gating is described. Further, the line structure in relativistic harmonic spectra is analyzed. It is shown that the harmonics have an intrinsic chirp and it can be responsible for experimentally observed spectral modulations. Finally, high harmonic generation is considered in realistic three-dimensional geometry. It is shown that free space diffraction can act as a high pass filter, altering the spectrum and the reflected field structure. The high harmonics tend to be self-focused by the reflecting surface. This leads to a natural angular divergence as well as to field boost at the focal position. Coherently focusing the harmonics using an optimized geometry may result in a significantly higher field than the field of the driving laser. 
Daniel an der Br\"ugge, Alexander Pukhov
physics.plasm-ph physics.optics