  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.

Plasma Physics;Optics