  The paper reports the results of two-dimensional particle-in-cell simulations
of proton beam acceleration at the interactions of a 130 fs laser pulse of
intensity from the range of 10^21-10^23 W/cm^2, predicted for the Extreme Light
Infrastructure (ELI) lasers currently built in Europe, with a thin hydrocarbon
(CH) target. A special attention is paid to the effect of the laser pulse
intensity and polarization (linear-LP, circular-CP) as well as the target
thickness on the proton energy spectrum, the proton beam spatial distribution
and the proton pulse shape and intensity. It is shown that for the highest,
ultra-relativistic intensities (10^23 W/cm^2) the effect of laser polarization
on the proton beam parameters is relatively weak and for both polarizations
quasi-monoenergetic proton beams of the mean proton energy about 2 GeV and
dE/E=0.3 for LP and dE/E=0.2 for CP are generated from the 0.1 micrometer CH
target. At short distances from the irradiated target (below 50 micrometers),
the proton pulse is very short (below 20 fs), and the proton beam intensities
reach extremely high values above 10^21 W/cm^2, which are much higher than
those attainable in conventional accelerators. Such proton beams can open the
door for new areas of research in high energy-density physics and nuclear
physics as well as can also prove useful for applications in materials research
e.g. as a tool for high-resolution proton radiography.
