  Laser plasma amplification of sub-picosecond pulses above the Joule level is
demonstrated, a major milestone for this scheme to become a solution for the
next-generation of ultra-high intensity lasers. By exploring over 6 orders of
magnitude the influence of the incident seed intensity on Brillouin laser
amplification, we reveal the importance of a minimum intensity to ensure an
early onset of the self-similar regime, and a large energy transfer with a very
high efficiency, up to 20%. Evidence of energy losses of the seed by
spontaneous backward Raman is found at high amplification. The first
three-dimensional envelope simulations of the sub-picosecond amplification were
performed, supplemented by one-dimensional PIC simulations. Comparisons with
the experimental results demonstrate the capability of quantitative predictions
on the transferred energy. The global behavior of the amplification process, is
reproduced, including the evolution of the spatial profile of the amplified
seed.
