  In this paper we present an ab initio real-time analysis of free polarization
decay and photon echo in extended systems. As a prototype material, we study
bulk GaAs driven by ultra-short laser pulses of 10 fs (energy spread of 0.4
eV), with frequency tuned in the continuum of the optical spectrum. We compute
the electronic polarization P(t), and define a computational procedure to
extract the echo signal in the dipole approximation. Results are obtained in
both the low and high field regime, and compared with a two-levels system (TLS)
model, with parameters extracted from the ab initio simulations. ab initio
results are in optimal agreement with the TLS in the low-field case, whereas
some differences are observed in the high-field regime where the multi-band
nature of GaAs becomes relevant. In the high field regime we compute the pulse
area, and look for fluences with pulse area close to {\pi}. We highlight that
such fluences are well below the damage threshold of GaAs. However a unique
value of the area cannot be defined, due to the strong dependence of the
transition dipoles in the energy window excited by the laser pulse.
