We have investigated terahertz (THz) sideband generation from bulk GaAs usi
ng intense pulses of coherent THz (or far-infrared) radiation from a free e
lectron laser. In contrast to previous studies, sidebands appeared inside t
he band gap and therefore were not resonantly enhanced from real states. Al
so, using picosecond pulses and changing the temporal overlap between the T
Hz and near-infrared pulses allowed us to monitor the evolution of the THz
sidebands directly in the time domain; this suggests a convenient method fo
r characterizing THz pulses using a conventional Si photodetector. In addit
ion to an expected second-order sideband, we detected a first-order sideban
d, which has previously been observed only in an asymmetrically coupled dou
ble quantum well system where the inversion symmetry was intentionally brok
en. Finally, the THz power dependence clearly revealed a deviation from per
turbative behavior, indicating the entrance into the strong-field regime.