  The effect of the photoinduced absorption of terahertz (THz) radiation in a
semi-insulating GaAs crystal is studied by the pulsed THz transmission
spectroscopy. We found that a broad-band modulation of THz radiation may be
induced by a low-power optical excitation in the spectral range of the impurity
absorption band in GaAs. The measured modulation achieves 80\%. The amplitude
and frequency characteristics of the resulting THz modulator are critically
dependent on the carrier density and relaxation dynamics in the conduction band
of GaAs. In semi-insulating GaAs crystals, the carrier density created by the
impurity excitation is controlled by the rate of their relaxation to the
impurity centers. The relaxation rate and, consequently, the frequency
characteristics of the modulator can be optimized by an appropriate choice of
the impurities and their concentrations. The modulation parameters can be also
controlled by the crystal temperature and by the power and photon energy of the
optical excitation. These experiments pave the way to the low-power fast
optically-controlled THz modulation, imaging, and beam steering.
