  We investigate the non-linear response and energy absorption in bulk silicon
irradiated by intense 12-fs near-infrared laser pulses. Depending on the laser
intensity, we distinguish two regimes of non-linear absorption of the laser
energy: for low intensities, energy deposition and photoionization involve
perturbative three-photon transition through the direct bandgap of silicon. For
laser intensities near and above 10$^{14}$ W/cm$^2$, corresponding to
photocarrier density of order 10$^{22}$ cm$^{-3}$, we find that absorption at
near-infrared wavelengths is greatly enhanced due to excitation of bulk plasmon
resonance. In this regime, the energy transfer to electrons exceeds a few times
the thermal melting threshold of Si. The optical reflectivity of the
photoexcited solid is found in good qualitative agreement with existing
experimental data. In particular, the model predicts that the main features of
the reflectivity curve of photoexcited Si as a function of the laser fluence
are determined by the competition between state and band filling associated
with Pauli exclusion principle and Drude free-carrier response. The non-linear
response of the photoexcited solid is also investigated for irradiation of
silicon with a sequence of two strong and temporary non-overlapping pulses. The
cumulative effect of the two pulses is non-additive in terms of deposited
energy. Photoionization and energy absorption on the leading edge of the second
pulse is greatly enhanced due to free carrier absorption.
