  The semiconductor Bloch equations for a two-band model including inter- and
intraband excitation are used to study the nonlinear absorption of single and
multiple light pulses by direct-gap semiconductors. For a consistent analysis
the contributions to the absorption originating from both the interband
polarization and the intraband current need to be included. In the Bloch
equation approach theses contributions as well as different excitation pathways
in terms of sequences of inter- and intraband excitations can be evaluated
separately which allows for a transparent analysis, the identification of the
dominant terms, and analyzing their dependence on the excitation conditions. In
the perturbative regime, we obtain analytical expressions for the multi-photon
absorption coefficients for continuous-wave excitation. These results are shown
to agree well with numerical results for short pulses and/or finite dephasing
and relaxation times and we confirm the previously predicted strong enhancement
of two-photon absorption for non-degenerate conditions for pulsed excitation.
We discuss the dependencies on the light frequencies, initial band populations,
and the time delay between the pulses. The frequency dependence of the
two-photon absorption coefficient for non-degenerate excitation is evaluated
perturbatively in third-order. The higher-order contributions to the optical
absorption include three- and four-photon absorption and show a rich frequency
dependence including negative regions and dispersive lineshapes.
Non-perturbative solutions of the Bloch equations demonstrate a strongly
non-monotonous behavior of the intensity-dependent optical absorption for a
single incident pulse and in a pump-probe set-up.
