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The semiconductor Bloch equations for a two-band model including inter- andintraband excitation are used to study the nonlinear absorption of single andmultiple light pulses by direct-gap semiconductors. For a consistent analysisthe contributions to the absorption originating from both the interbandpolarization and the intraband current need to be included. In the Blochequation approach theses contributions as well as different excitation pathwaysin terms of sequences of inter- and intraband excitations can be evaluatedseparately which allows for a transparent analysis, the identification of thedominant terms, and analyzing their dependence on the excitation conditions. Inthe perturbative regime, we obtain analytical expressions for the multi-photonabsorption coefficients for continuous-wave excitation. These results are shownto agree well with numerical results for short pulses and/or finite dephasingand relaxation times and we confirm the previously predicted strong enhancementof 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 thetwo-photon absorption coefficient for non-degenerate excitation is evaluatedperturbatively in third-order. The higher-order contributions to the opticalabsorption include three- and four-photon absorption and show a rich frequencydependence including negative regions and dispersive lineshapes.Non-perturbative solutions of the Bloch equations demonstrate a stronglynon-monotonous behavior of the intensity-dependent optical absorption for asingle incident pulse and in a pump-probe set-up.

Higher-order contributions and non-perturbative effects in the non-degenerate nonlinear optical absorption of direct-gap semiconductors