Higher-order contributions and nonperturbative effects in the nondegenerate nonlinear optical absorption of semiconductors using a two-band model

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 these 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 multiphoton 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. We confirm the previously predicted strong enhancement of two-photon absorption for nondegenerate conditions for pulsed excitation. We discuss the dependencies of the multiphoton absorption on the light frequencies, initial band populations, and the time delay between the pulses. The frequency dependence of the two-photon absorption coefficient for nondegenerate 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 line shapes. Nonperturbative solutions of the Bloch equations demonstrate a strongly nonmonotonous behavior of the intensity-dependent optical absorption for a single incident pulse and in a pump-probe setup.