Intensity-dependent degenerate and non-degenerate nonlinear optical absorption of direct-gap semiconductors

The nonlinear optical response of direct-gap semiconductors is investigated with a focus on non-degenerate multiphoton absorption processes. The theoretical approach is based on the semiconductor Bloch equations and yields the absorption rate either perturbatively or non-perturbatively in the incident light intensities. We describe the semiconductor by a two-band model and consider a pump-probe scheme where the weak probe pulse provides one of the simultaneously absorbed photons. The perturbative response can be described analytically within some approximations and we give simple expressions for two, three, and four-photon absorption coefficients. These are compared with numerical results for the absorption of pulses with a finite duration, where the influence of dephasing and relaxation as well as higher-order corrections are also investigated. For strong pump fields that are treated non-perturbatively we demonstrate non-trivial dependencies of the absorption on the time delay between the pulses. In the non-perturbative response of a single light pulse characteristic modulations appear in the absorption dependence on the field strength that may be interpreted as multi-photon Rabi oscillations. Finally, we present measurements of the non-degenerate two-photon absorption coefficient of bulk GaAs via time-delay and polarization-dependent transmissivity changes in a pump probe setup. The observed strong increase of the absorption coefficient with frequency ratios deviating from unity qualitatively agrees with theoretical expectations.