Calculations of band-filling optical nonlinearities in extrinsic semiconductors beyond the low injection limit

Theoretical calculations of room temperature band-filling optical nonlinearities in a bulk semiconductor are reported. The approach, based on self-consistent determination of pseudochemical potentials, improves on other existing calculations as it correctly takes into account an arbitrary optical injection level. The self-consistent approach also enables direct calculation of the nonlinear optical susceptibility without fixing the photogenerated electron-hole density as a parameter, as required in existing phenomenological models. Good agreement with experimental results is obtained, in the case of GaAs, when photoexcited carrier densities above the Mott transition are considered. Calculations of pair density and nonlinear refractive index are shown as a function of the doping level and of the pump intensity for bulk GaAs. Finally, the limits of the model and applications to calculations of optical behavior in more complex structures are discussed.