Dynamical calculation of third harmonic generation in a semiconductor quantum well

Non-linear phenomena in optically excited semiconductor structures are of high interest. We here develop a model capable of studying the dynamics of the photoexcited carriers, including Coulomb interaction on a Hartree-Fock level, on the same footing as the dynamics of the light field impinging on an arbitrary photonic structure. Applying this method to calculate the third harmonic generation in a semiconductor quantum well embedded in a Bragg mirror structure, we find that the power-law exponent of the intensity dependence of the third harmonic generation depends on the frequency of the exciting pulse. Off-resonant pulses follow the expected cubic dependence, while the exponent is smaller for resonant pulses due to saturation effects in the induced carrier density. Our study provides a detailed understanding of the carrier and light field dynamics during non-linear processes.