  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.
