Excitonic Nonlinearities at High Densities

We have already seen a couple of examples where optical non-linearities arise upon increase of the electron-hole pair density. Additional recombination bands can occur due to excitonic interactions or the transmission at the exciton resonance is modified due to absorption bleaching. Such many-particle effects show up in differential transmission or pump-probe absorption spectroscopy. These experiments show a variety of results, which on first sight seem to miss systematic explanations. Upon increasing the pump intensity there is always a bleaching of the exciton resonance in the spectra often but not always accompanied by a spectral broadening, and there are red shifts or blue shifts or a succession of both. We discuss in this chapter which many-particle effects are responsible for these observations and how to carefully isolate them in theory and experiment. Finally excitonic interaction can lead to optical gain and thus lasing of exciton polaritons occurs which is considered for realization of low-threshold lasers. For the characterization of excitonic gain we introduce here the experimental technique variable stripe-length method