Non-perturbative many-body theory of the optical nonlinearities in semiconductors

We discuss the various many-body effects that contribute to the large optical nonlinearities of semiconductors close to the band edge. Such effects are: band filling, screening due to the excited electron-hole pairs, band-gap shrinkage, energy broadening and excitonic enhancement. Compared to the Coulomb self-energy corrections, the radiative self-energies are normally small. However, they determine the transition rates in the rate equations of the photons and electrons.