Three-Level Description of Optical Nonlinearities in Semiconductors

ABSTRACT A description of the second–order nonlinear optical susceptibility of semiconductor materials is considered. The Lie algebra su(3) arises from a 3–level quantum model for each state in the Brillouin zone, which is obtained by truncation of the true infinite–dimensional basis. The accuracy of several approximations inherent in this approach is analysed, in particular the electric dipole and minimal replacement Hamiltonians which specify the electrodynainical interaction in a finite–dimensional quantum system. The three–level model is extended by adding relaxation processes and utilising the rotating wave approximation to account for resonant nonlinear effects. Analytical forms for the transition rates associated with two–photon absorption and electromagnetically induced transparency are derived.