Two-Level Description of Gain and Mixing Susceptibilities in Amplifying Semiconductor Materials

Optical-intensity-dependent gain and mixing susceptibilities of amplifying semiconductor materials have been calculated using the density matrix approach. The model, which takes intraband relaxation and carrier injection rate into account, allows for numerical computation of these susceptibilities whatever the medium saturation is. As a simplification, an equivalent two-level system is derived which represents quite well the gain and nearly degenerate four-wave mixing susceptibilities. Such an equivalence, which leads to the same field-induced polarization as the conventional rate equation model, also connects the two-level (or rate equation) parameters to the real characteristics of the semiconductor material. This two-level description is easy to handle and provides great simplifications when the susceptibilities are introduced into the propagation equations.