Theory of four-wave mixing

The present chapter is devoted to presenting the theory of four-wave mixing in semiconductor optical amplifiers (SOAs). At first, a model describing the dynamics in terms of rate equations is developed. The rate equations are derived from density matrix equations, and after coupling with the propagation equation for the field envelope and its phase, a rather general description of the four-wave mixing is arrived at. In the limit of zero scattering loss, the model leads to a very simple description of the effects of four-wave mixing. In the succeeding sections we will concentrate on the advantages and draw-backs of some analytical models based on the coupled-mode theory and used to calculate the FWM performance of SOAs. In addition, the effects of amplified spontaneous emission (ASE) noise are considered. The theoretical models presented here should be of interest for all those performing experimental FWM investigations. Particular attention is given to the validity of the assumptions used in the models.