Theory of four-wave mixing in quantum dot semiconductor optical amplifiers

The theory of four-wave mixing (FWM) in quantum dot (QD) semiconductor optical amplifiers (SOAs) has been discussed by the combination of the QD rate equations system and the pulse propagation in QD SOAs. This study has covered two types of QD structures: the two-level QD structure, where the ground state (GS) and wetting layer have been considered; and the three-level QD structure, where the excited state (ES) has been taken into account. The relations for differential gain were also discussed. FWM efficiency and its components, comprising spectral hole burning, carrier heating and carrier density pulsation (CDP), are calculated. The results show that inclusion of ES is essential. At a high carrier density and for a long term frequency, the FWM was found to be detuning independently while it is symmetric for short pulses. Neglecting CH makes the FWM in QD SOAs symmetric and detuning independent, which are desired characteristics for optical communication applications. The results corroborate available experimental observations. The effective capture time of QD is the main parameter and can be ascribed to the differences between the two- and three-level models.