New photon density rate equation for Fabry-Perot Semiconductor Optical Amplifiers

Two different approaches are commonly used for Fabry-Perot Semiconductor Optical Amplifiers (FP SOAs) performance analysis: the Fabry-Perot resonator approach and rate equation approach. Compared with the Fabry-Perot resonator approach, the rate equation approach is more powerful because noise and mode-related performance analysis can be included. However, it has been shown that the results based on Fabry-perot approach contains multiplicative factor which arise from an explicit consideration of the resonator and those factors are missing in the rate equation approach. As a result, the existing rate equations provide a poor description of FP SOAs. Our analysis shows that this is due to the fact that the interference between the injected optical field and the intracavity optical field has not been taken into account properly. In this paper, a new photon density rate equation for Fabry-Perot semiconductor optical amplifiers is derived based on the electric field rate equation. By taking this interference into account, our derivation shows that the input coupling term in the photon density rate equation is a function of the top and bottom mirror reflectivity, as well as the bias condition. Optical gain predictions from this new photon density rate equation match well with experimental measurements.