In this paper, a theoretical model is proposed to investigate and analyze an ultra-fast cross gain modulation (XGM) in quantum dot semiconductor optical amplifiers (QDSOAs). The proposed model is based on a set of carrier's rate equations, propagation equations for pump and probe signals and phase equation. To investigate XGM mechanism, nonreturn-to-zero (NRZ) pulse trains with various bit-rates are supposed to propagate as the input pump signals through the QDSOA's active layer. The probe signal is assumed to be a continuous wave (CW) signal. Furthermore, optical gain of quantum dots (QDs) is calculated using density matrix approach. For the first time, to the best of our knowledge, second excited state is considered in the band diagram of QDs, to obtain the ultra-fast XGM in QDSOA. Therefore in the presented model, the rate equations are written for the carriers in the ground state, first and second excited states (ES2), continuum state and the wetting layer. In the presence of ES2, gain recovery time and gain saturation is reduced and therefore, ultra-high bit-rate pulse trains can be modulated with negligible pattern effect and wave distortion. Effect of injection current density increment and carrier's relaxation lifetime decrement are illustrated to show the improvement of XGM mechanism in the QDSOA. It is shown theoretically that ultra-high bit-rate XGM up to 450 Gbps is possible due to the reduced gain recovery time in the presence of ES2. It is demonstrated that at the same pump power for higher injection current densities and lower carrier's relaxation lifetimes, the pattern effect and wave distortion has almost vanished. Although, in this case, extinction ratio (ER) is decreased. It is shown that to recover the ER, the input pump power should be increased. Furthermore, based on the results in the presence of ES2, ER is decreased by 0.5 dB.
