A simple and accurate dynamic model for QD-SOAs is proposed. The proposed model is based on the state space theory, where by eliminating the distance dependence of the rate equation model of the QD-SOA; we derive a state space model for the device. A comparison is made between the rate equation model and the state space model under both steady state and transient regimes. Simulation results demonstrate that the derived state space model not only is much simpler and faster than the rate equation model, but also it is as accurate as the rate equation model. 1. Introduction During the last decade, the potential capabilities of QD-SOAs for use in all-optical signal processing and optical communication systems have been intensively studied. Among these capabilities, ultrafast gain recovery [1–5], high saturated output power [6, 7], pattern-effect free signal amplification at high speeds up to 80？Gb/s [8–10], pattern-effect free XGM-based wavelength conversion at 160？Gb/s [11], capability of operation at Tb/s speeds in presence of a control signal [12], amplification of high bit rate multichannel signals [13, 14], low noise figure [15], small dimensions, and integration with other optoelectronic devices such as laser diodes and optical modulators have great importance in any optoelectronic system. In recent years, several models have been proposed for describing the electrical and optical characteristics of QD-SOAs. Among these theoretical models, the most accurate models are based on semiconductor Maxwell-Bloch equations [16–20]. However, the numerical calculations associated with this model are extremely time-consuming and require huge amount of memory. A simplified approach to model QD-SOAs which is known as rate equation model (REM), has demonstrated an excellent agreement with experimental results [4, 21]. The REM includes a set of coupled differential equations to give details of carrier dynamics and optical properties of QD-SOA. To include the carrier dynamics in the REM, in some papers the electron-hole pairs are considered as exciton and only the carrier dynamics in the conduction band (CB) is taken into account [22–25]. In some other papers, the holes dynamics is included by using quasi-Fermi level in the valence band (VB) [26]. Also, the dynamics of electron and hole are considered separately in some articles [4, 27–31]. This model is known as “electron-hole model” [30], where the rate equations for electrons and holes are written separately. In this paper, we have employed the last approach to give details of the investigated QD-SOA [29, 31].
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