## 3 Step Modulation Simulation and Discussion  
In order to analyze the effect of the parameter setting of the second stage modulated signal on the output light pulse, we establish the simulation models of single mode rate equations (Equations (1) and (2)) by SIMULINK, which is a visual simulation of MATLAB. To simulate the variation of the output pulse, we excite the semiconductor laser with a single current pulse. The amplitude of the first-stage modulation current is set to \(I_{1}=34\) mA, and the width is \(T_{1}=0.971\) ns, which is equal to the time of carrier density reaching the threshold for the first time. The bias current is set to 0 mA in order to get a high extinction ratio [23]. The block diagram of step modulation simulation is shown in Figure 2.  
Figure 3 shows the simulation results of output pulses at different \(I_{2}\) when the \(T_{2}=64\) ps. From Figure 3a, in which the dotted line corresponds to the end time of the modulation current, it is directly seen that with the increase of \(I_{2}\), the rising edge of the output pulse becomes steep, the peak time is short, and the peak power is high. However, the pulse width decreases at first and then increases, as shown in Figure 3b. If \(I_{2}=34\) mA, the step modulated signal can change into a rectangular modulated wave, it is clearly seen that using the step modulation can cause pulse energy increase and pulse duration decrease. When \(I_{2}=64\) mA, the output power reaches the maximum value at the time corresponding to the dotted line, also, the FWHM pulse width is smallest. When \(I_{2}<64\) mA, the peak pulse power lags behind the end time of current and the output pulse rise time is short, that is because the carrier density has not fallen to the threshold before the end of the current, even if terminating the injection current there will be excess carriers converted into photons. Therefore, as the accumulation rate of carriers increases proportionally to the \(I_{2}\), the output pulse becomes narrow, and the peak power becomes large. When \(I_{2}=64\) mA, the output pulse has reached the peak before the current  
Figure 2: Block diagram of the step modulation for simulation in the semiconductor laser. is terminated, and the pulse tail will appear with the injection of excess carriers. The bigger is the \(I_{2}\), and the more serious is the tailing. Thus, the conclusion one is: When \(T_{2}\) is certain, \(I_{2}\) should be set to meet the condition-the output power reaches the maximum time is equal to the current termination time, in order to minimize the width of the output pulse. The simulation results of the output pulses at different \(T_{2}\) are shown in Figure 4, in which the \(I_{2}=64\) mA. From Figure 4a, it is directly seen that the output pulses have the similar front-end when fixing \(I_{2}\), and the peak power increases with \(T_{2}\) until it reaches saturation. Similarly, with the increase of \(T_{2}\), the changing rule of FWHM is first reduced and then increased, before reaching a steady value, as shown in Figure 4b. When \(T_{2}=64\) ps, the peak power of output pulse reaches the maximum for the first time, which means the carrier density drops to the threshold at the moment of cutting the driving current completely. When \(T_{2}<64\) ps, the photon density is still on the rise, so the extended modulation time can increase the cumulative number of carriers and thus enhance the peak power. In such a situation, if \(T_{2}\) is small, the gain coefficient changes greatly with \(T_{2}\) and the accumulation rate of the photon is fast, which leads to the FWHM becomes small; else, the front-end of output pulses change slowly, and the FWHM becomes big. When \(T_{2}>64\) ps, the peak power does not change with the increase of \(T_{2}\) because of the photon density saturation phenomenon. However, the extension of the modulation time causes the post-stage oscillation to appear, and the pulse tail becomes worse. The fall time are 28.9 ps (64 mA), 32.7 ps (74 mA), 49.2 ps (94 mA) and 83.1 ps (124 mA) respectively.