## 1 Introduction  
In recent decades, the short pulsed laser has been widely utilized in the fields of production, medical, detection and communication, and so on, as the ultra-short pulse laser technology develops rapidly [1; 2]. Among various types of lasers, semiconductor lasers are suitable for producing ultra-short optical pulses because of their large gain bandwidth, small volume and high modulation efficiency [3; 4; 5]. The direct modulation technology of the semiconductor laser is mainly used to generate optical pulses, which has the advantages of simple operation, low cost, and mature technology. However, in order to achieve high-speed modulation in the optical communication system, the driving current is higher than the threshold current. As a result, the output pulse width is similar to that of the driving current, and the pulse power is proportional to the amplitude of the driving current. There is a trade-off between the high extinction ratio and the short pulse width [6; 7; 8; 9].  
Gain-switched technology is another direct modulation method to generate short optical pulses by using the relaxation oscillation of the semiconductor laser, and it has been widespread use because of its compact structure, stable performance, and flexible setting. The relaxation oscillation is a transient phenomenon in lasers, which refers to a series of gradually decaying spike pulse sequence attributing to the self-oscillation before the laser achieves stabilized output. The standard gain-switched arrangement is to drive a laser, biased below the threshold. The idea is to excite the first spike of relaxation oscillation, and terminate the electrical pulse before the onset of the second optical spike, resulting in a short light pulse. Repeat this process to achieve a pulse sequence on the order of picosecond [10; 11]. Compared with other pulse generation methods, this idea has an advantage that a simple driving circuit can be used to generate an ultra-short optical pulse, and the output pulse width is much smaller than the modulation current pulse. Theoretical analysis indicates that the photon lifetime of a typical semiconductor laser is 2-3 picosecond, so a ten picosecond laser pulse can be produced theoretically by using a hundred picosecond current pulse in the process of gain switching [12; 13].  
The characterization of the gain-switched semiconductor laser pulse is also affected by the modulation parameters. In Reference [14], it has been verified that using the rectangular wave modulation can achieve high pulse power and a small tail, compared to the sine and triangle waves with the same magnitude. Besides, the peak power of the output pulse increases with the increase of rectangular modulated signal width, and finally reaches saturation, according to the study on relaxation oscillation [15]. According to the typical study for the gain switching process of the semiconductor laser, the peak power and width of the output pulses are mainly determined by the accumulation speed after the carrier density reaches the threshold. Based on this theory, a step-pulse modulated signal is proposed on more peak power improvements. In this paper, we primarily focus on the effect of step modulated signal's variation on gain-switched semiconductor lasers, demonstrate the feasibility of the proposed methods and find the best modulation parameter. Moreover, we get a function between the amplitude of the signal and the pulse width by curve fitting technic. The simulation results show that the proposed scheme can further compress the laser pulse width and increase the amplitude value. The final simulation results show that the proposed method can further compress the laser pulse width and increase the amplitude value.