Laser has good directionality, high brightness, good monochromaticity, and strong coherence, making it significantly advantageous in the field of ranging. Satellite laser ranging (SLR) is the most accurate satellite ranging technology, and the kilohertz picosecond laser is the iconic light source of the fourth-generation satellite laser ranging. In kilohertz picosecond lasers, regenerative amplifiers are commonly used to amplify the mode-locked pulses, typically using Nd:YAG as the gain crystal with a gain bandwidth of 0.15 nm. In addition, the smaller the bandwidth of the narrowband filter used for satellite ranging, the less the influence of ambient light, and the higher the signal-to-noise ratio. The narrowband filter bandwidth used by several observatories we cooperate with is 0.2 nm, so the laser spectrum width needs to be less than 0.2 nm. To match the gain bandwidth of the regenerative amplifier with the bandwidth of the narrowband filter, a requirement of an output spectrum width of 0.15 nm was proposed for the oscillator. Semiconductor saturable absorber mirrors (SESAM) have the advantages of stable performance, simple structure, low mode locking threshold, and the ability to achieve full fiber integration. It has been widely used in mode-locked fiber lasers and has achieved product commercialization. Most commercial applications of picosecond lasers are generated by SESAM passive mode locking technology. SESAM products on the market have low selectivity and the consistency of each batch is poor. There may be unpredictable differences between the physical parameters of SESAM and the design requirements, resulting in uncontrollable oscillator parameters. Therefore, this study improved the passive mode locking model of SESAM to guide the design of oscillator parameters.By using the Split-Step Fourier Transform (SSFT) to solve the Ginzburg-Landau equation, a simulation model is established, and SESAM parameter requirements are proposed. The simulation results meet the design requirements (Fig.1) and can achieve dual peak, triple peak, and quad peak mode locking by adjusting the cavity length (Fig.3). When using this model to simulate oscillators with large bandwidth chirped fiber Bragg gratings (CFBG) as output couplers, the results are distorted (Fig.9). The chirp dispersion brought by CFBG was introduced into the Ginzburg-Landau equation.SESAM was prepared by low pressure metal organic compound vapor deposition (LP-MOCVD) method, and its parameters were tested as modulation depth 11.5%, non-saturated loss 7.6%, saturation fluence 39.3 μJ/cm², relaxation time 5.5 ps, and damage threshold 21.8 mJ. The linear cavity oscillator achieves laser output with an average power of 30.00 mW, a repetition rate of 44.57 MHz, a peak wavelength of 1 064.07 nm, a spectrum width of 0.14 nm and a pulse width of 31.50 ps when injected with a pump power of 150 mW (Fig.6), meeting the design requirements. It can also achieve dual peak, triple peak, and quadruple peak mode locking by adjusting the cavity length. The chirp dispersion brought by CFBG was introduced into the Ginzburg-Landau equation. The improved model was used to guide parameter design and obtain picosecond laser output with an average power of 55.70 mW, repetition rate of 26.32 MHz, peak wavelength of 1030.15 nm, spectrum width of 0.58 nm, and pulse width of 7.62 ps after fiber pre-amplification.In response to the SLR, we used the SSFT to solve the Ginzburg-Landau equation and established a simulation model and designed a set of SESAM parameters. The parameters of the linear cavity oscillator built on the basis of this SESAM meet the design requirements, and its application in SLR systems will improve the ranging signal-to-noise ratio and achieve better SLR accuracy. To solve the problem of the distortion in the simulation results of oscillators using large bandwidth CFBG as output couplers, the chirp dispersion brought by CFBG was introduced into the Ginzburg-Landau equation. An equation was established to describe the grating reflection spectrum. The improved model was used to guide parameter design, and the experimental results were consistent with the simulation results, verifying the rationality of the simulation model.