Firstly, other parameters except the length of the EDF fiber are fixed, and the process of establishing solitons in the laser cavity under different EDF lengths is simulated in turn. Specifically, the fixed single-mode fiber length is 3m, the pump power is 150mW, the pump center wavelength is 975nm, and the splitting ratio is 3:7(intracavity is 30%). The simulation results are shown in Fig. 2.

The simulation results show that with the change of the length of the erbium-doped fiber, the soliton establishment process in the cavity exhibits different characteristics. When the length of the erbium-doped fiber is short, the pulse undergoes significant compression in the time domain and broadens in the frequency domain at the same time, and finally forms a stable soliton. Comparing the EDF lengths of 0.1m and 0.12m, it is found that increasing the EDF length leads to greater compression of the pulse. The reason is that the longer EDF makes the pump light more fully absorbed, and more longitudinal modes are possible to lock.

However, as the length of EDF increase, the pulse undergoes more complex dynamics in both time and frequency domains. In the time domain, with the narrowing of the pulse, a multi-peak structure appears on both sides of the main peak and gradually increases and strengthens as the length of the EDF increases. According to previous related research, this may come from the interference effect between the dispersion wave and the main pulse. It leads to the oscillation and splitting of the main peak, and finally forms a bound state soliton morphology or an unsteady multi-pulse structure. As the length of the EDF continues to increase, the soliton undergoes a restart and reconstruction dynamics process due to the significant enhancement of the reabsorption effect, but it is different from the initial establishment process. In the frequency domain, the spectral width undergoes a process of first broadening and then compressing with the increase of the length of the EDF, which can also be explained by the reabsorption effect. It is worth noting that before the restart and reconstruction, significant respiratory dynamics can be observed from the edge to the center of the spectrum, which is likely to come from the effect of self-phase modulation. In addition, the central wavelength of the spectrum is slightly red-shifted with the increase of EDF length.

Then we fix other parameters except the SMF length to simulate the soliton establishment process in the laser cavity under different SMF lengths. Specifically, the length of the fixed erbium-doped fiber is 0.1m, the pump power is 150mW, the pump center wavelength is 975nm, the splitting ratio is 3:7(intracavity is 30%). The simulation results as shown in Fig. 3.

The simulation results show that with the increase of the SMF length, the soliton establishment in the cavity undergoes different dynamics. In the time domain, the increase in length makes the multi-peak structure gradually increase near the pulse, and finally forms many soliton molecules. Correspondingly, the long SMF makes the spectrum in the frequency domain experience a dynamic process of first broadening and then compressing. A respiration dynamics scene from the edge to the center was also observed across the spectrum, leading to a narrowing of the spectrum and significant oscillations at the central frequency position. The results show that selecting the appropriate SMF length is also of great significance to the formation of stable solitons.

Then we changed the pump power and simulated the soliton development process under different power parameters. Specifically, the length of the fixed erbium-doped fiber is 0.1 m, the length of the single-mode fiber is 3 m, the pump center wavelength is 975 nm, and the splitting ratio is 3:7. The simulation results as shown in Fig. 4.

The simulation results show that the increase of the pump power has a significant impact on the soliton establishment process in the cavity. With increasing pump intensity, the pulse undergoes a temporal change from simple narrowing to a multimodal structure. Correspondingly, in the frequency domain, it has undergone a change from simple broadening of the spectrum to broadening first and then compressing. The reason is that the increase of pump power mainly affects the energy of solitons in the cavity, which makes the accumulation of nonlinearity more rapid. In addition, the increase of the pump power makes the excited transition more fully under the fixed EDF length and doping concentration, and without considering the gain saturation, a single cycle in the cavity obtains a higher gain, thereby accelerating the soliton dynamics learning process.

Then we fixed other parameters except the pump center wavelength, and simulated the establishment process of solitons in the laser cavity under different pump center wavelengths. Specifically, the length of the fixed erbium-doped fiber is 0.1 m, the length of the single-mode fiber is 3 m, the pump power is 150 mW, and the splitting ratio is 3:7. The simulation results as shown in Fig. 5.

The results show that there are also significant differences in the dynamic process in the cavity under pumping with different central wavelengths. The establishment process similar to the above-mentioned simulation steady-state link has been experienced in the time domain and frequency domain. This phenomenon is easy to understand. The pump absorption at the peak position of the selected EDF absorption spectrum (at 975nm) is more sufficient, and a single round-trip obtains greater gain. The cavity must experience faster soliton establishment kinetics and have conducive to the formation of a steady state. However, pumping at a wavelength of 985nm far away from the absorption peak is not conducive to the rapid establishment of stable solitons. Therefore, it is very important to accurately select the pump center wavelength according to the absorption spectrum of the doped fiber and take auxiliary stabilization measures to obtain a high-efficiency ring cavity laser

Finally, we change the splitting ratio parameters to simulate the soliton establishment process in the cavity. Specifically, the length of the fixed erbium-doped fiber is 0.1 m, the length of the single-mode fiber is 3 m, the pumping power is 150 mW, and the pumping center wavelength is 975 nm. The simulation results are shown in Fig. 6.

The simulation results show that the change of the light splitting ratio directly changes the loss characteristics inside the ring cavity. When the light splitting ratio in the cavity increases, the loss in the cavity decreases, and more nonlinear effects must be accumulated in the cavity within the same time. Restricted by the peak power clamping effect22, the soliton establishment undergoes a dynamic development process from a steady state to an unsteady state in the time and frequency domains. It can be seen from the pulse evolution diagram that as the splitting ratio in the cavity increases, the pulse splits rapidly and forms symmetrical multiple soliton molecules. From the wavelength domain diagram, we can further observe the severe intensity modulation and phase modulation that occur on the frequency spectrum when the soliton molecules are generated. The splitting of the pulse and the deterioration of the spectrum can be avoided by configuring the light splitting ratio to maintain the balance between the gain and loss, and a stable pulse could be obtained quickly.

From the evolution diagram of intracavity pulse parameters in Fig. 7, it can be seen more clearly that the pulse width and spectral width are closely related to the compression and expansion process of the resonant cavity operation.

**Figure 8 Fine simulation results of pulse in time domain and frequency domain**

Figure 8 shows more detailed simulation information in the time domain and frequency domain, including parameters such as pulse energy, peak power, pulse width, center wavelength, and time-bandwidth product, and longitudinal mode distribution images can also be obtained. These simulation results have good guiding significance for the construction and optimization of fiber lasers.

Based on the above simulations, the optimal working parameter input range of the simulated ring cavity laser model can be finally obtained, that is, the length of the EDF is 0.1m ~ 0.12m, the length of the SMF is 2.8m ~ 3.2m, the pump power is 180mW ~ 220mW, and the center wavelength is 975nm ~ 980nm and the splitting ratio of the coupler is less than 3:7. By adopting any combination to configure the laser construction parameters in the optimal working range, a feasible fiber laser solution can be quickly obtained.