## 4 Discussion  
The evolutions of pulse envelope and chirp, together with the corresponding optical spectra and SA transmittance curves, were carefully studied in Figure 11 to reveal the influence of reverse absorption coefficient on the NLP formation process. Numerical simulation of the NLP formation process in different roundtrips was depicted in four typical stages: (a) pulse amplifying, (b) peak power clamping, (c) pulse instability, and (d) NLP envelope stability. First, in stage a, the initial pulse is amplified in the first 11 th roundtrips with a gaussian shape in Figure 11a, where its peak power is not sufficient to trigger the reverse absorption regime. In stage b, the next 12 th to 140 th roundtrips revolution, the pulse time domain is narrowed down by anomalous dispersive effect and the SA saturable absorption modulation, showing a typical broadened optical spectrum from SPM in Figure 11b3. The enhanced peak power in the SA transmittance curves triggers off the reverse absorption regime, rising the peak power clamping effect. In stage c, further narrowing pulse induces a significant increase in peak power, which induces the pulse time domain instability in Figure 11c1 in return. The SA transmittance curves record tiny pulse generation in pulse envelope, and the parasitic tiny pulse further enhances the single pulse shape instability and bursts into noise like pulse regime. Finally, in stage d, the NLP pulse time domain gradually broadens to decrease high nonlinearity from SPM and reverse absorption effect, as a balance among the SPM, dispersion, saturable absorption, and reverse absorption effects in this laser system. The final evolution state exhibits a rectangle shape pulse with free chirp as shown in Figure 11d1. The above simulation results demonstrate the ability of reverse absorption to switch the pulse state from single pulse to NLP through restricting the peak power infinite increase in the anomalous dispersion regime. Figure 10: Numerical simulation of NLP output pulse characteristics as a function of pump power using the BL-CNT SA setup. (**a1**)-(**c1**) the simulated envelope evolution of the NLP pulse at the gain coefficient g\({}_{0}\) values of 70, 100, and 150 W\({}^{-1}\); (**a2**)–(**a4**) the simulated time evolution, AC trace and optical spectrum at g = 70 W\({}^{-1}\); (**b2**)–(**b4**) g = 100 W\({}^{-1}\) and (**c2**)–(**c4**) g = 150 W\({}^{-1}\), respectively. The NLP envelope characteristics are directly corresponding to the reverse absorption mechanism. To figure out the relationship between NLP characteristics and reverse absorption effect, the variations of intracavity NLP features (including pulse energy, peak power, and pulse duration) are analyzed in Figure 12. In one round intracavity trip, the pulse energy increases from the EDF component then decreases through the OC and SA components. The remaining SMF component has no energy consumption. Under this situation, the peak power largely increases through EDF and monotonically increases through the OC and SA consumption components. It is clear that the SA component with reverse absorption is mainly responsible for the decrease in the intracavity peak power. Compared to the intracavity peak power evolution, the pulse duration evolution is slightly monotonically decreased through the whole position in cavity except for the EDF component. To further reveal their relationships on the NLP pulse characteristics, the comparisons in pulse energy, peak power, and pulse duration with modified relative gain coefficient and reverse absorption coefficient are provided in Figure 12. Increasing the gain coefficient from 70 to 150 m\({}^{-1}\) with identical reverse absorption coefficient (0.0015 W\({}^{-1}\)) leads to linearly increased pulse energies and pulse durations with nearly unchanged peak powers.