## 2 Experimental Results
We first performed a balanced intensity scan twin-detected method (I-scan) to distinguish the correlation between CNT-SA parameters and output characteristics, where the CS generated, abovementioned, was set as a seed laser and injected into an amplifier. Detailed configurations are demonstrated in Figure 5. The amplified laser was set as a test source of the I-scan technique to acquire the same intracavity power scale of the CNT-SA mode-locked fiber laser generated. The pulse duration associated with optical spectrum of the amplifier was kept identical in the ML CNT-SA mode-locked  
Figure 4: Function of experimental NLP characteristics and NLP behavior with pump power. (**a**) Typical NLP AC trace at the pump power of 280 mW, inserted shows the NLP spike area; (**b**) the corresponding spectrum; (**c**) NLP behavior with increasing pump power from 160 mW to 400 mW, inserted shows the NLP spike area; (**d**) the corresponding spectra evolution with zoomed-in NLP spectra. Figure 3: Function of experimental CS behavior with pump power. (**a1**)–(**a3**) CS pulse broadening and breaking-up with increasing pump power from 40 to 200 mW; (**b1**)–(**b3**) the corresponding spectra. fiber laser. Transmittance curves functioned with peak power using ML and BL CNT-SA are shown in Figure 6 and fitted by the saturable absorption formula:  
\[T(I)=1-\alpha\cdot\exp(-I/I_{sat})-\alpha_{ns}-\beta\cdot I \tag{1}\]  
where \(T\) represents the transmission, \(\alpha_{ns}\) is the non-saturable loss coefficient, \(\alpha\) is the modulation depth, \(\beta\) is reverse absorption coefficient, \(I_{sat}\) is the saturable intensity, and \(I\) is the incident laser intensity. By fitting the experimental data, the estimated ML CNT-SA modulation depth is about 3.1%, \(I_{sat}\) is 50 kW, and \(\alpha_{ns}\) is 41.5%, respectively. The estimated BL CNT-SA modulation depth is about 4.7%, \(I_{sat}\) is 38 kW, \(\beta\) is \(2.68\times 10^{-4}\) W\({}^{-1}\), and \(\alpha_{ns}\) is 61%, respectively. These results indicate different modulation depths and linear losses in the ML and BL CNT-SA configurations. Specifically, BL CNT-SA owns the ability to introduce reverse absorption coefficient into the laser cavity, whereas ML CNT-SA does not. The reasons can be concluded that single-wall CNT has large scattering loss than other nanomaterials, thus enhancing the nonlinear scattering loss with more CNTs. Meanwhile, the two-photon absorption effect of single-wall CNT will also excite reverse absorption coefficient. Both are considered as primary factors leading to the transformation from CS to NLP with BL CNT-SA setup. To be honest, polyvinyl alcohol (PVA) has a relatively lower thermal threshold compared to CNT nanomaterial, high peak power pulses may degrade the PVA polymer hence decreasing the laser transmittance ratio. These mechanisms of CNT polymer matrix may give an inspection of why ML-CNT and BL-CNT could respond to different transmittance curves in experiments. To decrease the possibility of PVA degradation, long time CS and NLP output stabilities were tested in experimental as shown in Figure 7a,b. Figure 5: Schematic of I-scan system. Seed laser pulse type is the CS, inserted shows the AC trace and corresponding spectrum of the CS laser; amplifier is used to increase the output CS power to reach the intra-cavity power level, insert shows the amplifier spectra evolution; I-scan setup is used to detect the saturable absorption of CNT-SA. Figure 6: Nonlinear saturable absorption of ML CNT-SA and BL CNT-SA using homemade I-scan system.