## 4 Experiment Setup and Results
### Optimized Experiments for MLS Signal Inhibition of SBS  
We measured the backward power at the back end of the beam splitter and defined the SBS threshold as the output power when the return power was 0.5%. For the AWG output signal, we used the feature polynomial \(\mathrm{x}^{9}+\mathrm{x}^{4}+1\) to write the PRBS-9 sequence, PRBS-9 MLS1, PRBS-9 MLS2, and PRBS-9 MLS3 by ourselves. We knew that MLS3 may reduce the SBS threshold even though it could better reduce the pulse intensity of the output light, and we tested this guess in our experiments. Figure 6 shows an \(f_{cr}\) of 8.5 GHz, an LPF cut-off frequency of 4.4 GHz, and the phase modulation of the original sequence and the optimized sequence in the output and backward power after seed laser amplification. Figure 5: Experimental setup of narrow-linewidth fiber laser based on spectrum broadening. Figure 6: The output power and backward power varied with the pump power using different sequence modulation: (**a**) the original sequence; (**b**) MLS1; (**c**) MLS2; (**d**) MLS3. As we can see from Figure 6a, the output power reached the SBS threshold at 2.844 W when the original sequence modulation was used, and the backward power was 1.637 mW. Figure 6b-d present that when MLS1 modulation was applied, the output power could be increased to 2.847 W, and the backward power was 1.606 mW, and the threshold was not reduced compared with the sequence. When MLS2 modulation was applied, when the output power reached 2.873 W, the backward power was 1.600 mW, and compared with the original sequence, the SBS threshold was not reduced but slightly increased. When MLS3 modulation was applied, the output power could reach 2.833 W, and the backward power was 1.595 mW, which was a relatively slight decrease in output power. In order to demonstrate universal applicability, we also changed the modulation parameters of the PRBS and performed control experiments, the results of which are available in Table 2.  
The results showed that the reasonable optimization of MLS sequences not only did not reduce the SBS threshold but also had certain advantages in improving the SBS threshold. MLS3 had the opposite effect on the output power increase, because the modification of the sequence reduced its randomness, resulting in the power spectral density no longer being the shape of the rigorous Sinc\({}^{2}\) envelope, which was consistent with the speculation in Section 3.2. Moreover, the effect of pattern 9 is better than that of pattern 7, which also confirmed the conclusion that a long sequence period inhibits SBS better, as in Ref. [23]. Figure 7 presents the output spectrum with a pattern n of 9, an \(f_{cr}\) of 8.5 GHz, an LPF cut-off frequency of 4.4 GHz, and an output power of 2.844 W. As can be seen from Figure 7a, the signal-to-noise ratio of the output spectrum was greater than 50 dB, and the spectrum contains only 1064 nm of signal light, indicating that the SBS effect was well suppressed by phase modulation, and Figure 7b shows a spectral pattern measured by an optical spectrum analyzer (OSA, HyperFine, HN-8995-2, Lightmachinery, Ottawa, ON, Canada) with a resolution of 0.8 pm, and the spectral half-height and width of 4.86 GHz were obtained. \begin{table}
\begin{tabular}{c c c c c c c} \hline \multirow{2}{*}{**n**} & **Clock Rate** & **LPF** & **Normal SBS** & **MLS1 SBS** & **MLS2 SBS** & **MLS3 SBS** \\  & **(GHz)** & **Frequency** & **Threshold** & **Threshold** & **Threshold** & **Threshold** \\  & & **(GHz)** & **(W)** & **(W)** & **(W)** & **(W)** \\ \hline  & 3.75 & 2 & 1.408 & 1.459 & 1.461 & 1.367 \\
7 & 8.5 & 4.4 & 2.801 & 2.808 & 2.812 & 2.756 \\  & 18 & 9.5 & 2.783 & 2.772 & 2.791 & 2.767 \\ \hline  & 3.75 & 2 & 1.448 & 1.516 & 1.670 & 1.440 \\
9 & 8.5 & 4.4 & 2.844 & 2.847 & 2.873 & 2.833 \\  & 18 & 9.5 & 2.895 & 2.898 & 2.902 & 2.858 \\ \hline \end{tabular}
\end{table} 
Table 2: SBS thresholds under different modulations under different n, clock rate, and LPF frequency.