## 4 Analysis and Discussion
\begin{table}
\begin{tabular}{c c c c c c c c c c} \hline \hline \multirow{2}{*}{**Pulse Energy (pJ)**} & \multicolumn{2}{c}{**12.0 °C**} & \multicolumn{2}{c}{**25.0 °C**} & \multicolumn{2}{c}{**52.8 °C**} \\ \cline{2-10}  & \multicolumn{2}{c}{**Centroid (nm)**} & \multicolumn{2}{c}{**Centroid (nm)**} & \multicolumn{2}{c}{**Centroid (nm)**} & \multicolumn{2}{c}{**Centroid (nm)**} \\  & **Left** & **Center** & **Right** & **Left** & **Center** & **Right** & **Left** & **Center** & **Right** \\ \hline
1.1 & 1548.4 & NON & 1584.3 & 1547.9 & NON & 1585.1 & 1524.5 & 1548.9 & 1582.9 \\
2.7 & 1536.9 & NON & 1586.3 & 1544.4 & NON & 1586.9 & 1516.8 & 1546.9 & 1585.6 \\
5.3 & 1536.9 & NON & 1586.3 & 1539.6 & NON & 1587.8 & 1506.8 & 1545.7 & 1587.0 \\
13.3 & 1527.0 & NON & 1586.2 & 1531.4 & NON & 1587.9 & 1528.9 & NON & 1587.6 \\
26.7 & 1520.1 & NON & 1585.3 & 1525.9 & NON & 1587.2 & 1519.3 & NON & 1586.1 \\
35.2 & 1517.6 & NON & 1585.1 & 1523.9 & NON & 1586.8 & 1517.4 & NON & 1585.8 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Spectral pulse centroids of the output pulses. Figure 13: Temporal centroid (**a,c**) and spectral centroid (**b,d**) for different input pulses energies while the SPNW is at different temperatures. \begin{table}
\begin{tabular}{c c c c c c c c c c c} \hline \hline \multirow{2}{*}{**Pulse Energy (pJ)**} & \multicolumn{2}{c}{**12.0 °C**} & \multicolumn{2}{c}{**25.0 °C**} & \multicolumn{2}{c}{**52.8 °C**} \\ \cline{2-10}  & \multicolumn{2}{c}{**Centroid (fs)**} & \multicolumn{2}{c}{**Centroid (fs)**} & \multicolumn{2}{c}{**Centroid (fs)**} & \multicolumn{2}{c}{**Centroid (fs)**} & \multicolumn{2}{c}{**Centroid (fs)**} & \multicolumn{2}{c}{**Back**} & **Total** \\ \cline{2-10}  & **Ahead** & **Back** & **Total** & **Ahead** & **Back** & **Total** & **Ahead** & **Back** & **Total** \\ \hline
1.1 & \(-\)423.6 & 463.6 & \(-\)14.1 & \(-\)674.0 & 153.1 & \(-\)199.0 & NON & NON & \(-\)842.0 \\
2.7 & \(-\)126.9 & 1009.6 & 218.9 & \(-\)495.1 & 464.7 & \(-\)60.1 & NON & NON & \(-\)825.3 \\
5.3 & \(-\)137.2 & 996.5 & 217.5 & \(-\)402.6 & 710.8 & 53.1 & \(-\)623.7 & \(-\)164.3 & \(-\)680.3 \\
13.3 & 105.4 & 1455.0 & 406.5 & 175.5 & 1105.1 & 224.7 & 101.5 & 1519.8 & 313.1 \\
26.7 & 192.9 & 1608.5 & 529.8 & 35.2 & 1474.4 & 384.9 & 346.0 & 1950.2 & 551.9 \\
35.2 & 360.6 & 1900.2 & 617.9 & 136.5 & 1619.0 & 454.0 & 582.1 & 2312.6 & 694.0 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Temporal pulse centroids of the output pulses. that the nonlinear influence of TOE makes the relative intensity distribution of pulse energy change, which causes the change in pulse velocity and pulse acceleration. With the increasing temperature, the output pulses will be split and broadened to a great extent with high input pulse energy, as shown in Figures 10-12 and Table 1. The TPA and FCD affect pulse broadening and splitting [35], which may lead to multi sub-peaks such as the left, the center, and the right peaks as shown in Table 1, Figure 13b, and Table 2.  
In brief, for low pulse energy inputs, we should make the waveguide work at low temperature to achieve major narrow spectral peaks and temporal peaks. While for high pulse energy input, the waveguide can work stably at a wide range of temperatures.