## 4 Analysis and Discussion
Therefore, the pulse propagation will not mainly depend on the temperature, which confirms that the FCA will dominate the propagation for high pulse energy cases, in which strong pulses will produce high concentration free carriers. Thus, for the high pulse energy cases, the output pulse is similar and independent of temperature and input energy, which leads to output pulses with narrow spectral bands. The data for Figures 7-12 are listed in Tables 1-3. The output sharp pulses perform enhanced acceleration and pulse compression with the increase of temperature when there is a higher input of pulse energy. Relative to 12 \({}^{\circ}\)C, the output of sharp pulse acceleration is 283.5 fs at 25 \({}^{\circ}\)C and 1278.6 fs at 52.8 \({}^{\circ}\)C for an input energy of 1.1 pJ, 554.9 fs at 25 \({}^{\circ}\)C and 1834.9 fs at 52.8 \({}^{\circ}\)C for an input energy of 2.7 pJ, and 285.7 fs at 25 \({}^{\circ}\)C and 1620.2 fs at 52.8 \({}^{\circ}\)C for an input energy of 5.3 pJ, as shown in Table 3. \begin{table}
\begin{tabular}{c c c c c c c c c} \hline  & & \multicolumn{2}{c}{**12.0 \({}^{\circ}\)C**} & \multicolumn{3}{c}{**25.0 \({}^{\circ}\)C**} & \multicolumn{3}{c}{**52.8 \({}^{\circ}\)C**} \\ \cline{2-10} \multirow{-2}{*}{**Pulse Energy (pJ)**} & \multicolumn{3}{c}{**FWHM (fs)**} & \multicolumn{3}{c}{**FWHM (fs)**} & \multicolumn{3}{c}{**FWHM (fs)**} \\  & **Ahead** & **Back** & **Total** & **Ahead** & **Back** & **Total** & **Ahead** & **Back** & **Total** \\ \hline
1.1 & 649.15 & 208.48 & 208.48 & 484.48 & 194.10 & 194.10 & 195.36 & NON & 195.36 \\
2.7 & 887.7 & 226.23 & 226.23 & 474.78 & 193.25 & 193.25 & 197.48 & NON & 197.48 \\
5.3 & 836.81 & 229.61 & 229.61 & 570.05 & 267.92 & 267.92 & 202.96 & 188.96 & 202.96 \\
13.3 & 1135.16 & 273.88 & 273.88 & 1046.80 & 321.30 & 321.30 & 1046.63 & 225.64 & 1046.63 \\
26.7 & 1230.85 & 276.72 & 1230.85 & 1126.26 & 246.35 & 246.35 & 1125.00 & 378.96 & 1125.00 \\
35.2 & 1353.32 & 271.32 & 1353.32 & 1092.72 & 242.68 & 242.68 & 1339.00 & 301.54 & 1339.00 \\ \hline \end{tabular}
\end{table} 
Table 1: Pulse duration of the output pulses measured by XFROG (FWHM). Figure 12: Temporal intensity profiles (**a**) and spectral intensity profiles (**b**) of the output pulses retrieved from the XFROG measurements for 352 pJ input pulse energy at temperatures of 12 \({}^{\circ}\)C, 25 \({}^{\circ}\)C, and 52.8 \({}^{\circ}\)C.  
As shown in Figure 13, the output pulse temporal centroids agree with the spectral centroids for different coupled input pulse energies at different temperatures. When the energy of input pulses increased, the TPA intensity increased, as did the enhancement of FCA and FCD, and the output pulses showed pulse deceleration and red shift. The same phenomenon was illustrated in Figure 13c,d. The FCA of SPNW for femtosecond pulses caused pulse deceleration, and the TOE caused the move in the opposite direction for the femtosecond pulse [36]. Further, Figure 13a shows that the TOE caused pulse acceleration and the effect was nonlinear. The FCD of SPNW for femtosecond pulse caused pulse red shift and the TOE caused the blue shift [36]. Figure 13b shows that the TOE caused pulse blue shift and the effect was nonlinear. As the silicon has a large temperature sensitivity due to the TOC, the indexes of the SPNW are influenced by TOC. The measurements indicate that the asymmetry of FCA and FCD is enhanced and