## 4 Analysis and Discussion  
According to the above experimental results, the femtosecond pulse will undergo a much different propagation in the waveguide for different temperatures and input pulse energy, which may owe to the thermal characteristics and the free carrier effects of the silicon. Silicon is temperature sensitive, with a large TOC of about \(1.86\times 10^{-4}\) K\({}^{-1}\). There may be many kinds of nonlinear effects with the femtosecond pulse propagation in the SPNW, such as the SPM, TPA, FCA, FCD, and Kerr nonlinearity. The main phenomena are pulse acceleration, blue shift and red shift, pulse broadening, and pulse compression with different temperatures and inputs of pulse energy, as shown in Figures 7-12. When only the SPM and GVD are considered, the produced chirp just affects the blue shift of the pulse and is symmetrical to the front and back edges of the pulse [35]. At the same time, the TPA is proportional to the light intensity in the SOI waveguide, which produces a large number of free carriers, and then the FCD and FCA change. Kerr nonlinearity is based on the second order refractive index, and the temperature changes the index of the SPNW. The experiment above changed the inputs of pulse energy and the temperatures of the SPNW, and then separated the effect of the temperature on the refractive index as the thermo-optic effect (TOE) [36] in order to discuss the influence of temperature of the pulse transmission in the SPNW more clearly. Figure 8: Temporal intensity profiles (**a**) and spectral intensity profiles (**b**) of the output pulses retrieved from the XFROG measurements for 2.7 pJ input pulse energy at temperatures of 12 \({}^{\circ}\)C, 25 \({}^{\circ}\)C, and 52.8 \({}^{\circ}\)C.  
Figure 7: Temporal intensity profiles (**a**) and spectral intensity profiles (**b**) of the output pulses retrieved from the XFROG measurements for 1.1 pJ input pulse energy at temperatures of 12 \({}^{\circ}\)C, 25 \({}^{\circ}\)C, and 52.8 \({}^{\circ}\)C.  
Figure 11: Temporal intensity profiles (**a**) and spectral intensity profiles (**b**) of the output pulses retrieved from the XFROG measurements for 26.7 pJ input pulse energy at different temperatures of 12 \({}^{\circ}\)C, 25 \({}^{\circ}\)C, and 52.8 \({}^{\circ}\)C.  
Figure 10: Temporal intensity profiles (**a**) and spectral intensity profiles (**b**) of the output pulses retrieved from the XFROG measurements for 13.3 pJ input pulse energy at temperatures of 12 \({}^{\circ}\)C, 25 \({}^{\circ}\)C, and 52.8 \({}^{\circ}\)C.  
Figure 9: Temporal intensity profiles (**a**) and spectral intensity profiles (**b**) of the output pulses retrieved from the XFROG measurements for 5.3 pJ input pulse energy at temperatures of 12 \({}^{\circ}\)C, 25 \({}^{\circ}\)C, and 52.8 \({}^{\circ}\)C.  
According to Figures 7-9, in the case of low pulse energy, with the increase of temperature, the blue shift will be more remarkable and the pulse acceleration will be more developed, which is considered to be mainly induced by the FCA in silicon nanowire waveguides [35]. We also can find that, in the case of low pulse energy, the femtosecond pulse will be split into two temporal sub-peaks at low temperature, while it will be split into three spectral sub-peaks at high temperature, i.e., 1520 nm, 1540 nm, and 1584 nm at 52.8 \({}^{\circ}\)C, which also confirms that the FCA effect has taken place, and that the red shift was simultaneously induced by the dispersive wave. For the high pulse energy cases, as shown in Figures 10-12, the temporal pulse split and pulse broadening was remarkable, while the spectral energy was concentrated on the red-shift wavelength, and the blue-shift part weakened and even disappeared gradually. Furthermore, the pulses decelerated rather than accelerated, which could be the result of the weakening and disappearing of the blue-shift part.