## 4 Results and Discussion
### Other Parameters Needed in SC Simulation  
In order to further validate the influence of an accurate Raman response function on the precise simulation of supercontinuum, this study compares the SC obtained using two different methods, namely, the single Lorentzian model and the multiple vibrational mode model, with experimentally measured results. Consequently, an experimental setup was prepared to generate SC using a Ge-Sb-Se SIF with a 11 \(\upmu\)m core diameter and a fixed core-cladding ratio of 11/305. The parameters required for SC simulation, such as refractive index, dispersion, effective model area and nonlinear coefficient, were calculated using Equation (1). Additionally, the fiber's loss coefficient was determined using a cut-back method, the loss spectrum of the Ge-Sb-Se SIF as shown in Figure 6. As noted in the figure, the Ge-Sb-Se SIF shows a lower loss of 1.62 dB/m at 6 \(\upmu\)m. The absorption peaks centered at 2.86 and 4.5 \(\upmu\)m, corresponding to O-H and Se-H bonds, respectively, are still present evidently due to pollution by oxygen or water molecules; therefore, we selected 3.8 \(\upmu\)m as the pumping wavelength for our experiments in this study. The wavelength-dependent linear refractive indices of the CHG glasses used for the design of the proposed fiber are expressed using the Sellmeier dispersive formula as follows [43]:  
\[n^{2}=1+\frac{B_{1}\lambda^{2}}{\lambda^{2}-C_{1}}+\frac{B_{2}\lambda^{2}}{ \lambda^{2}-C_{2}} \tag{7}\]  
where \(B_{1}\) and \(B_{2}\) are dimensionless coefficients, and \(C_{1}\) and \(C_{2}\) are related to the glass resonance wavelengths [44]. Table 2 provides the different values of the Sellmeier coefficients, and Figure 7 depicts the variation of the linear refractive index with wavelengths for both Ge\({}_{12.5}\)Sb\({}_{15}\)Se\({}_{72.5}\) and Ge\({}_{15}\)Sb\({}_{10}\)Se\({}_{75}\) ChG glasses. Figure 6: The loss spectrum of the Ge–Sb–Se SIF measured using the cut-back method. During the SC generation process, the impact of dispersion outweighs the impact of loss. The higher-order dispersion obtained by the propagation constant at any frequency relative to the pulse central frequency can be expanded as the Taylor series expansion as noted in Equation (8) [45]. \[\beta(\omega)=\beta_{0}+\beta_{1}(\omega-\omega_{0})+\frac{1}{2!}\beta_{2}( \omega-\omega_{0})^{2}+\frac{1}{3!}\beta_{3}(\omega-\omega_{0})^{3}+\ldots \tag{8}\]  
Here \(\beta_{k}=\left(\frac{d^{k}\beta(\omega)}{d\omega^{k}}\right)_{\omega=\omega_{ 0}}\), and the variable \(k\) takes values up to 10 in this study. The \(\beta_{2}\) in Equation (8) corresponds to the group velocity dispersion (GVD). It determines the extent to which the different spectral components of the ultrashort pulse propagate at different phase velocities in the SIF, resulting in these different frequency components having arrived at the output at different times. This feature is recognized as the main factor contributing to spectral broadening. To quantitatively represent GVD, the dispersion coefficient D is commonly incorporated into the calculation process, as illustrated in Equation (9) [46]. \[D(\lambda)=-\frac{\lambda}{c}\frac{d^{2}\text{Re}(n_{eff})}{d\lambda^{2}}=- \frac{2\pi c}{\lambda^{2}}\beta_{2} \tag{9}\]  
Here, \(\text{Re}(n_{eff})\) represents the real part of the effective refractive index, and \(c\) is the speed of light. In order to accurately calculate dispersion, it is essential to determine the effective refractive index of the fiber. As the effective refractive index is related to refractive index of the fiber's core and cladding as well as the waveguide structure of the fiber, we simulated our design to calculate the refractive index of the core and cladding of Ge-Sb-Se SIF in Figure 7. The dispersion curve of Equation (9) is shown in Figure 8.