# On the Impact of Wavelength Dependency on Supercontinuum Generation in Photonic Crystal Fibers
## 3 Results
### Comparison of Results  
Two different input pulses have been simulated for different powers. These simulations have been performed for the constant and functional parameter models, and the results showed the impact of the wavelength dependence over the propagation.  
In the first set of simulations, an input soliton pulse of a 50 fs width and a 2860 nm central wavelength were used. Also, the initial peak power values of 250, 500, and 1000 W complete the simulation set. In all cases, the distribution of the spectral intensity is represented on a logarithmic scale.  
In addition, Table 2 contains the fiber characteristic parameters, which have been used in the constant model, while the values with the wavelength dependence are those that appear in Figure 2.  
As we can expect, in both simulations, the appearance of notable power values can be observed for wavelengths that are not present in the original pulse. This, as we have already mentioned, is the essence of the supercontinuum-generation phenomenon.  
In the approach we propose, i.e., with a dependence on the wavelength of the simulation parameters, we observed a compression of the spectrum obtained with respect to the results of previous studies [16]. This effect is notable even for the lowest of the power values. Figure 4 shows the results for the propagation in the PCF, expressed as the power obtained for each of the wavelengths used.  
\begin{table}
\begin{tabular}{c c c c c} \hline \(\beta_{2}\) (\(ps^{2}\)/m) & \(\beta_{3}\) (\(ps^{3}\)/m) & \(\beta_{4}\)(\(ps^{4}\)/m) & \(\beta_{5}\) (\(ps^{5}\)/m) & \(\gamma\) (1/W/m) \\ \hline \(-0.0768\) & \(0.0031\) & \(-1.05\times 10^{-5}\) & \(7.858\times 10^{-8}\) & \(5.5\) \\ \hline \end{tabular}
\end{table}
Table 2: Linear and nonlinear propagation parameters in the wavelength constant case as taken from [16].  
Figure 3: Propagation profiles at different distances for the PCF, blue line. The wavelength dependence of the \(\beta_{2}\) parameter is superimposed. During propagation, the assigned power increases significantly in a wide range of wavelengths compared to the initial profile.  
In Figure 5, we can see the same results obtained in Figure 4, but using the temporal representation. This representation gives us the opportunity to interpret the supercontinuum generation process as being similar to the soliton fission mechanism [24; 25].  
A second case was simulated for a solitonic pulse with the same central wavelength, but with a 500 fs width. The same constant parameters of Table 2 were used, as well as the three same previous input powers. Figures 6 and 7 show the results for the wavelength and time domain representations.  
Figure 4: The upper row in the figure shows the spectral evolution of a 50 fs pulse when the wavelength dependence is included in the model, while the lower row contains the equivalent cases assuming constant values. The columns represent different input power values. As can be easily seen, the spectral width is narrower over all the propagation distance when the wavelength dependence is taken into account.  
Figure 5: In this figure, we can see the evolution, in the time window, of a 50 fs pulse through the PCF. The upper row corresponds to our model with functional dependence, and the lower row corresponds to the case of constant parameters. The columns represent different input power values.