## 6 Nonequivalent Influence of Pulses' GVM on the THG Efficiency under Cascading SHG  
Here, we discuss how GVM between the interacting waves influences the TH conversion efficiency. We show that the GVM between FW and SH does not remarkably influence THG's efficiency. However, it can change the shapes of interacting pulses. In contrast, the GVM between TH and FW can strongly decrease the generation process efficiency. Consequently, it is important to find a way to compensate (or, at least, decrease) the GVM influence in this case. One of the possible methods is proposed below. GVM between the SH and FW (\(\
u_{21}\
eq 0\), \(\
u_{31}=0\)): Weak Influence on the Frequency Conversion Efficiency  
Let us suppose first that the FW and TH have the same group velocity, which means that the dimensionless parameter \(\
u_{31}\) is equal to zero: \(\
u_{31}=0\). We explore three different cases: SH has the same group velocity as the FW (\(\
u_{21}=0\)). The next case is the following: the SH group velocity does not much differ from the first one; therefore, all three pulses propagate together (\(\
u_{21}=0.01\)) along the propagation distance under consideration. The last case corresponds to large GVM between SH and FW (\(\
u_{21}=1\)). Consequently,the pulse at doubled frequency leaves a time domain occupied by two other waves at the pulse propagation in a linear medium. The computer simulation results computed for the parameters \(\gamma=1,\Delta_{21}k=20\), \(\Delta_{31}k=0\), \(D_{1}=-0.000032\), \(D_{2}=-0.000083\), \(D_{3}=-0.000199\) which correspond to the incident pulse duration about 1 ps are presented in Figure 17. In other cases, they are proportionally changed (GVM parameters vary as a linear function of \(\tau_{p}^{-1}\), SOD coefficients vary as \(\tau_{p}^{-2}\)). One can see that there is no visible difference between the energy conversion efficiency occurring at \(v_{21}=0\) and \(v_{21}=0.01\) because the pulse center shift is small. If the GVM is large (\(v_{21}=1\)) for the remarkable shift of the pulse centers on chosen propagation distance, then it slightly disturbs the pulse shapes at FF and tripled frequency. On the other hand, its influence on the conversion efficiency is positive because we do not observe any conversion efficiency oscillations in Figure 17i which are present in Figure 17g,h. At the same time, the maximum conversion efficiency remains the same (about 67%). It should be underlined that the spectra of FW and TH pulses are broadened in comparison with the incident pulse spectrum. This means that it is possible to compress the pulse with tripled frequency. If the incident pulse duration is decreased until \(\tau_{p}=100\) fs, for which the SOD coefficients are equal to \(D_{1}=-0.0032\), \(D_{2}=-0.0083\), \(D_{3}=-0.0199\), then the GVM influence on the shape pulses is a little bit stronger (Figure 18). As in the previous case, there is no visible GVM influence if GVM is weak. For large GVM (\(v_{21}=1\), right column), the pulse deformation can be seen for the right sub-pulse of FW. The THG maximum energy conversion is lower in Figure 18i than in Figure 18g,h, and there are not any energy conversion efficiency oscillations as in Figure 17i. However, the TH pulse spectrum is narrower in comparison with the previous case. With further a further decrease in the pulse duration (\(\tau_{p}=50\) fs), the interaction of waves remains the same. However, due to greater SOD influence, pulse shapes are nearly symmetric, even in the case \(\
u_{21}=1\).