## 5 THG Efficiency in Dependence of SOD Coefficients and Phase Mismatching between Interacting Waves
### Crucial Influence of Phase Mismatching between TH and FW on Frequency Conversion Efficiency  
Below, we consider the influence of weak phase mismatching between FW and TH (\(\Delta_{31}k=\pm 0.01\), \(\pm 0.1\), \(\pm 0.2\), \(\pm 0.4\)) under a rather large phase mismatching between FW and SH (\(\Delta_{21}k=\pm 20\)) on THG's efficiency. Computer simulation results, obtained for the incident pulse duration 100  fs in both signs of SOD, are shown in Table 4.  
Its influence on the THG efficiency is weak enough for the positive phase mismatching between SH and FW if the absolute value of \(\Delta_{31}k\) is less than 0.01. However, when choosing the corresponding sign of the phase mismatching \(\Delta_{31}k\), one can even increase the THG efficiency by 3% (\(\Delta_{31}k=-0.01\)). With the growth of \(|\Delta_{31}k|\) until 0.1, the energy conversion efficiency decreases, and this decreasing depends on the \(\Delta_{31}k\) sign. Nevertheless, even in this case, about 45% of the incident energy is converted to the TH energy. A sign of the SOD at FF does not remarkably change the conversion efficiency. However, the TH pulse spectrum width is greater if a medium possesses anomalous dispersion at the FF. Comparing Tables 4 and 5, one can see the more pronounced influence of the phase mismatching between FW and TH on the THG efficiency if the phase mismatching between FW and SH is negative: \(\Delta_{21}k<0\) (Table 5). In this case, one can differentiate two modes occurring for small \(|\Delta_{31}k|\) (0.01 or smaller) and rather large \(|\Delta_{31}k|\) values: (0.1 and larger). In the first case, a product of \(D_{1}\) and \(\Delta_{31}k\) must be positive to increase the THG efficiency. As follows from Table 5, at normal dispersion of a medium, the maximum conversion efficiency may be increased by 14% by the appropriate \(\Delta_{31}k\) in comparison with its corresponding value achieved at \(\Delta_{31}k=0\). For the anomalous dispersion of a medium at FF, this conversion efficiency enhancement is not so big; however, it can be observed. At larger values of the phase mismatching between FW and TH, the sign of \(\Delta_{31}k\) strongly influences the THG efficiency regardless of normal or anomalous dispersion of the medium at FF. In both cases, the negative value of \(\Delta_{31}k\) is more preferable than the positive one. For example, the maximum THG efficiencies are equal to 0.44 and 0.38 at \(\Delta_{31}k=-0.2\), respectively, which are bigger than 0.32 and 0.35, reaching at \(\Delta_{31}k=0.1\) (the seventh row of Table 5). If phase mismatching between the FW and SH is much larger (for example, \(\Delta_{21}k=127\)), then acceptable values of the phase mismatching between the FW and TH \(\Delta_{31}k\) become less. We see in Table 6 that the difference between THG efficiency at \(\Delta_{31}k=\pm 0.01\) and \(\Delta_{31}k=\pm 0.1\) is very large. So, at \(\Delta_{31}k=\pm 0.01\), the THG efficiency remains rather high. Moreover, it is even bigger at \(\Delta_{31}k=-0.01\) than at \(\Delta_{31}k=0\) if a medium possesses the anomalous dispersion at the FF.