## 4 Computer Simulation Results
### Frequency Conversion to Radiation with the Wavelength 4 \(\mu\)m
#### 4.1.1 Incident IFW's Intensity Is Equal to Zero  
We begin our consideration from the case for which a non-zero value of the intensities of incident LFW and HFW takes place (of course, the HFW possesses much more energy, than LFW), meanwhile, the intensity of incident IFW is absent: \(|A_{20}|^{2}=0\). In this case, we analyze an influence of the intensity ratios between LFW and HFW on the effectiveness of energy conversion. First, we consider the positive phase mismatching between LFW and IFW (\(\Delta_{21}k=20\)). Figure 2 presents the computer simulation results for various maximal intensities of the incident LFW: \(|A_{10}|^{2}=0.05,\,0.07,\,0.08,0.1\). We emphasize that the first two values of the intensity lead to the low-effective mode of the frequency down-conversion, and the two last values--to its high-effective mode. Figure 2: Pulses’ shapes in the sections \(z=20\) (**a**), 25 (**b**), 30 (**c**), 40 (**d**); pulse intensity evolution at their centers (**e**–**h**), and the frequency conversion efficiency evolution (**i**–**l**) along the \(z\)-coordinate computed for \(|A_{10}|^{2}=0.05\) (**a**,**e**,**i**), 0.07 (**b**,**f**,**j**), 0.08 (**c**,**g**,**k**), 0.1 (**d**,**h**,**l**). Indeed, at the incident intensity \(|A_{10}^{2}|=0.05\), there is no remarkable frequency conversion between HFW and LFW (Figure 2i): \(\eta_{1}\) grows from 5% only to 7%. The LFW intensity at the pulse center also grows a little bit (Figure 2e). As for the shapes of the pulses (Figure 2a), the LFW pulse shape becomes flatter than the initial one, and the HFW pulse decompresses due to the SOD influence. Moreover, a weak IFW generation occurs (as it is supposed to). The same situation is practically observed in the two next cases. At \(|A_{10}|^{2}=0.07\), the frequency conversion is slightly more effective: \(\eta_{1}\) grows two times; from 7% to 15% (Figure 2j). Other peculiarities, such as the LFW intensity growth at the pulse center (Figure 2f), flattening of the LFW pulse shape, the HFW pulse decompression, and weak IFW generation (Figure 2b), are conserved. The incident intensity \(|A_{10}|^{2}=0.08\) does not experience enough improvement of the frequency down-conversion (\(\eta_{1}\), achieving only 19% (Figure 2k)) in contrast to those achieved in the framework of the long-duration pulse approximation. The explosive increasing frequency conversion efficiency occurs at \(|A_{10}|^{2}=0.1\). In this case, the LFW intensity at the pulse center (Figure 2h) rises much faster than in all previous cases and even achieves the incident HFW intensity. Moreover, the LFW pulse (Figure 2d) is a bit more narrow than the incident HFW one.Thus, the resulting frequency conversion is very impressive: more, than 69% of the sum energy transfers to LFW (Figure 2l). It is worth noting that the HFW pulse has a local minimum near the pulse center, in this case (Figure 2d). If we take into account the GVDs of the optical pulses, then a sign of the phase mismatching \(\Delta_{21}k\) will influence the conversion efficiency. So, if we choose a negative (\(\Delta_{21}k=-20\)), then the situation changes, essentially because an action of a medium leads to decompression of the interacting pulses due to changing of the effective nonlinear response (see above: \(\bar{x}=\gamma^{2}/\Delta_{21}k\)). Because the GVD coefficient \(D_{1}\) of the LFW is considerably small, this pulse undergoes decompression very weakly. As a consequence, the energy from the central part of the HFW converts to the energy of LFW, and the LFW intensity at the pulse center becomes larger than those occurring for \(\Delta_{21}k=20\) (compare Figure 3e-h with Figure 2e-h). However, the pulse of HFW spreads faster, and most of it locates out of the time interval in which two other pulses are located. Consequently, no remarkable frequency conversion occurs far from the pulse centers.