## 4 Computer Simulation Results
### Frequency Conversion to Radiation with the Wavelength 10 \(\mu m\)  
If the LFW's wavelength equals 10 \(\mu\)m, then the dimensionless SOD coefficients are equal to \(D_{1}=0.1633\), \(D_{2}=0.0755\), \(D_{3}=-0.0414\) for the crystal AgGaS\({}_{2}\), respectively. Thus, the HFW undergoes a normal dispersion, and the LFW and IFW undergo anomalous ones. In this case, LFW amplification is not monotonic as in the previous case.  
A significant increase of the conversion efficiency can be achieved by increasing the nonlinear coupling coefficient \(\gamma\) up to 4 to decrease the crystal length. In this case, the sum incident pulses intensity has to equal 330 GW/cm\({}^{2}\), keeping in mind the changing of the wavelength, increasing the coefficient \(\gamma\), and changing the quadratic susceptibility due to changing the wavelength. It should be noted that this value is relatively high and perhaps requires an account for the influence of the third-order susceptibility on the three pulse interactions. Our computation shows that the dimensionless third-order nonlinear coefficient is equal to 0.02 in the case under consideration. Therefore, analyzing laser pulse interactions in short distances, the third-order nonlinear effects can be neglected.  
The computer simulation results are depicted in Figure 4 for the phase mismatching between IFW and LFW equaling \(\Delta_{21}k=22\).  
As one can see, there is a very effective generation of the IFW, although this wave is not phase-matched with two other waves in this case (Figure 4a). The LFW amplification efficiency achieves 41% and the intensive energy conversion to this wave occurs between sections \(z=2\) and \(z=3\), including the explosive energy conversion of the interacting waves. Then the energy exchange between the interacting waves becomes very small.  
Figure 3: Pulse shapes in the section \(z=50\) (**a–c**), 30 (**d**); pulse intensity evolution at the 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**).  
Unfortunately, the pulse shapes have many local maxima and minima, which make the use of this mode of wave interactions for the frequency down-conversion impossible, in practice. It should be stressed that at a smaller incident intensity of the LFW (\(|A_{10}|^{2}\)), the process of the frequency conversion takes place in the same manner, but with lower efficiency.  
There is a similar conclusion with the LFW. The pulse shapes are also not smooth, and the HFW energy transfers to both LFW and IFW (Figure 4b). As a result, the frequency down-conversion efficiency achieves 21%.  
The quality of the pulse shape and the frequency conversion efficiency can be sufficiently improved by increasing the incident pulse duration, for instance, until \(\tau_{P}=1\) ps. This leads to decreases in the dimensionless GVD coefficients, for 100 times, and allows us to avoid developing the modulation instability of the pulses (Figure 4c,d). We see in this figure that even at a smaller value of the nonlinear coupling coefficient (\(\gamma=1\)) corresponding to the incident intensity 20.66 GW/cm\({}^{2}\), the conversion efficiency achieves a value of about 76% (Figure 4d). However, it requires increasing the length of the crystal: about 4 cm.