## 1 Introduction  
Infrared optics and THz optics have various practical applications, including spectroscopy [1, 2], optical metrology [3], material measurements [4], sensing [5], diagnostics, detection, identification of substances, etc. One of the possible ways to obtain laser radiation in these ranges of the frequencies is via a frequency down-conversion process, due to the difference frequency's wave generation in a medium with a quadratic nonlinear response. The difference frequency's wave generation, whose frequency belonging to an infrared frequencies range, has attracted the attention of many researchers. Below, we mention some of them. In [6], the femtosecond pulses with tunable wavelengths belonging to the interval (3.2-4.8 um), and possessing a maximal average power of about 1.1 mW, were generated in the MgO:LiNbO\({}_{3}\) crystal. In [7], a tunable source of the mid-infrared CW radiation with a maximal power of 51 mW at a wavelength \(\lambda_{1}=6543\) nm was created based on the difference frequency's wave generation in a GaAs crystal. Optical frequency combs with wavelengths belonging to their intervals (2.8-3.5 um) were generated in MgO:PPLN crystal using the difference frequency's wave generation [8]; a similar result was also obtained in GaSe crystal with the frequency combs generation, in the wavelength range 3-10 um [9]. Frequency down-conversion also consists of using the optical parametric oscillation process. Thus, in [10], by using this tool, a conversion efficiency of 34% was achieved with the average output power of 7.7 W at the power of the incident pump pulse equal to 23 W. The IR radiation at a wavelength 7 um with an energy of 0.71 mJ was obtainedwith a 7.8% quantum conversion efficiency in BaGa\({}_{4}\)Se\({}_{7}\) crystal [11]. Tunable IR radiation generation belonging to the wavelength range 4.4-5.7 \(\upmu\)m, with a maximal output energy of 13.1 \(\upmu\)J, was achieved in [12], using La\({}_{3}\)Ga\({}_{5.5}\)Nb\({}_{0.5}\)O\({}_{14}\) crystal. A review of the frequency down-conversion processes in non-oxide media can be found in [13]. A THz radiation source using difference-frequency generation was also obtained in many nonlinear media. For example, a THz pulse with the wavelength in the range of 290-140 \(\upmu\)m was realized in a LiNbO\({}_{3}\) crystal [14]. The periodically-poled LiNbO\({}_{3}\) crystal was used in [15], the frequency range was 1.5-1.8 THz; a maximal power was equal to 0.1 mW); and in [16], the wavelength range was 190-210 \(\upmu\)m and 457-507 \(\upmu\)m; the maximal energies were equal to 0.37 and 0.057 pJ, respectively; in [17], the authors explored the realization of a generation scheme of the difference-frequency equal to 0.5 THz with a conversion efficiency of 30%. It should be noted that, in a series of studies, i.e., [18; 19; 20; 21] and the corresponding references listed in those papers, the THz radiation with a wavelength range of 66.5 \(\upmu\)m, 5664 \(\upmu\)m was obtained in crystals GaSe, ZnGeP\({}_{2}\) GaP based on difference frequency's wave generation with conversion efficiency equal to 0.1%. Crystal ZnTe is often used for frequency down-conversion to obtain a THz radiation. We can note, for example, the following papers: [22], where pulse 1 THz was obtained as 365 and 364 THz frequency differences and with a 0.6% conversion efficiency. In Reference [23], the authors demonstrated the possibility of pulse generation with tunable frequency, in the range of 0.3-2.5 THz, and power up to 1 \(\upmu\)W based on difference-frequency generation involving interactions of picosecond pulses, with intensity at 2.58 \(\times\) 10\({}^{8}\) W/cm\({}^{2}\) generated with 1.5% conversion efficiency. In another THz pulse source with tunable frequency, the frequency range was 0.3-19.6 THz, with energy at 870 nJ, and was obtained in the DAST crystal lit by an incident pulse with a power density of 247 MW/cm\({}^{2}\)[24].