## 3 Discussion
The SH signal from the TWLA sample in air \(S_{entr}^{TWLA,Air}(\tau)\), similarly to SiO\({}_{2}\), mainly has a gas contribution. The difference in the \(S_{entr}^{TWLA,Air}(\tau)\) and \(S_{entr}^{SiO_{2}air}(\tau)\) profiles can be explained by the addition of the SH signal generated in air after the reflection from TWLA (\(A_{ref}^{air}(\tau)\) should be added to Equation (6)) by virtue of large TWLA reflection coefficients in optical and terahertz ranges. From the obtained values of the SH amplitudes \(\left|A_{ref}^{samp}\right|\), using Equation (8) we calculated the relation of the sample and SiO\({}_{2}\) susceptibilities \(\left|\chi_{samp}^{(3)}(2\omega)\right|/\left|\chi_{SiO_{2}}^{(3)}(2\omega)\right|\) (see Table 1). For tellurite glasses TWLA and TWLB, the ratio is 65 and 80, respectively. For chalcogenide glasses, it is more than 1000. IKS23 and As\({}_{2}\)S\({}_{3}\) exhibit equal nonlinear susceptibilities \(\sim 1200\left|\chi_{SiO_{2}}^{(3)}(2\omega)\right|\), which is consistent with their similar compositions. IKS25 has a nonlinearity about 1.5 times higher (\(\left|\chi_{IKS25}^{(3)}(2\omega)\right|\approx 1900\left|\chi_{SiO_{2}}^{(3)}(2 \omega)\right|\)), which is due to the stronger nonlinear response of Se contained in the sample [44]. Now we can compare the susceptibility values measured by the TFISHG technique with the data obtained from the z-scan. As mentioned in the Introduction, the nonlinear susceptibilities \(\chi_{SiO_{2}}^{(3)}(-2\omega;\omega,\omega,0)\) and \(\chi_{SiO_{2}}^{(3)}(-\omega;\omega,-\omega,\omega)\) for SiO\({}_{2}\) can be considered to be close, according to previous experimental measurements [22; 23; 24; 34]. For tellurite glasses and As\({}_{2}\)S\({}_{3}\), our measurements demonstrated that \(\chi_{samp}^{(3)}(-2\omega;\omega,\omega,0)\) is approximately a factor of 1.5 higher than \(\chi_{samp}^{(3)}(-\omega;\omega,-\omega,\omega)\). However, taking into consideration the measurement error of both methods, it is a very good agreement. Note that the main error in the TFISHG experiment was the calibration by the fused quartz. This calibration was made for the experimental conditions slightly differing from the main measurements, which could have produced a systematic error. For the IKS23 sample, the nonlinearity measured by the TFISHG method, in contrast, was 1.5 times smaller than that measured by the z-scan. As noted above, when considering z-scan measurements, this seems to be related to the different values of the intensity of the probe optical radiation. The intensity in the z-scan measurements was about 0.8 GW/cm\({}^{2}\) and was in the region of the increased nonlinear response of the sample, whereas in the TFISHG measurements, the optical intensity was about 25 GW/cm\({}^{2}\) and corresponded to a minimum saturation of nonlinearity [44]. This may explain the stronger nonlinear response of IKS23 in the z-scan. Finally, we can consider in brief the possible nuclear contribution to the SH generation. This contribution would evidently change the time-delay profile of the SH signal [56] (it will not trace the squared terahertz electric field). In our experiment, we observed some signal changes for the TWLA and TWLB glasses (see \(S_{entr}^{TWLA,He}(\tau)\) in Figure 3c). We explained these changes by the interference of the SH fields generated in helium and in the sample, which are in reasonable agreement with the experiment. The assumption of a nuclear contribution could also partially explain our experimental results, but it will add a tail in \(S_{entr}^{TWLA,He}(\tau)\), which was not observed in the experiment (Figure 3c). In the chalcogenide glasses, we did not find any deviation of the SH signal profile from the terahertz field squared within the accuracy of our experiment. Thereby, we do not expect that the nuclear contribution is essential in the SH response in the investigated samples.