## 4 Data Analysis and Discussion
The less intensive 5.81 THz feature on the \(I\)-\(V\) curves corresponds to the optical phonon mode at 5.82 THz in reflection measurements with \(E\ \mid\ c\) for YBa\({}_{2}\)Cu\({}_{3}\)O\({}_{6.95}\). However, it does not depend on oxygen deficiency, as follows from reflection measurements. The 5.71 THz feature on the \(I\)-\(V\) curves seems to belong to the 5.69 THz mode in reflection measurements with \(E\ \mid\ a\) for YBa\({}_{2}\)Cu\({}_{3}\)O\({}_{6.95}\), which does not change when going from YBa\({}_{2}\)Cu\({}_{3}\)O\({}_{6.95}\) to YBa\({}_{2}\)Cu\({}_{3}\)O\({}_{6.5}\). The intensities of the features at 2.69 and 3.54 THz on the \(I\)-\(V\) curves of JJs decrease with annealing in oxygen. Therefore, the collective modes in the bulk YBa\({}_{2}\)Cu\({}_{3}\)O\({}_{7-\rm x}\) with low oxygen content can be responsible for these features. Indeed, there are the modes at 2.79 THz in YBa\({}_{2}\)Cu\({}_{3}\)O\({}_{6.5}\) at \(E\ \mid\ c\) and at 3.48 THz in YBa\({}_{2}\)Cu\({}_{3}\)O\({}_{6.0}\) at \(E\ \mid\ \mid\ a\) (the third and second columns in Table 1). Moreover, there are no modes with close frequencies in YBa\({}_{2}\)Cu\({}_{3}\)O\({}_{7-\rm x}\) with higher oxygen content. The second-strongest feature on the \(I\)-\(V\) curves, with frequency transformation from 2.24 to 2.27 THz after annealing, has no candidate among the collective modes in YBa\({}_{2}\)Cu\({}_{3}\)O\({}_{7-\rm x}\) crystals. It looks like a replica of the 4.6 THz feature but at approximately twice as low frequencies. In weak perturbation of RSJ-like dynamics by external admittances of low values \(\mid\,Y_{c}(f_{c})\mid\,<<{R_{n}}^{-1}\) (see Equation (2)), a contribution to the \(I\)-\(V\) curve comes only from the first Josephson harmonic at the frequency \(f=2\)eV/h. However, the current-phase relation in the real JJ can contain the sin2\(\varphi\)-term, \(I_{\rm s}=I_{\rm c1}\)Sin\(\varphi+I_{\rm c2}\)Sin2\(\varphi\), and the \(I\)-\(V\) curve can demonstrate an additional feature at  
\begin{table}
\begin{tabular}{c c c c c c} \hline Our Data & [27,29] & [26,30] & [26] & [26] & [26,29] \\ YBa\({}_{2}\)Cu\({}_{3}\)O\({}_{7-\rm x}\) & YBa\({}_{2}\)Cu\({}_{3}\)O\({}_{6.0}\) & YBa\({}_{2}\)Cu\({}_{3}\)O\({}_{6.5}\) & YBa\({}_{2}\)Cu\({}_{3}\)O\({}_{6.7}\) & YBa\({}_{2}\)Cu\({}_{3}\)O\({}_{6.85}\) & YBa\({}_{2}\)Cu\({}_{3}\)O\({}_{6.95}\) \\ \(\rm{\rm J}\)/\(\rm{\rm k}\)(b) \(\rightarrow\) & \(F\)\(\mid\,\mid\,\)\(E\)\(\mid\,\mid\,\)\(E\)\(\mid\,\mid\,\)voltages \(V\) around \((1/2)\)h/\({}_{\mathrm{k}}\)/2e. In this case, the \(I\)-\(V\) curve of JJ should demonstrate a subharmonic resonance at \(V=(1/2)\)h/\(/2\)e on the \(I\)-\(V\) curves under weak THz irradiation. However, the experiments with similar bicrystal JJs and frequencies \(f\) of several THz did not reveal these subharmonic features [36]. In addition, from a theoretical point of view, bicrystal YBa\({}_{2}\)Cu\({}_{3}\)O\({}_{7-x}\) JJs with the mutually tilted \(c\)-axes are similar to so-called d0-d0 junctions and should have a pure sin\(\varphi\)-dependence of the current \(I_{s}\) vs. the phase difference \(\varphi\)[37]. Due to these experimental and theoretical grounds, we cannot consider this explanation of the subharmonic feature on the \(I\)-\(V\) curves by the sin2\(\varphi\)-term as a dominant one. Staying inside the RSJ model, one more explanation can be related to more intensive external shunting by \(\mid\)\(Y_{e}\)(\(f_{c}\)) \(\mid\) comparable with \(R_{n}\)\({}^{-1}\). In this case, the interaction of the second Josephson harmonic at the frequency \(f=2\times 2 eV/\)h with the collective modes at frequencies \(f_{k}\) around 4.6 THz can give the feature at \(V\) around \((1/2)\)h/\({}_{\mathrm{k}}\)/2e. To quantify this effect, one can either analytically consider the perturbation of RSJ dynamics by shunting in the second-order approximation, \(\sim\)(\(1\)\(Y_{e}\)(\(f_{c}\)) \(\mid\)\(R_{n}\))\({}^{2}\), or make numerical simulations for various values of \(\mid\)\(Y_{e}\)(\(f_{c}\)) \(\mid\)\(R_{n}\).