## 4 Data Analysis and Discussion
One can suggest that bicrystal junctions formed from two mutually tilted \(c\)-axis films can have inhomogeneous currents along the boundary with several dominating channels and behave as a superconducting interferometer with dynamics different from those of a single RSJ-like JJ [38]. Even for two JJs in the interferometer, the appearance of the subharmonic Shapiro steps is predicted [39]. An additional subharmonic feature at \(V=(1/2)\)h/\(/2\)e was on the 1 THz detector response of the \(c\)-axis bicrystal junction JJ of 8 \(\upmu\)m width but absent in a similar junction of 2.5 \(\upmu\)m width [20]. However, the appearance of the subharmonic features in the JJ with mutually tilted \(c\)-axes does not depend on the width of the JJ, as one can see from Fig. 6, where subharmonic features are the same for 6 \(\upmu\)m(N1) and 1 \(\upmu\)m(N4) junctions. Therefore, we can conclude that interferometric effects on Josephson dynamics of the JJs cannot be the only reason for the features at \(V\) around \((1/2)\)h/\({}_{\mathrm{k}}\)/2e. Nonlinear effects in YBa\({}_{2}\)Cu\({}_{3}\)O\({}_{7-x}\) material itself under an intensive THz electric field from Josephson oscillations can be an alternative option to clarify the nature of the subharmonic feature at \(V\) around \((1/2)\)h/\({}_{\mathrm{k}}\)/2e on the \(I\)-\(V\) curves of YBa\({}_{2}\)Cu\({}_{3}\)O\({}_{7-x}\) bicrystal JJs. THz emission due to a nonlinear optical rectification (OR) in YBa\({}_{2}\)Cu\({}_{3}\)O\({}_{7-x}\) has already been observed [40]. One can expect that a second harmonic generation (SHG) in this material because the OR and SHG processes result from the same nonlinearity in optical materials [41]. There are no data on the effective nonlinear susceptibilities for OR and SHG in YBa\({}_{2}\)Cu\({}_{3}\)O\({}_{7-x}\); however, the electric THz fields from Josephson oscillations are rather intensive. Estimates give the field values around \(5\times 10^{4}\) V/cm for the voltages near the subharmonic feature on the \(I\)-\(V\) curves. A detailed consideration of these effects deserves a separate publication. The differences between the frequencies of collective modes detected by Josephson spectroscopy in YBa\({}_{2}\)Cu\({}_{3}\)O\({}_{7-x}\) thin-film JJs and by reflection measurements of bulk YBa\({}_{2}\)Cu\({}_{3}\)O\({}_{7-x}\) crystals can exist, because the YBa\({}_{2}\)Cu\({}_{3}\)O\({}_{7-x}\) thin films are under considerable strain due to the differences in lattice constants and thermal expansion coefficients with the substrates. However, data comparison from Josephson and reflection spectroscopies shows that differences in the recovered frequency values are low. This circumstance stimulates further development of Josephson spectroscopy for studying collective modes in JJs and their environment. As a first step in this direction, the admittances Re\(Y\)(\(f\)) near the intensive mode at around 4.6 THz were recovered from the experimental curves d\(I\)/d\(V\) vs. \(V\) according to the procedure described in Section 2.2. Figure 7a shows the recovered Re\(Y\)(\(f\)) of the JJ (1a in Figure 6) after low-temperature annealing in atomic oxygen, while Figure 7b shows that before annealing (1b in Figure 6). The maximal value of the admittance Re\(Y\)(\(f\)) after annealing is twice as high as the same value before annealing. The forms of these absorption lines are asymmetric and different. The optical phonon lines in bulk crystals YBa\({}_{2}\)Cu\({}_{3}\)O\({}_{7-\rm x}\) determined by Fourier spectroscopy are usually close to Lorentz curves. However, each of the recovered Re\(Y\)(\(f\)) curves in Figure 7 is more complicated than a single Lorentzian.