## 3 Results and Discussion
It must be pointed out that the features visible in Figure 2b, i.e., the pulses at 185 ps and 368 ps, are already present in Figure 2a, but are hard to distinguish due to the superposition with the LiNbO\({}_{3}\) signal. Here, at 368 ps an acoustic pulse echo after one roundtrip through the SiO\({}_{2}\) becomes visible. To be more precise, the weaker Brillouin oscillation in the SiO\({}_{2}\) can now be observed in the time span from 185 ps to 368 ps. The decrease in amplitude is mainly due to the decrease in the acoustic pulse amplitude caused by the partial transmission of the acoustic pulse into the LiNbO\({}_{3}\) layer. For SiO\({}_{2}\), we cannot obtain any information about the acoustic damping due to the relatively small thickness of the layer. Fits to the experimental data do not reveal a significant decrease in the amplitude. However, the LiNbO\({}_{3}\) layer is thick enough to obtain information on the damping. We obtain a full width at half maximum of 1.56 \(\pm\) 0.2 GHz from a Lorentzian fit of the corresponding FFT peak, which is consistent to a damping time of 217 \(\pm\) 20 ps in the time domain obtained by a damped sinusoidal fit. This results in an acoustic absorption coefficient of \(\alpha_{1}=4.4~{}\times 10^{3}\) cm\({}^{-1}\). Compared to the acoustic absorption obtained from the data presented by [PERSON] et al. in Reference [23], for the Z-cut LiNbO\({}_{3}\) crystal (which is close to our orientation) a considerable decrease in the acoustic absorption is also readily apparent in the time domain measurements, and yields an acoustic absorption coefficient of \(\alpha_{2}=2.42~{}\times 10^{3}\) cm\({}^{-1}\) extracted from the data. The distinct difference may be caused by different film/crystal qualities as well as the fact that our strain pulse is only quasi-longitudinal. A more detailed look at the probe polarization dependence of the LiNbO\({}_{3}\) signal is shown in Figure 3. The polarization of the probe laser pulse was systematically varied with a half-wave plate. Figure 3 shows the maximum of the amplitude of the FFT resulting from the LiNbO\({}_{3}\) substrate plotted versus the rotation angle of the probe laser pulse polarization. The peak of the amplitude shows a sinusoidal behaviour with \(\pi\) periodicity fitted to the data points (solid red line) similar to the findings and theoretical considerations in Reference [23]. Here, it is important to note that only the detection sensitivity is influenced. The acoustic pulse still propagates in the LiNbO\({}_{3}\) layer of the sample. As described in detail in Reference [23] and summarized shortly above, the polarization-dependent elimination of the signal of LiNbO\({}_{3}\) can be explained by the mode conversion process and the polarization-dependent photoelastic constants in the uniaxial birefringent ferroelectric material. Dependent on the LiNbO\({}_{3}\) orientation, probing at normal incidence and in backscattering geometry up to three different Brillouin frequencies can be detected, for ordinary and extraordinary refractive indices as well as a combination of both. This raises the question why we observe only a single Brillouin frequency. In fact, the expected shift for the two polarizations is about 1.4 GHz (as \(f_{o}\)/\(f_{e}=n_{o}/n_{e}=1.037\) for 820 nm) and is thus close to the resolution limit of our system. However, a closer look reveals that we indeed observe a small shift of approximately 0.4 GHz of the Brillouin frequency for orthogonal polarizations, as depicted in the inset in Figure 2d. Nevertheless, with the current system configuration we will not be able to resolve two or three individual modes. This information would indeed be highly desirable to obtain, as the mode occurrence yields information about the LiNbO\({}_{3}\) crystal orientation. It would be possible to improve the results by lowering the probe wavelength to around 400 nm in order to increase the obtained frequency shift and reduce the influence of measurement inaccuracies.