## 3 Results and Discussion
demonstrate in their work the ultrafast acousto-optic mode conversion induced by coherent acoustic phonons in LiNbO\({}_{3}\). In particular, they observe a strong polarization dependence of the observed Brillouin mode amplitudes caused by different photoelastic constants for their respective polarization orientations. X-ray measurements revealed for our LiNbO\({}_{3}\) layer a crystal orientation of \((\overline{1}14)\), which results in a tilt of the crystal of \(6.1^{\circ}\) against the Z-axis. From this, we can calculate the refractive indices to be \(n_{\rm o}=2.250\) and \(n_{\rm e}=2.249\), i.e., almost identical values, for the negative birefringent crystal. Thus, we obtain for the measured frequency \(f=38.9\) GHz in LiNbO\({}_{3}\) a sound velocity of \(v=7090\) m/s (\(\pm 90\) m/s). We can calculate with the Christoffel equation [24] the expected sound velocities in LiNbO\({}_{3}\) along the \((\overline{1}14)\) direction, which are \(v_{1}=7245\) m/s for the quasi-longitudinal mode, and \(v_{11}=3662\) m/s and \(v_{12}=3540\) m/s for the two quasi-transverse modes. In order to check the possibility of a signal contribution from the transverse components, we also calculate the expected Brillouin frequency of \(f\approx 20\) GHz. Indeed, we observe an additional mode close to this frequency in the FFT spectrum displayed in Figure 2. However, an unambiguous assignment is not possible due to the overlap with the SiO\({}_{2}\) mode. We will  
Figure 2: **(a,b)** Extracted oscillations for different polarization angles; (**c,d**) respective the Fast Fourier Transformations (FFTs). In the orange graphs, the superimposed response of LiNbO\({}_{3}\) and SiO\({}_{2}\) can be seen (data from the rotation angle of 120\({}^{\circ}\) of Figure 3). In the blue graphs, the part of LiNbO\({}_{3}\) is “turned off” (data from the rotation angle of 40\({}^{\circ}\) of Figure 3). The inset in (**d**) shows the shift of the LiNbO\({}_{3}\) frequency for the FFT at 120\({}^{\circ}\) and 40\({}^{\circ}\). The green line is a guide to the eye to enable better visibility of the occurring frequency shift. show in the following how the polarization-dependent signal detection of the quasi-longitudinal mode can be utilized in our measurements. Figure 2b,d depict the extracted oscillation and the respective FFT of a measurement of the sample with a different probe pulse polarization (roughly perpendicular polarization with 40\({}^{\circ}\) instead of 120\({}^{\circ}\), the 0\({}^{\circ}\) polarization angle was chosen arbitrarily). While there is a strong contribution from the LiNbO\({}_{3}\) layer to the time domain signal in Figure 2a, a change in the probe pulse polarization can almost completely suppress it, as evidenced by the signal in Figure 2b and the corresponding FFTs where the respective contributions are marked. This behaviour contains different types of information which we can exploit. If only the contributions from SiO\({}_{2}\) are detected, as in Figure 2b, the discontinuities caused by the acoustic pulse while propagating through the SiO\({}_{2}\)/LiNbO\({}_{3}\) interface and the arrival at the sample surface can be clearly identified. This allows us to obtain the time of flight \(t\) = 185 ps in the SiO\({}_{2}\) layer, which yields (in combination with the earlier calculated sound velocity) the thickness \(d\) = \(tv\) = 1072 nm (\(\pm\)26 nm) of the SiO\({}_{2}\) layer. Here, we are in excellent agreement with the nominal thickness of \(d\) = 1140 nm measured with ellipsometry. We want to emphasize at this point that the only a priori knowledge we use for the data evaluation is the index of refraction of the SiO\({}_{2}\) layer, a quantity which is readily available by means of e.g., ellipsometry. Thus, we can obtain the longitudinal sound velocity and the layer thickness simultaneously in one measurement.