## 3 Results and Discussion  
The sample is excited from the Cr film side. In Figure 1, a typical transient of the reflectivity change \(\Delta R/R\) after the optical excitation is shown. A strong response in the first few tens of picoseconds is visible, which is caused by the fast electronic response in the Cr film [17; 18; 19]: the short laser pulse excites hot electrons inside the optoacoustic metal transducer which transfer their excess energy to the lattice via electron-phonon scattering. This process generates an impulsive strain pulse in the Cr film which propagates with the longitudinal speed of sound through the layer structure. Through the semi-transparent Cr film, the propagating strain pulse is monitored. Partially reflected probe light from the strain pulse is the origin of the associated change in the refractive index. This light interferes with the light being reflected from the top of the sample, giving rise to so-called time-resolved Brillouin oscillations with frequencies corresponding to the speed of sound in the material [20]. The acoustic pulse causes a small variation of the local index of refraction, which in turn results in a small portion of the probe light to be reflected at this position. Due to interference of the reflected light from the travelling pulse and the static sample interfaces, an oscillatory behavior can be observed in the time domain. The beginning of the oscillation is dominated by the signal from the SiO\({}_{2}\) layer. After the pulse propagates through the SiO\({}_{2}\), it is back reflected at the interface to the LiNbO\({}_{3}\) layer which can be vaguely observed as a phase shift in the transient at 185 ps. From this point on, both SiO\({}_{2}\) and LiNbO\({}_{3}\) contribute to the signal of the transient, which consists of their time-resolved Brillouin oscillations. Figure 2a shows the extracted oscillations without the electronic background from the transient of Figure 1. The fast and slow decay components of the background signal mainly stem from electron-phonon scattering and thermal diffusion in the Cr layer, respectively [17; 18; 19]. In Figure 2c, the Fast Fourier Transformation (FFT) of the extracted signal of Figure 2a is shown. We present the FFT of the full measurement range because the results obtained for each region separately for the respective  
Figure 1: Transient reflectivity changes of the sample. Inset: Sample structure; from top to bottom, the sample consists of a layer of 18-nm Cr, 1140-nm SiO\({}_{2}\), 325-\(\upmu\)m LiNbO\({}_{3}\), and 100-nm Al (thicknesses are not to scale). frequency peaks are within the error of 1 GHz. The peak at 20.5 GHz originates from the Brillouin oscillation in SiO\({}_{2}\) and the one at 38.9 GHz from the Brillouin oscillation in LiNbO\({}_{3}\). This allows us to calculate the longitudinal sound velocities \(v\) in the respective media by the Brillouin frequencies, which are given by \(f=2\;nv/\lambda\), with \(n\) representing the refractive index in the respective media and \(\lambda\) representing the wavelength of the probe light. For SiO\({}_{2}\), we obtain a longitudinal sound velocity of \(v=5797\) m/s (\(\pm 141\) m/s) which is in very good agreement with the literature value of 5800 m/s [21]. The uncertainty of the sound velocity takes into account that we have a measurement inaccuracy of the frequency of \(\pm 0.5\) GHz. This approach is, however, more complicated in LiNbO\({}_{3}\), as we will discuss in the following. We observe no contribution from the Al layer in our measurements, which would yield a mode at \(f=(2n-1)v/4d=16\) GHz for \(n=1\) and with the longitudinal sound velocity of Al of \(v=6320\) m/s [22] and the thickness \(d=100\) nm of the Al layer. Recent findings show that the birefringence in LiNbO\({}_{3}\) can give rise to several Brillouin modes which show a distinct dependence on the crystal orientation and the incident probe light polarization, as [PERSON] et al. showed in Reference [23]. [PERSON] et al.