## 3 Results and Discussions
### Low Frequency Mini-Brillouin-Zone Mode
#### 3.2.3 MBZ-Edge Mode Excitation and Detection
The mirror symmetry operation with respect to \(\pm k_{max}/2\) boundaries enables the MBZ-edge modes (\(\omega(0)/2+\Delta\omega\), \(+k_{max}\)) and (\(\omega(0)/2-\Delta\omega\), \(-k_{max}\)) to be folded into the MBZ-center \(k\cong 0\). In our situation, due to \(\Delta\omega\ll\omega(0)/2\), the difference between \(\omega(0)/2+\Delta\omega\), \(\omega(0)/2\) and \(\omega(0)/2+\Delta\omega\) are not given in the plot. We assume that all those modes are \(\cong\omega(0)/2\). \(\omega_{1}(0)=32\) GHz provides an explanation to the otherwise unexplainable \(\sim\)15 GHz frequency. In terms of other frequency components at \(\omega_{i}(0)\) (\(i=1\), \(2\), \(3\),... ) and \(\omega_{i}(0)/2\) (\(i=2\), \(3\), \(4\),... ) detected in our experiment, several sources can contribute compared to that of \(\sim\)15 GHz mode. Based on the demonstration in Figure 6, the frequency components at 32, 64 and 96 GHz consist of the MBZ-center modes \(\omega_{i}(0)\) (\(i=1\) for 32 GHz, \(i=2\) for 64 GHz, \(i=3\) for 96 GHz) generated by electrostriction and the modes generated via the subharmonic decay process at \(\omega_{i}(0)/2\) (\(i=2\) for 32 GHz, \(i=4\) for 64 GHz, and \(i=6\) for 96 GHz), Subsequently, those modes become detectable through dynamic zone folding and Raman-Nath processes. Those frequencies at 32, 64 and 96 GHz can also be high-order replicas at \(m\omega_{i}(0)/2\) provided by probe light Raman-Nath-like scattering process ((\(m\),\(i\)) = (2,1) for 32 GHz, (\(m\),\(i\)) = (4,1), (2,2) for 64 GHz, and (\(m\),\(i\)) = (6,1), (3,2), (2,3) for 96 GHz). Due to the involvement of MBZ-center modes \(\omega_{i}(0)\), the frequencies at approximately 32, 64 and 96 GHz can be observed without the hypothesis of a subharmonic decay, dynamic zone folding and Raman-Nath-like detection. In contrast, the frequencies at approximately 80, 112 GHz can only be observable by assumption of the above-discussed hypothesis. As can be seen from Figure 6, the frequency components 80 GHz and 160 GHz consist of the modes generated via the subharmonic decay process at \(\omega_{i}(0)/2\) (\(i=5\) for 80 GHz and \(i=7\) for 160 GHz), and detected via dynamic zone folding and Raman-Nath processes. Those frequencies at 32, 64 and 96 GHz can be present as high-order replicas at \(m\omega_{i}(0)/2\) ((\(m\),\(i\)) = (5,1) for 80 GHz and (\(m\),\(i\)) = (7,1) for 160 GHz) in the Raman-Nath-like probe light scattering process. The previous discussion shows that the observed frequency spectrum is most probably formed by a non-trivial interplay between different excitation and detection mechanisms in the DBR. In order to strengthen our main assumptions, starting from the next paragraph, some arguments will be presented to provide strong indications that the 15 GHz mode is excited via a stimulated subharmonic decay. Additionally, although we only discussed MBZ-center and -edge modes in the DBR, the process could also potentially take place beyond the DBR in our sample due to structure-related feature. In order to obtain a full view of the low frequency MBZ modes, Table 4 lists all the low frequencies that could be potentially detected in this sample including MBZ modes in the DBR and MBZ modes in the SL formed by triple-QW stacks and the 112-nm spacers, and Brillouin frequencies in all materials. The presence of a significant number of loosely-separated frequencies enhances the complexity of our interpretation, and will be discussed in Appendix A.  
Figure 6: Illustration of MBZ coherent acoustic phonon distribution in the DBR. The plot demonstrates MBZ-center modes \(\omega_{i}(0)\) distribution, the subharmonic decay of \(\omega_{i}(0)/2\) and subsequent new zone folding (MBZ edge is folded onto MBZ center), and the detectable Raman-Nath-like (RN-like) phonon sequences \(m\omega_{i}(0)/2\), where \(m\) (\(m=1\), \(2\), \(3\),... ) denotes the replicas order of each RN-like sequence and \(i\) (\(i=1\), \(2\), \(3\),... ) denotes the order of MBZ center mode.