## Appendix A Complexity of Acoustic Spectrum  
(1) The triple-QW stacks and the GaAs spacers between triple-QW stacks together are forming a periodic structure with a period of \(d_{MQW\cdot SL}\) = 145 nm, which is rather close to the DBR period \(d_{DBR}\) = 160.4 nm. Therefore, resembling the MBZ-center modes excitation in the DBR, in principle the observable acoustic frequencies MBZ-center mode \(\omega\)(0) (32, 63, 95 GHz,... ) could also be excited in this long-period SL due to the electrostriction mechanism induced by the counter-propagating light field, where the triple-QW stacks and their spacers form a SL whose period also satisfies the relation \(d_{MQW\cdot SL}\approx\lambda_{pump}^{MQW-SL}/2\). However, due to the light absorption in QWs (In\({}_{0.27}\)Ga\({}_{0.73}\)As) of this SL with a period of 145 nm, the zone center modes could also be potentially excited through deformation potential. Meanwhile, resembling MBZ-edge modes excitation and detectability in the DBR, the observable MBZ-edge modes (15, 78, 110 GHz,... ) could also be excited through the stimulated subharmonic decay of zone center mode generated in this 145-nm SL and be detectable through dynamic zone folding (the presence of modes higher than 15 GHz could also be due to higher-order replicas via Raman-Nath probe light scattering process). Interestingly, as illustrated by the acoustic dispersion relation depicted by the magenta line for the 145-nm SL and the blue line for the DBR in Figure 4b, if we take a close look at the MBZ-edge modes, the experimental peaks marked by green solid dots are always closer to the lower frequencies at the forbidden gap edge in the DBR than to the edge frequencies in the 145-nm SL (here forbidden gaps are very small), so the MBZ edge modes (15, 78, 110 GHz,... ) are more likely excited in the DBR than in the 145-nm SL. Furthermore, there are two pronounced closely adjacent peaks with comparable amplitudes spaced by approximately 2 GHz at \(\sim\)78 GHz and also at \(\sim\)110 GHz, which are consistent to the frequency difference between the lower frequency at the forbidden gap edge in the DBR and the edge mode of 145-nm SL at the corresponding order (as calculated in Table 4 and illustrated in Figure 4b), which means the upper peaks \(\sim\)80 GHz and \(\sim\)112 GHz could be possibly assigned to edge modes excited in the 145-nm SL. However, MBZ-zone center modes excited in DBR and those modes excited in 145-nm SL at the corresponding order are too close to be distinguished in the experiment. (2) Multiple contributions to each MBZ-center and edge frequency component in the DBR or in the 145-nm SL are involved by means of the subharmonic decay of center modes, dynamic zone folding and Raman-Nath type detection processes. In terms of zone center frequency, there are potential three kinds of contributions to the detected signals including zone center modes generated via electrostriction, the subharmonic decay of zone center mode, and the higher replicas of the dynamically folded lower frequencies through the Raman-Nath-like probe light scattering process. In terms of zone edge frequency, their occurrences in the acoustic spectra requires the hypothesis of a subharmonic decay of the zone center mode, dynamic zone folding and Raman-Nath-like probe light scattering process. Except the case of the 15 GHz mode, all other frequencies equal to edge mode frequencies contain simultaneous contributions from the subharmonic decay of the zone center mode and contributions from higher-order replicas of dynamically folded lower frequencies through the Raman-Nath-like probe light scattering process, which is why only the 15 GHz mode rather than the 80 GHz and the 110 GHz modes excitation via stimulated subharmonic decay is demonstrated through a few approaches in Section 3.2. Despite the theoretically predicted occurrence of a mode with a frequency of \(\sim\)48 GHz as demonstrated in Figure 6, this phonon mode is absent in our experiment.