## 3 Results and Discussions
### Low Frequency Mini-Brillouin-Zone Mode  
#### 3.2.1 Overview of Experimental Results  
If the extraction of the acoustic phonon contributions from the original signal trace is numerically optimized for the lower frequencies in the signal via a larger smoothing scale for electronic and thermal background subtraction, a damped long-period oscillation (around 15 ps) over a long time delay is revealed, as shown in Figure 4a. The corresponding acoustic spectrum in Figure 4b exhibits multiple low frequency modes, which are the origin of the weak beatings in the time domain signal. Since the DBR in the sample has a long period \(d_{DBR}=160.4\) nm which could, in theory, pave the way for the generation of the folded CLAP starting from 32 GHz, we propose that those low frequency modes referring to harmonics and subharmonics of 32 GHz are photo-excited in the DBR for some reason. Thus, the acoustic dispersion relation in the DBR is plotted in Figure 4b, represented by the blue line, and the calculated potential modes are listed in Table 4. As a result, the experimental modes at 32.0 GHz, 63.1 GHz, and 95.1 GHz (marked by blue dots) agree well with the MBZ-center modes \begin{table}
\begin{tabular}{l l l l l l l l l} \hline \hline
**Experiment** & & & \multicolumn{3}{c}{**Calculation MQWs**} & \multicolumn{3}{c}{**Calculation InGaAs/GaAs**} \\  & & & & & & & & & \\  & & & & & & & & & \\ \(f_{0}\) (GHz) & Comb (GHz) & \(f_{0}\) (GHz) & Comb (GHz) & \(f_{c}\),\(f_{f_{c}}\) (GHz) & \(f_{2d}\) (\(k=2q_{probe}\)) & \\  & & & & & & & & (0.176\(\pi\)/\(d_{QW}\)) \\
366.5 & 299.9 & 633.0 & 353.5 & 293.4 & 619.4 & \
\begin{tabular}{l} \(k=\pi/d_{QW}\) \\ L 175.5 \\ U 179.4 \\ \end{tabular} & Lowest & \\  & & & & & & & & \\ \(\Delta\beta\) (GHz) & 332.1 & 666.1 & \(\Delta B\) (GHz) & 326.0 & 652.0 &
\begin{tabular}{l} \(k=0\) \\ L 354.7 \\ U 355.3 \\ \end{tabular} & \(p=-1\) & 323.7 \\
109.6 & 364.6 & 700.1 & \begin{tabular}{l} \(86.9\) (G\({}^{2}\)) \\ 124 (R\({}^{2}\)) \\ \end{tabular} & 358.6 & 684.6 & \
\begin{tabular}{l} \(k=\pi/d_{QW}\) \\ L 530.5 \\ U 534.3 \\ \end{tabular} & \\ \(\Delta\beta\) (GHz) & 397.1 & 732.0 & \(\Delta\beta\) (GHz) & 391.2 & 717.2 &
\begin{tabular}{l} \(k=0\) \\ L 709.3 \\ U 710.6 \\ \end{tabular} & \(p=-2\) & 678.7 \\
32.6, 33.3 & 430.3 & 766.0 & 32.6 & 423.8 & 749.8 &
\begin{tabular}{l} \(k=\pi/d_{QW}\) \\ L 885.7 \\ U 889.3 \\ \end{tabular} & \\ \hline \hline \end{tabular}  
* \({}^{1}\) L denotes the lower frequency of phonon bandgap, while U denotes the upper frequency of phonon bandgap. \({}^{2}\) G stands for Gaussian profile and R stands for rectangular profile of triple-QW in the calculation.  
\end{table} 
Table 3: Acoustic phonon spectrum in the high frequency region 32.17/32.18 GHz, 64.33/64.35 GHz and 96.50/96.53 GHz at \(k=0\). Due to the small forbidden gap (0.01 GHz, 0.02 GHz and 0.03 GHz for the 1 st, 2 nd and 3 rd dispersion branches, respectively) at \(k=0\), it is hard to resolve if the center modes belong to lower or upper branches. In addition, the long period of the DBR requires Umklapp processes for the wavevector \(k=2q_{probe}^{DBR}\), and thus, after the Umklapp processes the wavevector \(k=1\,2q_{probe}^{DBR}-2\pi/d_{DBR}\,|=0.028\pi/d_{DBR}\) is very close to \(k=0\) as the blue horizontal line indicates. Thus, this is a possible explanation why seemingly only the center modes are present in the spectrum in the reflection geometry. Meanwhile, the experimental modes 15.1 GHz, 78.3 GHz, and 110.1 GHz (marked by green dots) show a remarkable agreement with the MBZ-edge modes 15.28 GHz, 79.62 GHz and 110.8 GHz at \(k=\pi/d_{DBR}\). Normally, the generation of folded CLAPs is not expected in a DBR undergoing a below bandgap light irradiation due to the absence of light absorption. MBZ-edge modes are not detectable due to non-fulfillment of the wavevector conservation rule.