## 3 Results and Discussions
### High Frequency Coherent Acoustic Phonon Combs
#### 3.1.4 Broadband Acoustic Spectrum
In order to understand the generated coherent acoustic phonons from the perspective of a SL rather than individual QWs, a folded CLAP dispersion relation calculated by the Rytov model in the SL formed by the GaAs (6 nm)/In\({}_{0.27}\)Ga\({}_{0.73}\)As (7 nm) units is plotted in Figure 2b. The dispersion relation of folded acoustic modes in a SL consisting of alternative layer A and layer B takes the following form in the slightly modified Rytov model [37]  
\[\cos(kd)=\cos\biggl{[}\omega\biggl{(}\frac{d_{A}}{v_{A}}+\frac{d_{B}}{v_{B}} \biggr{)}\biggr{]}-\frac{\varepsilon^{2}}{2}\sin\biggl{(}\frac{\omega d_{A}}{ v_{A}}\biggr{)}\sin\biggl{(}\frac{\omega d_{B}}{v_{B}}\biggr{)}, \tag{3}\]  
where \(\varepsilon\) is expressed as  
\[\varepsilon= \frac{\rho_{B}v_{B}-\rho_{A}v_{A}}{\left(\rho_{B}v_{B}\rho_{A}v_{A }\right)^{1/2}}. \tag{4}\]  
In Equations (3) and (4), \(k\), \(d\), \(\omega\), \(d_{A}\), \(v_{A}\), \(d_{B}\), \(v_{B}\), \(\rho_{A}\) and \(\rho_{B}\) denote the wavevector, the SL period, the angular frequency, the thickness of layer A, the longitudinal sound velocity in layer A, thickness of layer B, longitudinal sound velocity in layer B, density of layer A and density of layer B, respectively. In pump-probe experiments in reflection geometry, typical triplet-like mode structures usually arise due to the \(k=0\) modes at the Brillouin zone center and the detection of two additional modes of the nearby dispersion branches [37], as marked by solid dots in Figure 2b. The calculation yields the expected triplet mode frequencies at 323.7, 354.7, and 386.2 GHz. The 354.7 GHz mode belongs to Raman active MBZ-center mode. 323.7 GHz and 386.2 GHz modes belong to lower branch \(p=-1\) and upper branch \(p=+1\) at \(k=2q_{probe}^{GaAs/InGaAs}=0.176\pi/d_{QW}\), respectively, where \(p\) represents the acoustic phonon order, and \(k\) represents the wavevector. The calculated triplet (323.7, 354.7, 386.2) is nearly coincident with three frequency comb center components (332.1, 364.6, 397.1) if the deviation between experimental and calculated comb spacings is considered. In addition, the unfolded mode of 31.2 GHz at \(k=0.176\pi/d_{QW}\) is nearly coincident with the first comb component at around 33 GHz. However, due to the overlapping frequency region with the acoustic frequency comb generated in the QWs, it is difficult to say how much those folded/unfolded CLAP modes contribute to the detected frequency components. In addition, the frequency amplitudes also exhibit uncertainty arising from difficulties of acquiring the exact profile of the detection spectral sensitivity function. Further investigations are required in order to distinguish coherent acoustic phonons generated in the GaAs/In\({}_{0.27}\)Ga\({}_{0.73}\)As SL from those generated in the QWs. For example, the same pump-probe experiment can be applied to a new sample where the triple-QW stacks distance \(d_{ss}\) is carefully adjusted to result in an acoustic frequency comb with a spacing distinctly differing from 33 GHz, while the rest of the structure remains equal. In summary, a comb-like acoustic spectrum is generated and detected in the QWs in the MQW-SESAM sample where optical absorption takes place. Consisting of up to 24 detectable frequency components spaced by \(\sim\)33 GHz, it covers the frequency domain from \(\sim\)30 GHz to \(\sim\)800 GHz, but is most pronounced in the vicinity of 365 GHz. The detectability of a large number of frequency components can be attributed to the fact that the spectral sensitivity functions are nearly identical to the spectral generation functions in our structure by applying the two almost degenerate \(\sim\)1050-nm lasers for pump and probe. The observed spectral features can be readily understood in terms of single QWs or a SL description. In this case, we prefer the former, because the spatial excitation and detection functions are directly available and immediately result in the observed comb spectra. Still, we think the discussion of the latter is instructive in this scenario.