## 3 Results and Discussions
### High Frequency Coherent Acoustic Phonon Combs  
#### 3.1.1 Generation and Detection Mechanisms  
Since the pump light energy is absorbed in the QWs in our sample, stresses could potentially be photo-excited by three mechanisms including the inverse piezoelectric effect, the thermo-elastic effect and the deformation potential,  
\[\sigma(z,t)=\sigma_{PE}(z,t)+\sigma_{TE}(z,t)+\sigma_{DP}(z,t). \tag{1}\] \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \multirow{2}{*}{**Material**} & **Refractive** & **Extinction** & **Energy Gap \(E_{g}\)** & **Acoustic** & **Density \(\rho\)** \\  & **Index \(n\)** & **Coefficient \(K\)** & **(eV)** & **Velocity \(v\) (m/s)** & **(g/cm\({}^{3}\))** \\ \hline GaAs & 3.48 [(26)] & 0 (\(\alpha\) = 7.4 \(\times\) 10\({}^{-3}\) cm\({}^{-1}\)) & 1.424 [(27)] & 4730 [(27)] & 5.317 [(28)] \\ \hline In\({}_{0.27}\)Ga\({}_{0.73}\)As & 3.60 [(29; 30)] & 0.028 (\(\alpha\) = 3.4 \(\times\) 10\({}^{3}\) cm\({}^{-1}\)) [(31)] & 1.052 [(1.177) quantization] & 4487 [(33)] & 5.410 [(33)] \\ \hline Al\({}_{0.85}\)Ga\({}_{0.05}\)As & 2.98 [(34)] & 0 [(35)] & 2.148 [(26)] & 5592 [(36)] & 3.838 [(36)] \\ \hline DBR (GaAs/Al\({}_{0.95}\)Ga\({}_{0.05}\)As) & 3.22 [(37)] & & & 5160 [(37)] & \\ \hline QW-heterostructures (GaAs/In\({}_{0.27}\)Ga\({}_{0.73}\)As) & 3.54 [(37)] & & & 4596 [(37)] & \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Properties of MQW-SESAM sample at a wavelength of \(\lambda\) = 1048.3 nm. Figure 1: Schematic diagram of the sample structure. The beige-colored areas denote GaAs layers. The violet areas denote In\({}_{0.27}\)Ga\({}_{0.73}\)As layers while the green areas denote Al\({}_{0.95}\)Ga\({}_{0.05}\)As layers. Optical pulses are incident from the left. However, the inverse piezoelectric effect only dominates when the semiconductor heterostructure is grown along a high index piezo-electrically-active direction where large built-in electric fields can be formed, especially in the [111] direction. The [100] direction is non-piezo-electric (our sample) [38]. Additionally, although the laser light can heat up the sample and induce a thermal expansion, unlike in metals, in semiconductors such a thermo-elastic effect is usually considerably weaker than the deformation potential effect, especially when the energy of the pump optical quantum is close to the semiconductor band gap [39]. Therefore, it makes sense to ignore the contributions from \(\sigma_{PE}\) and \(\sigma_{TE}\). In other words, stresses related to light absorption are considered to take place in the nine QW layers in our sample mainly through deformation potential interaction,  
\[\sigma_{DP}(z,t)=-d_{eh}N(z,t), \tag{2}\]  
where \(d_{eh}\) denotes the electron-hole phonon deformation potential parameter and \(N\)(z,\(t\)) denotes the photo-excited carrier concentration [4]. Equation (2) indicates that the generation of coherent acoustic phonons largely depends on the concentration of photo-excited electrons and holes in the bottom of the conduction band and in the top of the valence band when the photon energy is very close to the material bandgap, which holds true for our QWs with a bandgap only ~7 meV below the pump photon energy (1.184-eV photon energy and 1.177-eV bandgap of QW). In terms of detection, the presence of acoustic phonons is able to induce a displacement of the surface and interfaces of the medium (interferometric effect) and perturb the optical refractive index of the medium (photo-elastic effect), which are monitored by the reflected probe light via the optical reflectivity change. Because the probe light exhibits approximately the same wavelength as the pump light, the generated forward and backward propagating stress waves are also detected in the QWs layers through the photo-elastic effect. The interferometric effect can in principle contribute to the detection of the acoustic waves. The MQW-SESAM structure is designed to maximize the optical electric field at the position of the QWs, and thus, efficient light absorption, generation, and detection of elastic waves can be expected.