## 3 Results and Discussions
### High Frequency Coherent Acoustic Phonon Combs
#### 3.1.3 Generation, Propagation and Detection of Acoustic Waves in MQW Region  
In III-V semiconductor multilayer structures, the acoustic reflection from the internal interface is usually insignificant, due to the small acoustic impedance mismatch between constituent materials. If the densities \(\rho_{GaAs}\) and \(\rho_{InGaAs}\), as well as longitudinal acoustic velocities \(v_{GaAs}\) and \(v_{InGaAs}\), are taken from Table 2, the reflection coefficient of the GaAs/In\({}_{0.27}\)Ga\({}_{0.73}\)As interface can be calculated as \(\Gamma=\mid(\rho_{GaAs}v_{GaAs}-\rho_{InGaAs}v_{InGaAs})/(\rho_{GaAs}v_{GaAs} +\rho_{InGaAs}v_{InGaAs})\mid=1.8\times 10^{-2}\). As illustrated in Figure 3, if the small acoustic impedance mismatch between GaAs and In\({}_{0.27}\)Ga\({}_{0.73}\)As is neglected, in total six discrete wave-packets should be detected after the sample is irradiated by the pump light. The first wave-packet, which is not presented in Figure 2a because of the difficulties in removing the background signal at times close to the pump/probe overlap, stems from the detection of the forward and backward propagating stress bursts (S\({}_{\text{ib}}\) and S\({}_{\text{ir}}\), i = 1, 2, 3) generated in each of the triple-QW stacks when they are escaping from the corresponding local stacks (Figure 3, line 1). The second detected wave-packet stems from the detection of five stress bursts in the neighboring/local triple-QW stacks at the same time when the photo-generated stresses after the propagation between the triple-QW stacks start to move across the stacks. These five stress bursts include two pairs of bursts excited in the first and the second triple-QW stacks (S\({}_{\text{ib}}\) and S\({}_{\text{ir}}\), i = 1, 2) and the backward propagating burst excited in the third triple-QW stack, i.e., S\({}_{\text{3r}}\) (Figure 3, line 2). The third wave-packet stems from the detection of four stress bursts (Figure 3, line 3), and so on. In consequence, a smaller and smaller number of stress bursts contribute to the detection as stress waves propagate along the \(z\)-axis, which can also partly explain the damping of the wave-packet train (see Figure 2a). Thereby, in the end, there  
Figure 2: (**a**) Coherent acoustic phonon wave-packets after background removal. Top inset: the original time trace. Bottom inset: zoom in of the wave-packet at around 30 ps. (**b**) Acoustic spectrum and dispersion relation in GaAs/In\({}_{0.27}\)Ga\({}_{0.73}\)As SL. The brown line represents the acoustic spectrum. The magenta curve depicts the FFT of the wave-packet at 30 ps. The z-like blue line represents the dispersion relation and the horizontal blue line indicates the wavevector position \(k=2q_{probe}^{GaAs/InGaAs}\). The vertical gray lines are spaced by the comb spacing of 33.15 GHz. is only the detection of S\({}_{3r}\) in the third triple-QW stack, which corresponds to the sixth wave-packet signal. After S\({}_{3r}\) leaves the last triple-QW stack, acoustic wave-packets excited in the QWs are not expected to be further detected in the MQW region, under the condition of their negligible reflections in the DBR region. However, our experimental results, presented in Figure 2a, clearly show more than five wave-packets (the 2 nd\(\sim\)6 th wave-packets) in the time domain (the first wave-packet at 0 ps is not shown there). In order to explain the existence of wave-packets beyond the expected number of occurrences given by the sample geometry, the small acoustic impedance mismatch between GaAs and In\({}_{0.27}\)Ga\({}_{0.73}\)As should be taken into account. In this way, the reflection of acoustic phonons from the interfaces between these materials can contribute to wave-packets bouncing between neighboring triple-QW stacks and between the first triple-QW stack and the air/GaAs interface. These multiple reflections produce \"ringing\" of the triple-QW stacks/air region, which lasts longer than the time necessary for the acoustic wave just to traverse it twice.