## 3 Results and Discussions
### Low Frequency Mini-Brillouin-Zone Mode
#### 3.2.2 MBZ-Center Mode Excitation  
One potential mechanism for the photo-excitation of MBZ-center modes is electrostriction. This mechanism can manifest itself in transparent media when, for example, two oblique pump  
Figure 4: **(a)** Coherent acoustic phonon oscillation from 70 ps to 800 ps when background subtraction is optimized for low frequencies extraction. **(b)** FFT of **(a)** and dispersion relations in SL formed by DBR with period \(d_{DBR}=160.4\) nm as well as SL formed by MQWs and GaAs spacers with period \(d_{MQW-SL}=145\) nm. Brown line represents FFT, where MBZ-center modes at 32.0 GHz, 63.1 GHz and 95.1 GHz and MBZ-edge modes at 15.1 GHz, 78.3 GHz and 110.1 GHz are marked. Blue line represents dispersion relation in the DBR (horizontal blue line represents \(k=|2q_{probe}^{DBR}-2\pi/d_{DBR}\,|=0.028\pi/d_{DBR}\) in the DBR). Magenta line represents dispersion relation in MQWs and GaAs spacers formed SL (horizontal magenta line represents \(k=|2q_{probe}^{MQW-SL}-2\pi/d_{MQW-SL}\,|=0.066\pi/d_{MQW-SL}\) in the SL formed by MQWs and GaAs spacers). **(c)** Calculated electric intensity field (red line) in the MQW-SESAM structure given the incident pump wavelength of 1047.5 nm. The interface of air/cap layer is at position 0. Beige areas denote GaAs. Violet areas denote In\({}_{0.27}\)Ga\({}_{0.73}\)As. Green areas denote Al\({}_{0.95}\)Ga\({}_{0.05}\)As. laser beams are incident on the transparent medium to create an optical interference pattern inside the medium for excitation of counter-propagating acoustic waves [13]. When the acoustic phonons are excited through electrostriction, the energy is directly coupled from electro-magnetic fields of the laser to the acoustic field. The excited phonon momentum then matches the interference electric field via the momentum conservation law \(\overset{\rightarrow}{k}_{g}=\pm\left(\overset{\rightarrow}{k}_{1}-\overset{ \rightarrow}{k}_{2}\right)\), where the subscript \(g\) denotes generated acoustic phonon and subscripts 1 and 2 denote the two incident photons. In the case of two laser beams with the same frequency, the generated phonon wavelength \(\Lambda\) is matched to the light field wavenumber by \(k_{g}\)= \(2q_{pump}\)sin(\(\theta/2\)), where \(k_{g}\) denotes the excitation (pump) light wavenumber in the medium and \(\theta\) denotes the angle between the two pump beams. Therefore, the generated phonon wavevector is tunable by adjusting \(\theta\) in such a configuration. When two incident pump beams propagate in opposite directions, the acoustic phonon exhibits a wavelength of \(\lambda_{pump}/2\), corresponding to \(k_{g}=2q_{pump}\). In our experiment, the incident pump beam is reflected by the DBR, whose reflectance is up to 99.7% for the pump wavelength of \(\sim\)1050 nm. Multiple scattering of the incident light in the DBR creates two evanescent counter-propagating light fields with comparable amplitudes, opening the way for the generation of high frequency CLAPs in the DBR via the electrostriction mechanism. As shown in Figure 4c, the pump light field intensity distribution in the DBR contains oscillating and evanescent average components covering nearly the whole DBR thickness. The sinusoidal component of the light field generates the phonons with \(k=k_{g}\)= \(2q_{pump}^{DBR}\), where \(q_{pump}^{DBR}\) denotes the wavevector of the pump light in the DBR, which is modelled as an infinite SL. However, the magnitude of the evaluated \(k_{g}\) appears to be outside the first Brillouin zone of the DBR, which can also be treated as a phononic crystal. This means that the generation of the phononic crystal eigenmode by the sinusoidally modulated part of the interference pattern created by our pump light should include Umklapp processes and the wavenumber of the generated phonon is \(k=k^{\prime}_{g}=\left|2q_{pump}^{DBR}-2\pi/d_{DBR}\right|=\frac{0.026\pi}{d_{ DBR}}<<\frac{\pi}{d_{DBR}}\), where \(d_{DBR}\) denotes the DBR period.