## 1 Introduction  
Periodic structures such as multiple quantum wells (MQWs) and superlattices (SLs) have been used as attractive tools for the observation of folded longitudinal coherent acoustic phonons (LCAPs) [1; 2]. A broad range of possible applications based on periodic structures have been proposed and investigated ranging from tailored heat transport for thermoelectric applications to new optomechanical systems and the development of acoustic phonon amplification, i.e., sasers [3; 4; 5]. Despite the intense research in this field, even periodic planar film systems still exhibit new and surprising features regarding their acoustic behavior, in particular in pump-probe experiments. All-optical femtosecond pump-probe spectroscopy allows us to gain insightful knowledge of the acoustic phonon behavior in both the light absorbing and transparent regions of a semiconductor SL structure by the selection of optimal pump and probe wavelengths [6]. If light absorption is involved in semiconductors, then coherent acoustic phonons are excited mainly due to the deformation potential interaction or the inverse piezoelectric effect related to electron-hole excitation via inter-band light absorption [7; 8]. If the deformation potential mechanism is suppressed by the process of ultrafast electron-hole recombination as in amorphous semiconductors, the thermo-elastic effect can also play a role in coherent acoustic phonon generation through energy transfer from excited hot electrons to phonons in semiconductors [7]. Although direct semiconductors do not exhibit photoexcitation of carriers for optical pump below-bandgap excitation, the electric field of the incident light itself can induce stress via electrostriction [7]. So far, a great number of observations have been obtained regarding folded LCAPs in light absorbing periodic materials [9; 10], and coherent acoustic phonons have also been studied near the absorption region of spacer materials sandwiched by two distributed Bragg reflectors (DBRs) in cavity optomechanical semiconductor devices [11; 12]. When the laser energy was around 10 meV below the bandgap of the spacer material, electrostriction was ruled out as the driving mechanism for mechanical cavity modes, while optoelectronic deformation potential interactions turned out to play an important role in the near-bandgap acoustic phonon excitation. There are also some observations of acoustic phonon excitation through electrostriction in ferroelectric materials and liquids [13; 14]. However, it is not common to find experimental demonstrations of the electrostriction excitation mechanism in transparent semiconductor heterostructures and SLs where the LCAPs spectrum exhibits mini-Brillouin-zone (MBZ) center and edge modes. Because the artificial periodic structure introduces a much larger period than the lattice constant of bulk materials (e.g., GaAs, AlAs), the original Brillouin zone is required to be folded into a MBZ with a new boundary of \(k=\pi/d_{SL}\), where \(k\) denotes the wavevector and \(d_{SL}\) denotes the SL period. Therefore, multiple high frequency modes can appear at and near the MBZ-zone center \(k=0\). The folded modes with wavevectors \(0\leq k\leq 2q_{probe}\), where \(q_{probe}\) denotes the wavevector of the probe light in the SL, can fulfill the wavevector conservation selection rule, and thus become Raman active in optical spectroscopy [15]. Once the wavevector \(2q_{probe}\) exceeds the boundary of the MBZ, Umklapp processes have to be taken into account, making it possible to detect LCAP modes with \(k=1\,2q_{probe}-2m\pi/d_{SL}\), where \(m\) is an integer [16]. Nonetheless, mini-zone-edge modes are usually not observable in optical spectroscopy because the wavevector conservation rule cannot be satisfied at \(k=k_{max}=\pi/d_{SL}\). However, there are indeed a few experiments showing that MBZ-edge modes can be observed in some structures [17; 18; 19; 20].