## 1 Introduction
In quantum cascade laser structures consisting of SL formed by a doped and non-doped GaAs and AlGaAs layers with a thickness range from several nm to around 35 nm, edge modes were observed above a temperature of 150 K and at room temperature, which is attributed to a symmetry breakdown and the effects of the doping of some of the constituting layers [17]. [PERSON] et al. [18] observed edge modes in a n\({}^{+}\)-GaAs/AlAs SL at low temperature and proposed that the free-carriers in the SL enable momentum conservation through photon-phonon scattering. The electrons confined in quantum wells (QWs) can absorb a momentum that is less than \(k_{max}\approx\pi/L_{\text{QW}}\), where \(L_{\text{QW}}\) means the thickness of the QW. Thus, the excess momentum \(k-2q_{probe}\) in the backward scattering of probe light can be absorbed if \(|\pi/d_{SL}-2q_{probe}|\leq\pi/L_{\text{QW}}\). In stationary or frequency-domain Raman experiments on thermal phonons, the observations of mini-zone-edge phonons are attributed to disorder-induced \(q_{x}\)-non-conserving scattering, which can be caused, for example, by interface roughness [19] and interface defects [20] in GaAs/AlAs superlattices. Finally, Brillouin zone edge phonons in KTaO\({}_{3}\) and TiO\({}_{2}\) crystals, coherently and resonantly induced by crossed two near-infrared laser beams, are observed in coherent anti-Stokes Raman scattering (CARS) spectroscopy [21; 22; 23; 24]. The observation of the overtones of Brillouin edge modes in those crystals is supported by the folding of X-point phonons onto the \(\Gamma\)-point due to grating formation by coherent phonons. In this paper, we report on the generation and detection of CLAPs in a MQW- semiconductor saturable absorber mirror (SESAM) structure performed by femtosecond time-domain spectroscopy (high-speed asynchronous optical sampling) in a reflection geometry at a wavelength of around 1050 nm for both pump and probe laser sources. The MQW-SESAM structure exhibits multiple QWs as embedded saturable absorber layers and a distributed Bragg mirror (DBR) which are spatially separated by GaAs and AlGaAs layers. Both of the pump and probe photon energies are above the bandgap of the saturable absorber layers but below that of constituting materials of the DBR, whose reflectance is close to 100% for our laser wavelengths. Due to the high detection sensitivity of our pump-probe system, we are able to observe not only very pronounced LCAPs excited in the MQW region, but also much weaker acoustic phonon contributions which can be attributed to folded LCAPs excited in the transparent DBR region. Our findings demonstrate the first simultaneous observation of MBZ-center and -edge modes in a transparent non-doped long-period semiconductor SL. The detailed discussion of the MBZ mode excitation and detection in our experiment will be given in Section 3.2. In addition, the broadband coherent acoustic frequency combs ranging from \(\sim\)30 GHz to \(\sim\)800 GHz monitored in the light absorbing MQW region enables us to non-destructively characterize our SESAM structure (Section 3.1). Finally, the structure-related complexity of our experimental phonon spectrum will be discussed in Appendix A.