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Following the advances in femtosecond laser technology, significant progress was achieved during the last 10 years in excitation of terahertz coherent lattice vibrations [W. A. Kütt, W. Albrecht, and H. Kurz, IEEE J. Quantum Electron. 28, 2434 (1992)]; [R. Merlin, Solid State Communications, 102, 207 (1997)]. Coherent terahertz phonons were excited in various type of crystals (in particular, in semiconductors and superconductors). However, until recently all-optical excitation and detection were reported on optical phonons only [W. A. Kütt, W. Albrecht, and H. Kurz, IEEE J. Quantum Electron. 28, 2434 (1992)]; [R. Merlin, Solid State Communications, 102, 207 (1997)]. Last year, ultrafast impulsive excitation of coherent acoustic phonon oscillations at frequencies around 4 THz was achieved [M. D. Cummings and A. Y. Elezzabi, Appl. Phys. Lett. 79, 770 (2001)]. We present here the results of theoretical analysis of acoustic signals excited by laser-induced mechanical stresses, which have spectral components around and above the cutoff frequency for propagating acoustic waves. For the analysis of both excitation process and of photo-excited wave propagation, discrete periodic structure of material should be taken into account. We are using for this purpose the simplest chain model of crystal. Analytical solutions, which reveal the role of strong acoustic velocity dispersion and the role of forbidden frequency band existence (where only evanescent modes are excited), are derived. Frequency spectra and temporal profiles of mechanical displacement are determined both at front (laser-irradiated) surface and at rear surface of photo-excited thin film. The contribution of the excited evanescent modes to the motion of the front surface is found. It is expected that evanescent modes might be very sensitive to possible surface and subsurface defects, and because of this they might be useful in nondestructive photoacoustic testing of surfaces and interfaces. © 20- 03 American Institute of Physics.