With the use of a lattice-dynamical model which reproduces observed phonon dispersion curves very accurately, the isotope scattering of near-zone-boundary acoustic phonons in Ge is investigated theoretically. We show that the lattice dispersion which becomes appreciable in the THz-frequency region leads to the phonon relaxation time that decreases more rapidly than w-4 • This deviation from the w-4 dependence (the w-4 behavior is predicted by the continuum elasticity theory) amounts to about 20% at I THz and is enhanced heavily at the zone boundaries. Calculations are based on the lowest-order perturbation ~heory. Higherorder corrections are estimated as well and shown to be negligibly small.

The finite-difference time-domain method is applied to the calculation of dispersion relations of acoustic waves in two-dimensional ͑2D͒ phononic lattices, i.e., periodic solid-solid, solid-liquid, and solid-vacuum composites, for which the conventional plane-wave-expansion method fails or converges very slowly. Numerical examples are developed for 2D structures with polyethylene, mercury, and vacuum cylinders forming a square lattice in an aluminum matrix. The implication of the calculated dispersion relations for ultrasound transmission experiments is discussed.

With the use of a face-centered cubic model of lattice dynamics we calculate the group velocity of acoustic phonons in the growth direction of periodic superlattices. Comparing with the case of bulk solids, this component of the phonon group velocity is reduced due to the flattening of the dispersion curves associated with Brillouin-zone folding. The results are used to estimate semiquantitatively the effects on the lattice thermal conductivity in Si/Ge and GaAs/AlAs superlattices. For a Si/Ge superlattice an order of magnitude reduction is predicted in the ratio of superlattice thermal conductivity to phonon relaxation time ͓consistent with the results of P. Hyldgaard and G. D. Mahan, Phys. Rev. B 56, 10 754 ͑1997͔͒. For a GaAs/AlAs superlattice the corresponding reduction is rather small, i.e., a factor of 2-3. These effects are larger for the superlattices with larger unit period, contrary to the recent measurements of thermal conductivity in superlattices.

Acoustic waves localized at the surface of two-dimensional ͑2D͒ periodic elastic structures, or 2D phononic crystals, are studied theoretically by taking account of the elastic anisotropy of constituent materials. The surface considered is perpendicular to the axis of a periodic array of cylinders embedded in a background material. The dispersion relations of the surface modes are calculated for circular cylinders of AlAs which form a square lattice in a GaAs matrix. The folding and anisotropy of the surface wave branches, as well as the existence of pseudosurface waves, are found. The stop band distributions of the surface, pseudosurface, and bulk waves are plotted in a form relevant for comparison with ultrasound imaging experiments.

We report on molecular dynamics studies of heat flow in superlattices. The computer simulations are performed using classical mechanics with periodic boundary conditions. The heat flow is in the direction normal to the layers. We have studied the variation of the conductivity with the repeat distance and the effect of interfacial roughness. We discuss the relation of these results to experimental data in the literature.

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We present a new method for imaging surface phonon focusing and dispersion at frequencies up to 1 GHz that makes use of ultrafast optical excitation and detection. Animations of coherent surface phonon wave packets emanating from a point source on isotropic and anisotropic solids are obtained with micron lateral resolution. We resolve rounded-square shaped wave fronts on the (100) plane of LiF and discover isolated pockets of pseudosurface wave propagation with exceptionally high group velocity in the (001) plane of TeO 2 . Surface phonon refraction and concentration in a minute gold pyramid is also revealed. DOI: 10.1103/PhysRevLett.88.185504 PACS numbers: 63.20.Dj, 62.65. +k, 68.35.Iv, 77.65.Dq Sound waves in crystals, dependent on the fourth-order elastic constant tensor, display a rich array of anisotropic propagation phenomena. Despite a crystal being homogeneous, a point acoustic source in the bulk can lead to singularities in acoustic flux in certain directions owing to the angular dependence of the phase and group velocities of the three acoustic polarizations [1]. This phonon focusing effect was first discovered in the bulk [2], but surface phonons were predicted to produce equally intriguing focusing patterns [3]. In the 10 MHz -1 GHz range, where acoustic wavelengths are typically 3 300 mm, various methods have been suggested for two-dimensional surface phonon imaging, such as stroboscopic probing, the sprinkling of powder on the surface, or detection by immersed point-focus transducers [4][5][6]. However, despite the growing interest in the field of surface acoustic wave devices, no technique has been successful in imaging surface phonon focusing in real time. Such imaging allows direct access to the dispersion characteristics of the wave propagation and the possibility of following the temporal evolution of cuspidal structures. In this Letter we image the propagation of coherent surface phonons at frequencies up to 1 GHz in real time, allowing animations of pointexcited surface phonon wave packets to be made with picosecond temporal and micron spatial resolutions.We use an ultrafast optical pump and probe technique with a common-path interferometer [7]. Surface phonon wave packets are thermoelastically excited in thin metal films on transparent substrates with optical pulses of wavelength 415 nm, repetition rate 80 MHz (one pulse every 12.5 ns), duration ϳ1 ps, and pulse energy ϳ0.3 nJ, producing a maximum transient temperature rise ϳ100 K. This pump light is focused at normal incidence through the substrate to a circular spot of diameter D ഠ 2 mm (full width at half maximum intensity; see Fig. 1). Out-ofplane (z) surface motion is detected interferometrically with ϳ1 pm resolution by the use of two probe pulses at an interval of t 510 ps, focused at normal incidence to a single spot of diameter ϳD on the front surface of the film. These pulses, of wavelength 830 nm, are derived from the same laser as the pump. In a simple modification of the apparatus of Ref.[7], we divide the output beam from ...

Scatterings of near-zone-boundary phonons by isotopic disorder in diatomic GaAs and InSb crystals are studied theoretically. In multiatomic lattices the scattering rate depends importantly on the vibrational amplitudes of constituent atoms. We find that the wave-vector dependences of these amplitudes, which are predicted by sortle lattice models, show quite dissimilar behaviors as compared to others. The typical examples investigated in this paper are the deformation-dipole model and the overlap-shell model. With the use of these models the frequency dependence of the relaxation time of phonons is calculated. Both models, however, predict the relaxation time of about 0.1 J1-sec for 1-THz T A phonons in GaAs, which is at least 1 order of magnitude shorter than the lifetime reported by Ulbrich et al.