Intersections of the Lamb mode dispersion curves of free isotropic plates.

The intersections between Lamb mode dispersion curves of free isotropic plates at real values of frequency and wave number are examined for the full allowed range of Poisson's ratio σ. The generic intersections between the dispersion curves for symmetric and anti-symmetric branches are classified into three types. Type F intersections are conditioned by the two additional real solutions of Rayleigh's cubic equation that occur for σ<0.

Optimized determination of elastic constants of crystals and their uncertainties from surface Brillouin scattering.

Surface Brillouin scattering of light allows the angular-dependent velocities of Rayleigh surface acoustic waves (SAW), pseudo-SAW and longitudinal lateral waves (L) on the surface of an opaque crystal to be measured, and the elastic constants thereby determined. Closed form expressions exist for the surface wave velocities in high symmetry directions on crystallographic symmetry planes, and these have been exploited in the past for obtaining the values of the elastic constants. This paper describes a procedure for obtaining an optimized set of elastic constants from SAW, pseudo-SAW and L velocities measured in arbitrary directions in the (001) and (110) surfaces of cubic crystals.

Supersonic surface acoustic waves on the 001 and 110 surfaces of cubic crystals.

Criteria are reported here for the existence of supersonic surface acoustic waves (SSAW) on the (001) and (110) surfaces of cubic crystals. These are the common crystal cuts for which SSAW have been observed experimentally using surface Brillouin scattering and other techniques. Two categories of SSAW are distinguished.

Dispersion of an acoustic pulse passing through a large-grained polycrystalline film.

Propagation of a short acoustic pulse through a polycrystalline film comprised of large randomly oriented elastically anisotropic grains is analyzed theoretically. For average grain size much larger than the film thickness, a short acoustic pulse launched normally into the film will traverse each grain in a time determined by the acoustic slowness in the direction normal to the film, which will depend on the local grain orientation. A typical measurement averages over a large number of grains resulting in the broadening of the composite output pulse.

Acoustic field radiated into a transversely isotropic solid from a small aperture spherical surface.

The acoustic field modelling reported in this paper finds application in the design of a scanning probe tip for measuring the near-surface elastic properties of solids and surface structures at high frequencies and with high spatial resolution. The underlying concept is for a longitudinally polarized pulse to be launched from a spherically-shaped portion of the upper surface of the pyramidal or conical shaped tip, and focused towards the narrow lower end. The change in the reflectivity when the narrow end is brought into contact with a solid will provide a measure of the local frequency dependent compliance of that solid.

Ray splitting in the reflection and refraction of surface acoustic waves in anisotropic solids.

This paper examines the conditions for, and provides examples of, ray splitting in the reflection and refraction of surface acoustic waves (SAW) in elastically anisotropic solids at straight obstacles such as edges, surface breaking cracks, and interfaces between different solids. The concern here is not with the partial scattering of an incident SAW's energy into bulk waves, but with the occurrence of more than one SAW ray in the reflected and/or transmitted wave fields, by analogy with birefringence in optics and mode conversion of bulk elastic waves at interfaces. SAW ray splitting is dependent on the SAW slowness curve possessing concave regions, which within the constraint of wave vector conservation parallel to the obstacle allows multiple outgoing SAW modes for certain directions of incidence and orientation of obstacle.

Effect of spatial dispersion on transient acoustic wave propagation in 3D.

Spatial dispersion is the variation of wave speed with wavelength. It sets in when the acoustic wavelength approaches the natural scale of length of the medium, which could, for example, be the lattice constant of a crystal, the repeat distance in a superlattice, or the grain size in a granular material. In centrosymmetric media, the first onset of dispersion is accommodated by the introduction of fourth order spatial derivatives into the wave equation.

On interference effects in the elastodynamic Green's functions G33(x, omega) of Si and GaAs.

In this paper, we analyze interference effects present in the elastodynamic Green's functions G33(x,omega) of the cubic crystals Si and GaAs, which are associated with folded portions of the wave surface of the slow transverse (ST) acoustic mode. G33(x,omega) represents the three dimensional extension of the amplitude distribution imaged in the transmission acoustic microscopy of these crystals. The intensity contrast for oscillations of a particular wave vector k in the interference pattern is determined essentially by the 3D Fourier transform of G33(x,omega)G33*(x,omega).

The study of guided waves in surfaces and thin supported films using surface Brillouin scattering and acoustic microscopy.

This paper reviews the use of surface Brillouin scattering (SBS) and acoustic microscopy (AM) in studying the surface dynamics of solids in order to obtain information about the near-surface elastic properties of solids and thin supported films. The vibrational modes that are probed by these means include Rayleigh surface and pseudo-surface acoustic waves, longitudinal lateral waves (surface skimming bulk longitudinal waves) and various thin film guided modes, such as Sezawa and Love waves. SBS is the inelastic scattering of light, mediated by thermodynamic fluctuations in the surface elevation and near surface elastic strains.

Inversion of acoustic diffraction fields in anisotropic solids.

We show that the fast Fourier transform (FFT) technique provides a computationally efficient method of calculating 2D amplitude and phase images of complex wave fields generated and measured in elastically anisotropic solids by phase sensitive acoustic microscopy. Further, we discuss how this technique can be used to treat inverse problems such as source reconstruction, image quality assessment, and the determination of elastic constants.

Principal surface wave velocities in the point focus acoustic materials signature V(z) of an anisotropic solid.

This paper deals with the point focus beam (PFB) acoustic materials signature V(z) of an anisotropic solid, and in particular how it tends to be dominated by a limited number of principal surface rays. These rays are associated with propagation directions in which the Rayleigh wave (RW), pseudo-surface acoustic wave (PSAW) or a lateral wave slowness has an extremum. The phenomenon is interpreted in terms of the complex azimuthally averaged reflectance function of the surface, and also explained on the basis of a ray model.

Angular spectrum method and ray algorithm for the acoustic field of a focusing transducer in an anisotropic solid.

The angular spectrum method is applied to calculating the acoustic field of a liquid-coupled focusing transducer in an anisotropic slab-shaped solid with surfaces normal to the axis of the transducer. The stationary phase approximation (SPA) is used to determine the dominant contributions to this field and calculate the echo signals produced by waves that have been reflected off the rear surface of the solid. The dominant features of this field and of the echoes are reproduced well by a hybrid ray method devised to simulate the finite point-spread function of the lens.

Characteristic features of the velocity dispersion of surface acoustic waves in anisotropic coated solids.

Basic patterns of the velocity versus wavenumber dispersion of the surface waves in solids coated by a relatively light or dense, "slow" or "fast" layer are discussed in the general case of an arbitrary anisotropy of substrate and coating materials. The onset of the subsonic wave branch, characterized by either a speeding or a slowing trend, is examined. Competitive tendencies, which pertain to the low-frequency dispersion in the case of dense "fast" layer, are revealed.

Tomography of joint P-wave traveltime and polarization data: a simple approach for media with low to moderate velocity gradients.

An elastic wave tomography method utilizing joint traveltime and polarization data is proposed that is computationally simpler than the existing methods [Hu and Menke, Geophys. J. Int.

Transverse curvature of the acoustic slowness surface in crystal symmetry planes and associated phonon focusing cusps.

Conditions are derived for the existence of focusing cusps in ballistic phonon intensity patterns for propagation directions in crystal symmetry planes. Line caustics are known to be associated with lines of vanishing Gaussian curvature (parabolic lines) on the acoustic slowness surface, while cusps are associated specifically with points where the direction of vanishing principal curvature is parallel to the parabolic line. A parabolic line meets a crystal symmetry plane sigma at a right angle, and so it is the vanishing of the slowness-surface curvature transverse to sigma that conditions the existence of a cusp.

Observation of Scholte-like waves on the liquid-loaded surfaces of periodic structures.

The observation of Scholte-like ultrasonic waves travelling along the water-loaded surfaces of solids with periodically varying properties is reported. Results are presented for two 2D superlattices that intersect the surface normally: a laminated solid of alternating 0.5 mm thick layers of aluminium and a polymer, and a hexagonal array of polymer rods of lattice spacing 1 mm in an aluminium matrix.

Elastic measurements of layered nanocomposite materials by Brillouin spectroscopy.

Surface Brillouin spectroscopy makes it possible to measure surface elastic wave propagation parameters at frequencies up to 20 GHz or more. This enables us to measure the elastic properties of surface layers only a small fraction of a micrometre thick. The wavelength and incident angle of the light determine the wavenumber of surface elastic waves (SAW) that scatter the light inelastically, and their frequency can be found by measuring the change in wavelength of the scattered light.

Surface Brillouin scattering of opaque solids and thin supported films.

Surface Brillouin scattering (SBS) has been used successfully for the study of acoustic excitations in opaque solids and thin supported films, at both ambient and high temperatures. A number of different systems have been investigated recently by SBS including crystalline silicon, amorphous silicon layers produced by ion bombardment and their high temperature recrystallisation, vanadium carbides, and a nickel-based superalloy. The most recent development includes the measurement of a supported gold film at high pressure.