Acoustic flux imaging in anisotropic media

Structure of phonon focusing patterns in tetragonal crystals

A set of critical conditions for the characteristic caustic points in the phonon focusing patterns in tetragonal crystals is formulated. A caustic line segment in the focusing pattern is generally associated with either a fold or a cusp on the wave surface. Most of the caustic lines are symmetrical with respect to the principal symmetry plane and can be characterized by the caustic points at the centers of the caustic lines. These characteristic caustic points originated from inflection/parabolic points with zero in-plane/ex-plane curvature, respectively. By employing the Stroh formalism, the inflection/parabolic points on the slowness surface are studied in terms of the so-called zero-curvature transonic states. Since these transonic states are related to extraordinary degeneracies in the Stroh eigenvalue equation, the conditions for the degeneracies can be regarded as critical conditions for the characteristic caustic points. These conditions provide an overview of global structure of the phonon focusing patterns in tetragonal crystals. A set of caustic lines in vicinity of (001) plane is also investigated and exemplified.

Scanning phononic lattices with surface acoustic waves

We have examined the propagation of surface acoustic waves across structures with periodically varying elastic properties. These so-called phononic lattices include a) alternating layers of aluminum and polymer in a multilayer structure, b) a 2-d hexagonal lattice of holes drilled in an aluminum substrate and filled with polymer, and c) a 2-d hexagonal array of Al posts surrounded by polymer. A simple method is employed for probing the elastic properties of these periodic structures with ultrasound in the 0.5–5 MHz range. Ultrasonic surface waves are introduced and detected by water-immersion transducers, cylindrically focused to a line on the sample surface. Transmission and reflection patterns are observed by continuously scanning the wavevector angle with respect to the symmetry axes of the lattice. By Fourier transforming the transmitted signals using a broadband source, we obtain the frequency responses of the lattices as a function of propagation angle. Phononic band gaps, waveguide channeling and Scholte-like interface modes are observed. The results are compared to models of the propagation of transverse waves through analogous bulk structures, for which theories are available. These preliminary models explain the basic features of the experimental results, such as frequency gaps and wave channeling. A number of observations, however, remain to be explained. The angle-scanning technique provides a powerful probe of these modulated structures.

Caustic and anticaustic points in the phonon focusing patterns of cubic crystals

Phonon focusing patterns are dependent on the existence of concave/saddle regions and acoustic axes in the slowness surface. The main feature of the focusing patterns in cubic crystals can be characterized by the caustic and anticaustic points in the symmetry planes. By applying the Stroh formalism, the caustic and anticaustic points in the symmetry planes are investigated in relation to degeneracies in the Stroh eigenvalue equation. A set of analytical expressions for the locations of the caustic and anticaustic points is derived for cubic crystals.

Temporal and spatial apodization in defocused acoustic transmission microscopy

Two non-confocally adjusted spherical transducers are employed to implement an acoustic microscope operating in transmission with an approximately line-shaped point spread function (PSF). Such a PSF is of advantage in acoustic transmission line tomography and spatially resolved velocity measurements in solids. The foci of the transducers are viewed as diffraction-limited point transducers and appropriate time-selective signal acquisition is designed to restrict the ultrasound wave paths to the line connecting them. It is found that for typical commercially available transducers the largest contribution to the detected signal is not due to the direct ultrasound wave but due to the edge waves emanating from the rim of the focusing transducer. This poses constraints on achieving a line-shaped PSF in defocused acoustic transmission microscopy. It is shown that, due to the strong contribution from edge waves, it is impossible to achieve a line-shaped PSF in the case of application of a long exciting toneburst. The influence of the exciting pulse length, as well as the position of the time gate on the obtainable PSF is investigated.

Interference of non-aligned Airy diffraction patterns in transmission acoustic microscopy images of crystals

This paper describes interference effects present in narrow band transmission acoustic microscopy images of crystals that arise from the superposition of pairs of non-aligned but symmetry equivalent Airy diffraction patterns. In the cases we examine, these Airy patterns are associated with folded portions of the slow transverse (ST) sheet of the acoustic wave surface of cubic crystals intersecting in the {110} symmetry planes. Each set of Airy fringes is inclined in the (001) observation plane to its overlapping counterpart, giving rise to curved Moiré-like fringes. Also, because of tilting of the two portions of the wave surface in opposite directions out of the (001) plane, each composite Airy fringe breaks up along its length into a large number of narrow, regularly spaced fringes, in a manner akin to wedge diffraction. We present calculations of these effects in GaAs and Ge, based on the elastodynamic Green's function, , for the infinitely extended anisotropic elastic continuum. A measured time-gated diffraction image is presented for GaAs, which is in good agreement with calculation.

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.

Modeling piezoelectric and piezomagnetic devices and structures via equivalent networks

A history of equivalent circuit modeling of acoustic structures is presented. This is followed by a tutorial development of their use to represent piezoelectric (PE) and piezomagnetic (PM) plate transducers and bimorph cantilever beams for the purpose of facilitating transition of modern micro/nanotechnology creations to practical sensor, actuator, and transducer applications. Circuit approximations of various types are derived from the more general networks.

Angular spectrum approach for the computation of group and phase velocity surfaces of acoustic waves in anisotropic materials

The decomposition of an acoustic wave into its angular spectrum representation creates an effective base for the calculation of wave propagation effects in anisotropic media. In this method, the distribution of acoustic fields is calculated in arbitrary planes from the superposition of the planar components with proper phase shifts. These phase shifts depend on the ratio of the distance between the planes to the normal component of the phase slowness vector. In anisotropic media, the phase shifts depend additionally on the changes of the slowness with respect to the direction of the propagation vector and the polarization. Those relations are obtained from the Christoffel equation. The method employing the fast Fourier transformation algorithm is especially suited for volume imaging in anisotropic media, based on holographic detection in transmission of acoustic waves generated by a point source. This technique is compared with measurements on crystals performed by phase-sensitive scanning acoustic microscopy.