Acoustic dispersion

Abstract: A plane elastic wave propagating in a piezoelectric crystal may be accompanied by longitudinal electric fields which provide an additional elastic stiffness When the crystal is also semiconducting, these fields produce currents and space charge resulting in acoustic dispersion and loss A linear theory of this effect is developed, taking into account drift, diffusion, and trapping of carriers for both extrinsic and intrinsic semiconductors Conductivity modulation sets an upper limit on strain amplitude for a linear theory The directional characteristics and the magnitude of the effects are illustrated for CdS and GaAs The Appendix treats the interaction of an arbitrary acoustic plane wave with the electromagnetic fields in a piezoelectric crystal (based on a treatment by Kyame [J J Kyame, J Acoust Soc Am 21, 159 (1949); 26, 990 (1954)]) and further shows explicitly that only the effects of longitudinal electric fields need be considered

Abstract: State-of-the-art finite-element methods for time-harmonic acoustics governed by the Helmholtz equation are reviewed. Four major current challenges in the field are specifically addressed: the effective treatment of acoustic scattering in unbounded domains, including local and nonlocal absorbing boundary conditions, infinite elements, and absorbing layers; numerical dispersion errors that arise in the approximation of short unresolved waves, polluting resolved scales, and requiring a large computational effort; efficient algebraic equation solving methods for the resulting complex-symmetric (non-Hermitian) matrix systems including sparse iterative and domain decomposition methods; and a posteriori error estimates for the Helmholtz operator required for adaptive methods. Mesh resolution to control phase error and bound dispersion or pollution errors measured in global norms for large wave numbers in finite-element methods are described. Stabilized, multiscale, and other wave-based discretization methods developed to reduce this error are reviewed. A review of finite-element methods for acoustic inverse problems and shape optimization is also given.

Abstract: One of the outstanding challenges in phononic crystals and acoustic metamaterials development is the ability to tune their performance without requiring structural modifications. We report on the experimental demonstration of a tunable acoustic waveguide implemented within a two-dimensional phononic plate. The waveguide is equipped with a periodic array of piezoelectric transducers which are shunted through passive inductive circuits. The resonance characteristics of the shunts lead to strong attenuation and to negative group velocities at frequencies defined by the circuits' inductance. The proposed waveguide illustrates the concept of a controllable acoustic logic port or of an acoustic metamaterial with tunable dispersion characteristics.

Abstract: The efficient simulation of wave propagation through lossy media in which the absorption follows a frequency power law has many important applications in biomedical ultrasonics. Previous wave equations which use time-domain fractional operators require the storage of the complete pressure field at previous time steps (such operators are convolution based). This makes them unsuitable for many three-dimensional problems of interest. Here, a wave equation that utilizes two lossy derivative operators based on the fractional Laplacian is derived. These operators account separately for the required power law absorption and dispersion and can be efficiently incorporated into Fourier based pseudospectral and k-space methods without the increase in memory required by their time-domain fractional counterparts. A framework for encoding the developed wave equation using three coupled first-order constitutive equations is discussed, and the model is demonstrated through several one-, two-, and three-dimensional simulations.

Abstract: A careful study of the dispersion of the transverse acoustic phonons and the low-frequency transverse optic phonons in KTa${\mathrm{O}}_{3}$ has been carried out by inelastic neutron scattering. In addition to the well-known temperature dependence of the optic-mode frequencies, both the acoustic-phonon frequencies and the neutron-scattering cross sections of the TO and TA phonons with q along [100] show a marked temperature dependence. This anomalous behavior is not, however, revealed in ultrasonic velocity measurements. By means of a long-wavelength expansion of the lattice-dynamical equations, we show that these phenomena are the result of quasiharmonic coupling of optic- and acoustic-like excitations. In centrosymmetric crystals, this interaction vanishes as the wave vector q\ensuremath{\rightarrow}0, in such a way as to leave the limiting acoustic velocity unaffected. The existence of this interaction suggests the possibility of a soft Brillouin-zone-center optic phonon precipitating an instability in a mode with mixed acoustic-optic character and nonzero wave vector, giving rise to an antiferroelectric (or microtwinned ferroelectric) phase.