A simple closed form dispersion equation for shear types of surface waves propagating in periodic structures

A closed-form dispersion relation is found for shear surface acoustic waves (SAWs), namely, Bleustein-Gulyaev waves (BGWs), surface transverse waves (STWs), and leaky waves, propagating in periodic structures in the frequency range corresponding to the Bragg stopband. Changes in the spatial structure of the waves mutually reflecting on the grating as well as bulk wave scattering are considered. A comparison with numerically obtained dispersion curves for leaky waves on 36-LiTaO (3) shows good agreement.     

Acoustic waves in bounded anisotropic media: theorems, estimations, and computations

This paper discusses some basic achievements in theoretical studies on acoustic wave propagation along boundaries in anisotropic solids. In particular, the following issues are reviewed: existence theorems for subsonic surface and interface waves, leaky surface acoustic waves (SAW) and their relation to "supersonic" SAWs and fast exceptional bulk waves, the resonance reflection of bulk waves in the vicinity of leaky wave branches. General conclusions are illustrated by numerical examples.     

Optimized reflector stacks for solidly mounted bulk acoustic wave resonators

The quality factor (Q) of a solidly mounted bulk acoustic wave resonator (SMR) is limited by substrate losses, because the acoustic mirror is traditionally optimized to reflect longitudinal waves only. We propose two different design approaches derived from optics to tailor the acoustic mirror for effective reflection of both longitudinal and shear waves. The first one employs the stopband theory in optics; the second one takes advantage of the periodic nature of reflection spectra in a Bragg reflector: the diffraction grating design approach. The optimized design using stopband theory reaches a calculated minimum transmission of 25 dB and 20 dB at resonance frequency for longitudinal and shear waves, respectively, for various practical reflector material combinations. Using the diffraction grating approach, a near quarter-wave performance is maintained for longitudinal waves, whereas shear waves reach minimum transmission below 26 dB. However, this design does necessitate relatively thick layers. The experimental results show good agreement with finite element models (FEM). The extracted 1-D Q for the realized shear optimized devices was increased to around 3300.     

Periodic Green's functions analysis of SAW and leaky SAWpropagation in a periodic system of electrodes on a piezoelectriccrystal

A method of periodic Green's functions with a propagation factor exp(iβx), unknown in advance, is used to calculate dispersion curves and attenuation coefficients for Rayleigh- and leaky- waves propagating in a periodic system of thin electrodes on a piezoelectric surface. To describe the charge distribution on the electrodes both a step approximation and Chebyshev polynomials are used, the last being more adequate in most cases. Numerically determined values of the Green's function are used and interpolated either linearly or using a modified variant of Ingebrigtsen's formula. Such basic parameters as stopband width, stopband center frequency, wave velocity and attenuation in the stopband are found. These parameters can be used in the coupling-of-modes (COM) analysis and design of SAW devices. The analysis includes bulk wave radiation and scattering. The dependence of the corresponding attenuation coefficient on frequency is determined. Results obtained allow the determination directly and properly of the COM parameters and the design of SAW devices having large number of electrodes most precisely and rapidly. Numerical results for Rayleigh waves on YZ-LiNbO₃ and leaky waves on 36°YX-LiTaO₃ substrates are presented     

Gap acousto-electric waves in structures of arbitrary anisotropy

A theoretical study has been performed of the acousto-electric waves guided by an air gap between two identical piezoelectric crystals of arbitrary anisotropy. The permissible number of such gap waves traveling slower than all bulk modes in the structure has been established. The interdependence between the existence of these "subsonic" gap waves and surface acoustic waves on the mechanically free surface of crystals constituting the structure has been investigated. The occurrence of leaky gap waves also has been discussed. In addition, the specific features of the resonance reflection in gap structures caused by the excitation of leaky waves have been analyzed.     

Excitation and propagation of shear-horizontal-type surface and bulk acoustic waves

This paper reviews the basic properties of shear-horizontal (SH)-type surface acoustic waves (SAWs) and bulk acoustic waves (BAWs). As one of the simplest cases, the structure supporting Bleustein-Gulyaev-Shimizu waves is considered, and their excitation and propagation are discussed from various view points. First, the formalism based on the complex integral theory is presented, where the surface is assumed to be covered with an infinitesimally thin metallic film, and it is shown how the excitation and propagation of SH-type waves are affected by the surface perturbation. Then, the analysis is extended to a periodic grating structure, and the behavior of SH-type SAWs under the grating structure is discussed. Finally, the origin of the leaky nature is explained     

A method of determining acoustical physical constants for piezoelectric materials by line-focus-beam acoustic microscopy

We developed a new method of determining acoustical physical constants (elastic constant, piezoelectric constant, dielectric constant, and density) of piezoelectric materials with high accuracy. This method acquires velocities of leaky surface acoustic waves (LSAWs) excited on the water-loaded specimen surface, measured by line-focus-beam (LFB) acoustic microscopy, and bulk velocities of longitudinal and shear waves, measured with planewave transducers replacing the LFB device in the same system, together with the dielectric constants and density measured independently, for a small number of specimens. For LiNbO₃ and LiTaO₃ crystals, we demonstrated that we could accurately determine the constants by choosing proper propagation directions of LSAWs and bulk waves for three principal X-, Y-, and Z-cut specimens and one rotated Y-cut specimen [(104) plate for LiNbO₃ and (012) plate for LiTaO₃]. The accuracy is nearly the same as that for the constants determined only from the bulk wave velocities     

Characteristic parameters of surface acoustic waves in a periodic metal grating on a piezoelectric substrate

The coupling problem between electrodes due to the propagation of acoustic waves in a periodic metal grating on a piezoelectric substrate is theoretically studied. A method for the determination of the mutual admittance between the grating electrodes is presented, and an analytical expression for the contribution of surface acoustic waves (SAWs) is proposed. The SAW characteristic parameters are determined with a numerical technique that is able to deal with a leaky SAW as well as a true SAW (conventional Rayleigh type or Bleustein-Gulyaev type). Using this technique, the SAWs' contribution to the mutual admittance can be removed, and the analysis of other contributions becomes possible. In particular, the amplitude decay rate of the residual mutual admittance with electrode separation gives information about the propagation of the surface skimming bulk waves (SSBWs). The method presented is applied to several currently used material-cut configurations.     

Propagation properties of longitudinal leaky surface waves on lithium tetraborate

Theoretical and experimental results of longitudinal leaky surface waves with a higher phase velocity than that of ordinary leaky surface waves and a low propagation loss on lithium tetraborate (LBO) are investigated in detail. They propagate along the surface with a phase velocity close to that of longitudinal bulk wave, slightly radiating two kinds of shear bulk waves (or one shear bulk wave in the case that one of two shear wave terms is uncoupled) into the solid. Most surface components of the mode consist of a longitudinal wave term and an electromagnetic wave term. The detailed propagation properties of the longitudinal leaky surface waves on LBO with the Euler angles (phi, theta, 90 degrees ) are investigated theoretically and experimentally. The (011) cut of LBO was found to be desirable for higher frequency SAW devices. One of the reasons why that mode on LBO has a low propagation loss is also discussed.     

Time-resolved line focus acoustic microscopy of layered anisotropic media: application to composites

This paper presents theoretical and experimental studies of the time-domain response of line focus acoustic microscopy from a layered anisotropic medium. A method for elastic constant reconstruction from acoustic microscopy signatures also is presented. The microscopy response is complicated by multiple reflections in the layers and by the anisotropic nature of the material. The model is based on a new, stable recursive stiffness matrix algorithm developed for a multilayered anisotropic medium, which is applied to the interpretation of the time-resolved acoustic microscopy signature. Specific examples are given for unidirectional and multidirectional graphite epoxy composites. It is shown that the fluid load has a significant effect on the leaky surface waves in these composites, increasing surface wave speed above that for the slow transverse wave. This results in its absence from the microscopy signature of the surface wave. The theoretical results are compared with experiments carried out using a line focus PVDF transducer developed at National Institute of Standards and Technology (NIST). Time-resolved acoustic microscopy has been applied to the determination of elastic constants of a unidirectional composite or of one lamina in a cross-ply composite. The lateral waves and multiple reflections of bulk waves appearing in the microscopy signatures are used for the elastic properties reconstruction. The reconstruction results are compared to data obtained by the self-reference double-through-transmission ultrasonic bulk wave method.     

High-accuracy standard specimens for the line-focus-beam ultrasonic material characterization system

We prepared standard specimens for the line-focus-beam ultrasonic material characterization system to obtain absolute values of the propagation characteristics (phase velocity and attenuation) of leaky surface acoustic waves (LSAWs). The characterization system is very useful for evaluating and analyzing specimen surfaces. The calibration accuracy of these acoustic parameters depends on the accuracy of acoustical physical constants (elastic constants, piezoelectric constants, dielectric constants, and density) determined for standard specimens. In this paper, we developed substrates of non piezoelectric single crystals (viz., gadolinium gallium garnet [GGG], Si, and Ge) and an isotropic solid (synthetic silica [SiO₂] glass) as standard specimens. These specimens can cover the phase velocity range of 2600 to 5100 m/s for Rayleigh-type LSAWs. To determine the elastic constants with high accuracy, we measured velocities by the complex-mode measurement method and corrected diffraction effects. Measurements of bulk acoustic properties (bulk wave velocity and density) were conducted around 23°C, and bulk wave velocities were obtained with an accuracy of within ±0.004%. We clearly detected differences in acoustic properties by comparing the obtained results with the previously published values; the differences were considered to be due to differences of the specimens used. We also detected differences in acoustic properties among four SiO₂ substrates produced by different manufacturers     

Suppression of the leaky SAW attenuation with heavy mechanical loading

We discuss effects on the propagation of surface acoustic waves (SAW) due to heavy mass loading on Y-cut lithium niobate and lithium tantalate substrates. An abrupt reduction in the leaky-SAW (LSAW) attenuation is observed in the measured admittance of a long resonator test structure on 64 degrees -YX-cut lithium niobate for aluminum electrodes of thickness h/lambda(0) beyond 9-10%. This experimental fact is explained theoretically as the slowing down of the leaky wave below the velocity of the slow shear surface-skimming bulk wave (SSBW), such that energy dissipation into bulk-wave emission becomes inhibited. An infinite transducer structure is modeled using the periodic Green's function and the boundary-element method (BEM); the computed theoretical properties well explain for the experimental findings. The model is further employed to quantify the leaky surface-wave attenuation characteristics as functions of the crystal-cut angle and the thickness of the electrodes. The resonance and antiresonance frequencies and the corresponding Q values are investigated to facilitate the selection of crystal cuts and electrode thicknesses. The transformation of the leaky SAW into a SAW-type nonleaky wave is also predicted to occur for gold electrodes, with considerably thinner finger structures.     

Resonance reflection of acoustic waves in piezoelectric bi-crystalline structures

The paper studies the bulk wave reflection from internal interfaces in piezoelectric media. The interfaces of two types have been considered. Infinitesimally thin metallic layer inserted into homogeneous piezoelectric crystal of arbitrary symmetry. Rigidly bonded crystals whose piezoelectric coefficients differ by sign but the other material constants are identical. Analytic expressions for the coefficients of mode conversion have been derived. An analysis has been carried out of specific singularities arising when the angle of incidence is such that the resonance excitation of leaky interface acoustic waves occurs. The conditions for the resonance total reflection have been established. The computations performed for lithium niobate (LiNbO3) illustrate general conclusions.     

A method for calibrating the line-focus-beam acoustic microscopy system

Absolute accuracy of the line-focus-beam (LFB) acoustic microscopy system is investigated for measurements of the leaky surface acoustic wave (LSAW) velocity and attenuation, and a method of system calibration is proposed. In order to discuss the accuracy, it is necessary to introduce a standard specimen whose bulk acoustic properties, (e.g., the independent elastic constants and density) are measured with high accuracy. Single crystal substrates of gadolinium gallium garnet (GGG) are taken as standard specimens. The LSAW propagation characteristics are measured and compared with the calculated results using the measured bulk acoustic properties. Calibration is demonstrated for the system using two LFB acoustic lens devices with a cylindrical concave surface of 1-mm radius in the frequency range 100 to 300 MHz.     

套管井中泄漏弯曲型Lamb波声场的模拟与分析

基于套管中传播的最低阶泄漏弯曲型Lamb波(以下简称弯曲型Lamb波)对套管后介质尤其是低阻抗慢速水泥声学参数的敏感性,通过建立多层介质模型并利用实轴积分方法,数值模拟了有限尺寸定向辐射探头激发的声场和定点接收的全波波列。结果表明,在声源辐射到套管内壁上的入射角度约为33°时,在套管中主要激发弯曲型Lamb波。声场快照显示弯曲型Lamb波在沿着套管传播时,还会向与套管耦合的泥浆或水泥中泄漏比它速度低的波。若套管后介质是纵横波速度均低于弯曲型Lamb波相速度的慢速水泥,则套管中弯曲型Lamb波的衰减较大。利用弯曲型Lamb波对套管后耦合不同参数介质时的敏感性,可以有效地区分声阻抗接近的固体和液体,提高低阻抗水泥固井质量评价的效果。     

Characterization of a Polycrystalline Material with Laser-Excited Nonlinear Surface Acoustic Wave Pulses

High-amplitude nonlinear surface acoustic waves (SAWs) generated by laser pulses were observed in polycrystalline material (stainless steel), and the nonlinear acoustic parameters were evaluated. The velocities of bulk waves and the elastic moduli of the second order were determined by detecting the surface perturbations produced by longitudinal and shear bulk waves (precursors). Consequently, a consistent set of elastic and acoustic constants was obtained by performing all necessary measurements with the same sample using laser excitation and detection techniques.     

Micromachined thin film plate acoustic resonators utilizing the lowest order symmetric lamb wave mode

Thin film integrated circuits compatible resonant structures using the lowest order symmetric Lamb wave propagating in thin aluminum nitride (AlN) film membranes have been studied. The 2-mum thick, highly c-oriented AlN piezoelectric films have been grown on silicon by pulsed, direct-current magnetron reactive sputter deposition. The films were deposited at room temperature and had typical full-width, half-maximum value of the rocking curve of about 2 degrees. Thin film plate acoustic resonators were designed and micromachined using low resolution photolithography and deep silicon etching. Plate waves, having a 12-mum wavelength, were excited by means of both interdigital (IDT) and longitudinal wave transducers using lateral field excitation (LW-LFE), and reflected by periodical aluminum-strip gratings deposited on top of the membrane. The existence of a frequency stopband and strong grating reflectivity have been theoretically predicted and experimentally observed. One-port resonator designs having varying cavity lengths and transducer topology were fabricated and characterized. A quality factor exceeding 3000 has been demonstrated at frequencies of about 885 MHz. The IDT based film plate acoustic resonators (FPAR) technology proved to be preferable when lower costs and higher Qs are pursued. The LW-LFE-based FPAR technology offers higher excitation efficiency at costs comparable to that of the thin film bulk acoustic wave resonator (FBAR) technology     

Experimental study of construction mechanism of V(z) curves obtained by line-focus-beam acoustic microscopy

The propagation characteristics, viz., phase velocity and attenuation, of leaky surface acoustic waves (LSAWs), excited on the water/sample boundary are obtained through analyzing the V(z) curves measured by line-focus-beam acoustic microscopy. However, different values of these characteristics are obtained, depending upon different ultrasonic devices and operating frequencies employed. The construction mechanism of V(z) curves was investigated experimentally by measuring the amplitude and phase for Teflon to provide an understanding of the device performance for velocity measurements. A V(z) curve measured for Teflon, on which no leaky waves are excited when water is the coupling medium, can be used for the characteristic device response, depending only upon the device parameters and the operating frequencies. From the investigation of the ultrasonic device and the frequency dependences of the characteristic device responses, the phase gradient was found to be directly related to values of measured LSAW velocities. From this result, apparent frequency dependences in LSAW velocity measurements are explained quantitatively for a specimen of gadolinium gallium garnet.     

Effects of bulk wave radiation on IDT admittance on 42 degrees YX-LiTaO3

This paper investigates the effects of bulk acoustic wave (BAW) radiation on the admittance of interdigital transducers (IDTs) with significant internal reflections of shear horizontal (SH) type leaky surface acoustic waves (SAWs) on 42°YX-LiTaO₃(42-LT). Theoretical analysis is made by using the discrete Green function theory, and synchronous one-port resonators are analyzed. It is shown that the BAW radiation significantly affects the IDT characteristics even for resonators; under certain circumstances, BAWs launched from an IDT are converted into SH-type SAWs by the strong internal reflections, and they interact with the BAWs radiated by the IDT. Then, the net amount of the radiated BAW power is highly dependent upon the number of IDT finger pairs. For the precise simulation of devices based on the SH-type SAWs with strong internal reflections, the BAW radiation should carefully be taken into consideration. If the BAW radiation is ignored, the radiated power of the SH-type SAWs may seem to be negative above the BAW cut-off frequency