Generation of time-independent torque by ultrasonic guided waves

The excitation of acoustic waves by a unidirectional transducer, integrated in a piezoelectric cylindrical tube or disk, can lead to a time-independent torque. This phenomenon, demonstrated earlier in experiments and analyzed with coupling-of mode theory, is explained in detail, starting on the level of lattice dynamics of a piezoelectric crystal. Expressions are derived for the stationary torque in the form of integrals over the volume or surface of the piezoelectric, involving the electric potential and displacement field associated with the acoustic waves generated by the transducer. Simulations have been carried out with the help of the finite element method for a tube made of PZT for two cases: A pre-defined potential on the surface of the tube and metal electrodes buried in the piezoelectric. The displacement field and electric potential of the high-frequency acoustic waves (between 200 and 300 kHz) were computed and used in the evaluation of the integrals. The attenuation due to various loss channels of the acoustic waves in the system has been analyzed in detail, as this plays a crucial role for the efficiency of torque generation. It is conjectured that time-reversal symmetry, present in the absence of attenuation, prohibits the generation of a static torque at least in the linear limit. A qualitative comparison is made between the simulations and earlier experiments. Discrepancies are attributed to lack of knowledge of the relevant material constants of the piezoelectric and to a simplified modeling of the electrode geometry in the cylindrical tube, which was necessary for reasons of numerical accuracy.

Experimental and numerical investigations of mechanical displacements in surface acoustic wave bounded beams

The present paper studies experimentally and numerically the surface acoustic wave (SAW) field on a piezoelectric substrate generated by interdigital transducers (IDT). On the one hand, mechanical displacements produced by the SAW are measured with the help of a laser Doppler vibrometer. On the other hand, mechanical displacements are computed by the two-dimensional finite element method in frequency domain followed by the spatial Fourier transform. Combining these two steps of computations results in the intended two-dimensional distribution of mechanical displacements on the substrate surface. The comparison of experimental and numerical data obtained for a series of different IDTs reveals that it is possible to estimate the shape of the SAW beam and the absolute value of mechanical displacement amplitude using only the basic parameters of the IDT and its electrical admittance measured by a network analyzer.

The complexity of surface acoustic wave fields used for microfluidic applications

Using surface acoustic waves (SAW) for the agitation and manipulation of fluids and immersed particles or cells in lab-on-a-chip systems has been state of the art for several years. Basic tasks comprise fluid mixing, atomization of liquids as well as sorting and separation (or trapping) of particles and cells, e.g. in so-called acoustic tweezers. Even though the fundamental principles governing SAW excitation and propagation on anisotropic, piezoelectric substrates are well-investigated, the complexity of wave field effects including SAW diffraction, refraction and interference cannot be comprehensively simulated at this point of time with sufficient accuracy. However, the design of microfluidic actuators relies on a profound knowledge of SAW propagation, including superposition of multiple SAWs, to achieve the predestined functionality of the devices. Here, we present extensive experimental results of high-resolution analysis of the lateral distribution of the complex displacement amplitude, i.e. the wave field, alongside with the electrical S-parameters of the generating transducers. These measurements were carried out and are compared in setups utilizing travelling SAW (tSAW) excited by single interdigital transducer (IDT), standing SAW generated between two IDTs (1DsSAW, 1D acoustic tweezers) and between two pairs of IDTs (2DsSAW, 2D acoustic tweezers) with different angular alignment in respect to pure Rayleigh mode propagation directions and other practically relevant orientations. For these basic configurations, typically used to drive SAW-based microfluidics, the influence of common SAW phenomena including beam steering, coupling coefficient dispersion and diffraction on the resultant wave field is investigated. The results show how tailoring of the acoustic conditions, based on profound knowledge of the physical effects, can be achieved to finally realize a desired behavior of a SAW-based microacoustic-fluidic system.

FE analysis of surface acoustic wave transmission in composite piezoelectric wedge structures

The paper numerically investigates the transmission of harmonic surface acoustic waves (SAWs) across the perfectly bonded and perfectly sliding contacts between two 90°-wedges, at least one of which possessing piezoelectric properties. The finite element method in frequency domain is used. The structures are constructed of lithium niobate, fused quartz, silicon and gallium arsenide. The SAW is always incident from lithium niobate. The dependences of the transmission coefficient on the combination of materials and the orientation of the lithium niobate, as well as on the height of the step at the interface between the two parts of the structure are computed and analyzed. This step can appear in the process of fabrication of the composite substrate. The obtained results demonstrate that SAWs are able to transmit fairly efficiently across a wedge-like contact. Therefore such structures can be useful, in particular, in cases when it is advantageous to generate a SAW in one strongly piezoelectric material and observe its action, e.g., due to the transmitted surface normal displacement in another material like in SAW-driven microfluidics.

Acoustomicrofluidic application of quasi-shear surface waves

The paper analyzes the possibility of using predominantly boundary polarized surface acoustic waves for actuating fluidic effects in microchannels fabricated inside containers made of PDMS. The aim is to remove a shortcoming peculiar to conventionally utilized predominantly vertically polarized waves. Such waves strongly attenuate while they propagate under container side walls because of the leakage into them. Due to a specific feature of PDMS - extremely small shear elastic modulus - losses of boundary polarized modes should be far smaller. The amplitude of vertical mechanical displacements can be increased right inside the channel owing to the scattering of acoustic fields. As an example, the predominantly vertically polarized surface wave on 128YX LiNbO₃ is compared with the quasi-shear leaky wave on 64YX LiNbO₃. Our computations predict that, given the electric power supplied to the launching transducer, the quasi-shear wave will drive the fluid more efficiently than the surface wave on 128YX LiNbO₃ when the container wall thickness is larger than 25-30 wavelengths, if there are no additional scatterers inside the channel. In the presence of a scatterer, such as a thin gold strip, the quasi-shear wave can be more efficient when the wall thickness exceeds 10-15 wavelengths.

Finite element analysis of the Rayleigh wave scattering in isotropic bi-material wedge structures

The numerical study is performed of the harmonic Rayleigh wave scattering in a composite structure constructed from two elastically isotropic 90°-wedges. These wedges are in contact along one pair of their faces. It is assumed that either the perfectly sliding contact or the perfectly rigid one is realized. The other pair of faces forms a plane border between the resulting bi-material wedge and the exterior half-infinite space occupied by vacuum. The finite element method is used. The perfectly matched layer spatially confines the computational domain. The dependences of the reflection and transmission coefficients of the Rayleigh wave on the angle of incidence, the Poisson ratio and the type of contact are obtained and analyzed for different combinations of materials. The behavior of the coefficient of the Rayleigh wave conversion into the interfacial wave which may exist on the internal boundary of the structure is also investigated. A number of relations between the coefficients of conversion are derived from symmetry considerations for structures with sliding contact and composed of identical isotropic materials.

Computation of the pressure field generated by surface acoustic waves in microchannels

The high-frequency pressure induced by a surface acoustic wave in the fluid filling a microchannel is computed by solving the full scattering problem. The microchannel is fabricated inside a container attached to the top of a piezoelectric substrate where the surface wave propagates. The finite element method is used. The pressure found in this way is compared with the pressure obtained by solving boundary-value problems formulated on the basis of simplifications which have been introduced in earlier papers by other research studies. The considered example shows that the difference between the results can be significant, ranging from several tens of percent up to several times in different points inside the channel.

Surface acoustic wave reflection/transmission at vertical borders of piezoelectric substrates

The paper studies by the finite element method the harmonic surface acoustic wave scattering at 90° corners of piezoelectric substrates. The SAW is incident perpendicular to the vertical border. The dependencies of the reflection and transmission coefficient on the radius of the fillet at the corner are found for 128°YX and YZ LiNbO3 as well as ST-X SiO2 substrates. In particular, the obtained results reveal that, like in the case of isotropic solids, the magnitude of the reflection coefficient first increases with the fillet radius to wavelength ratio r/λ, reaches a maximum at r/λ≈0.3-0.5, and then decreases tending to zero. The magnitude of the transmission coefficient across the rounded corner first decreases, reaches a minimum at r/λ≈0.3-0.5, and then increases up to a value around which it slightly oscillates as r/λ increases. It is demonstrated that if the substrate is anisotropic, then in the general case a SAW is scattered off differently at the right-hand border and the left-hand border. The difference between the "right-hand" and "left-hand" transformation coefficients can be very substantial. Computations for YZ LiNbO3 illustrate possible levels of the anisotropy of the scattering for mutually reverse directions of incidence. It is shown that if the substrate is specially oriented, then the scattering from the right-hand border is identical to the scattering from the left-hand border. There are four types of such orientations. Examples of the specially oriented substrates are 128°YX LiNbO3 and ST-X SiO2.

Rayleigh wave scattering from a vertical edge of isotropic substrates

The paper numerically studies the harmonic Rayleigh wave scattering at the 90-degree corner of isotropic substrate. The finite element method is used. The main attention is paid to two cases. The first one is the apex of the substrate corner is rounded off. The second one consists in that a layer of foreign material is deposited on the face which scatters the Rayleigh wave. The dependence of the reflection and the transmission coefficients on the Poisson ratio, the angle of incidence, the fillet radius, and the layer thickness are obtained. It is found that if the Rayleigh wave is incident perpendicularly to the substrate border, then the fillet of small radius as compared to the wavelength increases the reflection coefficient and decreases the transmission coefficient by factors 1.3-1.8. At normal incidence, the Poisson ratio does not change qualitatively the dependence of the reflection and transmission coefficients on the fillet radius. But the Poisson ratio can substantially affect the angle dependence of these coefficients if the wave is incident obliquely on the corner rounded off. It is also found out that a layer can modify the conditions of scattering such that the incident wave is totally reflected without transmission and conversion into bulk waves in a wide interval of angle of incidence, although, in principle, the bulk wave generation is allowed within a part of this angle interval.

Mutual conversion of bulk and surface acoustic waves in gratings of finite length on half-infinite substrates. II. FE analysis of bulk wave generation

The paper studies numerically the bulk acoustic wave generation by the surface acoustic wave propagating across a grating created on the surface of an elastically anisotropic half-infinite substrate. The computations are fully based on the finite element method. Applying the discrete Fourier transformation to the displacement field found inside the substrate and using an orthogonality relation valid for plane modes we determine separately the spatial spectrum of the quasi longitudinal and the quasi transverse bulk waves, that is, the dependence of the amplitudes of these waves on the tangential component of the wave vector. The dependence is investigated of the central spectral peak height and shape on the frequency of the incident surface wave as well as on the thickness, the width, and the number of strips forming the grating. In particular, it is found that under certain conditions the central peak can be approximated fairly precisely by the central peak of a sinc-function describing the spectrum of the bounded acoustic beam of rectangular shape and of width equal to the length of the grating.

Mutual conversion of bulk and surface acoustic waves in gratings of finite length on half-infinite substrates. I. FE analysis of surface wave generation

A numerical study is carried out of the surface acoustic wave generation by a bulk acoustic wave in a half-infinite anisotropic half-space without piezoeffect. The efficient conversion of bulk waves into surface waves occurs due to a grating area created on the surface of the substrate. Our simulations are fully based on the finite element method. Given the incident bulk wave, we directly determine the amplitude of the surface wave and investigate its dependence on various parameters specifying the situation under consideration, such as the frequency and the polarization of the bulk wave, the length of the grating, the geometrical size of grooves or strips forming the grating.

Surface acoustic wave resonators as novel tools for multiparametric blood analysis

In this paper a new tool to assess viscoelastic and dielectric properties of human fluids is presented. Shear horizontal polarized surface acoustic waves (SH-SAW) are used to detect the viscoelastic properties of coagulating blood and blood plasma samples. One-port SAW resonators, with fundamental modes of 85, 170 und 340 MHz were developed. Additionally, their electrode structures can be used simultaneously to detect the dielectric behavior of the whole system by impedance spectroscopy while the frequency ranges from kHz to MHz. The combination of both methods offers the detection of clinical relevant blood parameters like the blood coagulation time and the hematocrit value within one measurement.

A new tool to assess mechanical and dielectric properties of tissues

In this paper a new tool to assess viscoelastic and dielectric properties of biological samples is presented. Shear horizontal polarized surface acoustic waves (SH-SAW) are used to detect the viscoelastic properties of the extracellular matrix (ECM) expelled by adhering fibroblast cell cultures. Therefore a one-port SAW resonator, with a fundamental mode of 85 MHz was developed. Its electrode structure can be used simultaneously to detect the dielectric behavior of the whole system by impedance spectroscopy (IS) while the frequency ranges from kHz to MHz. The applicability of the combination of both methods appearing as new tool is exemplary shown by cell adhesion experiments performed with L929 and NIH-3T3 fibroblasts.

Interface acoustic waves in piezoelectric bi-crystalline structures of specific types

The paper discusses the properties of the acoustic waves guided by an interface inside piezoelectric media. The interfaces of two types have been considered: (i) an infinitesimally thin metallic layer inserted into homogeneous piezoelectric crystal of arbitrary symmetry; (ii) rigidly bonded crystals whose piezoelectric coefficients differ by sign while the other material constants are identical. Several general theorems have been proved regarding the existence of interface acoustic waves (IAWs) propagating more slowly than bulk waves. In particular, a sufficient condition for the existence of such ‘slow’ IAWs has been derived. The propagation of leaky IAWs has been studied. Special attention has been paid to the analysis of the situation when the imaginary component of the leaky IAW velocity vanishes, resulting in the appearance of non-attenuating IAWs travelling faster than the slow transverse bulk wave. The computations performed for LiNbO 3 and LiTaO 3 illustrate general conclusions.

Fundamental frequency degeneracy of standing surface acoustic waves under metallic gratings on piezoelectric substrates

The paper studies specific features of surface acoustic waves on piezoelectric substrates under infinite periodic grating arrays. The grating is made up of identical metallic electrodes of finite thickness and has one electrode per cell. It has been shown via the analysis of numerical algorithms and the coupling-of-modes equations that one of the fundamental frequencies of the standing wave under short-circuited grating necessarily coincides with one of the fundamental frequencies corresponding to the open-circuited grating if the substrate assumes particular orientations connected with its crystallographic symmetry. The existence of degeneracy does not depend on the material constants of the substrate and the electrode, the thickness of the electrode, and the specific electrode shape provided that the electrode is uniform along the wave normal and shaped symmetrically in the same direction. The proof applies both to ordinary and leaky surface waves.

Subsonic leaky Rayleigh waves at liquid-solid interfaces

The paper is devoted to the study of leaky Rayleigh waves at liquid-solid interfaces close to the border of the existence domain of these modes. The real and complex roots of the secular equation are computed for interface waves at the boundary between water and a binary isotropic alloy of gold and silver with continuously variable composition. The change of composition of the alloy allows one to cross a critical velocity for the existence of leaky waves. It is shown that, contrary to popular opinion, the critical velocity does not coincide with the phase velocity of bulk waves in liquid. The true threshold velocity is found to be smaller, the correction being of about 1.45%. Attention is also drawn to the fact that using the real part of the complex phase velocity as a velocity of leaky waves gives only approximate value. The most interesting feature of the waves under consideration is the presence of energy leakage in the subsonic range of the phase velocities where, at first glance, any radiation by harmonic waves is not permitted. A simple physical explanation of this radiation with due regard for inhomogeneity of radiated and radiating waves is given. The controversial question of the existence of leaky Rayleigh waves at a water/ice interface is reexamined. It is shown that the solution considered previously as a leaky wave is in fact the solution of the bulk-wave-reflection problem for inhomogeneous waves.

Properties of sensors based on shear-horizontal surface acoustic waves in LiTaO3/SiO2 and quartz/SiO2 structures

Acoustic wave devices based on waveguide modes with shear-horizontal polarization, i.e., Love modes, are very promising for sensor application, especially in liquid environments. They can be used for the determination of liquid density and viscosity as well as for chemical sensors. Up to now, several systems have been reported based on standard ST quartz. Those devices lack temperature stability, which is essential for field application. Thus, temperature-compensated systems based on different Y-rotated quartz and lithium tantalate (LiTaO3) plates with SiO2 guiding layers have been investigated. Temperature behavior as well as relevant acoustic properties were considered. Furthermore, experimentally determined data for device sensitivity are compared with theoretical predictions from numerical calculations.

Incredible negative values of effective electromechanical coupling coefficient for surface acoustic waves in piezoelectrics

The extraordinary case of increase in velocity of surface acoustic waves (SAW) caused by electrical shorting of the surface of the superstrong piezoelectric crystal potassium niobate, KNbO3, is numerically found. The explanation of this effect is based on considering SAWs as coupled Rayleigh and Bleustein-Gulyaev modes. A general procedure of approximate decoupling of the modes is suggested for piezoelectric crystals of arbitrary anisotropy. The effect under study takes place when the phase velocity of uncoupled sagittally polarized Rayleigh waves is intermediate between the phase velocities of uncoupled shear-horizontal Bleustein Gulyaev waves at the free and metallized surfaces. In this case, the metallization of the surface by an infinitely thin layer may cause a crossover of the velocity curves of the uncoupled waves. The presence of the mode coupling results in splitting of the curves with transition from one uncoupled branch to the other. This transition is responsible for the increase in SAW velocity, which appears to be greater than its common decrease produced by electrical shorting of the substrate surface.

Prolonged acousto-optic interaction with Lamb waves in crystalline plates

The propagation and acousto-optic interaction of Lamb modes in an anisotropic plate of tellurium dioxide (TeO2) are studied numerically and analytically. In the case of a Y-cut X-propagating TeO2 plate, the very high elastic anisotropy of the crystal greatly modifies the dispersion curves, giving rise to their multiple oscillations. The existence ranges of backward Lamb modes increase with the mode order contrary to the case of isotropic plates. The quasi-collinear light scattering by Lamb waves is considered. Owing to the structure of Lamb wave field, a simultaneous light diffraction at two different optical frequencies can take place while Lamb waves are excited only at the single frequency. It is demonstrated with the Z-cut (110)-propagating plate that a small change in the acoustic frequency can result in a significant shift in the frequency of the scattered light.

Properties of shear-horizontal surface acoustic waves in different layered quartz-SiO2 structures

Acoustic wave devices based on waveguide modes with shear-horizontal polarisation in Y-rotated quartz plates are very promising for sensor application. Up to now, several systems have been reported based on standard ST-quartz. Those devices lack temperature stability, which is essential for field application. However, appropriate combinations of crystal cut angle and SiO2 overlay thickness should provide temperature compensation. Thus, different systems based on Y-rotated quartz plates with cut angles between 30 and 42.75 degrees have been investigated. First- and second-order temperature coefficients of frequency change have been calculated and measured. Moreover, properties are compiled that are relevant for the device design, i.e. acoustoelectric coupling coefficients, effective dielectric constants, and phase as well as group velocities. In summary, device configurations could be identified that combine temperature stability comparable to that of surface skimming bulk waves in the AT-cut, a suitable coupling coefficient, and high gravimetric sensitivity.

A Green's function approach to the reflection behavior of SAW in layered structures

A Green's function method is used to derive expressions for the mechanical part of complex SAW reflection coefficients for layered structures of any material symmetry with transverse perturbations of arbitrary shape and material symmetry. The computed data are in qualitative agreement with published results that have been derived using the variational principle or the perturbation theory. Deviations arise from quite different situations concerning the point of observing the reflected wave.