Phase Velocity Shift Research Articles

Phase velocity shifts of shear surface waves in flexoelectric wave-guide clamped on piezomagnetic base

Surface acoustic wave devices featuring periodic layers of piezomagnetic and piezoelectric-flexoelectric layers are subject to intense investigation. In miniaturized devices, large strain gradients are possible that produce significant flexoelectric fields in piezoelectric components. In the present theoretical research, surface acoustic wave transference has been manifested in a flexoelectric waveguide clamped over a piezomagnetic base. This endeavor involves the formulation and solution of coupled magneto-electro-elastic field equations governing the structure’s behavior. Coupled magneto-electro-elastic field equations for the structure have been derived and solved utilizing analytical techniques. By accounting for pertinent boundary conditions, the dispersion relations characterizing the velocity of surface waves, both in scenarios with and without electrodes have been obtained. Based on proper numerical examples, the frequency and phase velocity spectrum have been plotted offering insights into key parameters i.e. modal frequency, phase velocity, and wave attenuation. The outcomes of the theoretical study may be helpful in providing insights into mechanical wave propagation in coupled piezoelectric/piezomagnetic structures.

Analysis of different wave characteristics in a fiber-reinforced thermo-piezoelectric rotating medium influenced by gravity

Fiber-reinforced polymer composites possess a lightweight nature, corrosion resistance, high strength, and specific stiffness. As a result, they play a crucial role in the construction and rehabilitation of structures, providing reinforcement with their versatile and beneficial properties. Owing to this, proposed mathematical model is intended to give a detailed analysis of the characteristics of surface waves in a homogeneous, transversely isotropic fiber-reinforced thermo-piezoelectric (FRTPC) composite half-space rotating with uniform angular frequency including Coriolis and centrifugal forces. Recently proposed Moore–Gibson–Thompson thermoelasticity theory with two-temperature is employed to describe the mathematical framework. The free surface is considered to be stress free, electrically shorted/charge free, and thermally insulated/isothermal. The FRTPC structure is analytically modeled by the Strength of Materials technique with the Rule of Mixtures approach. Normal mode technique is used to derive the expression for mechanical stresses, electrical displacement, and temperature gradient. Depending upon four different boundary conditions, corresponding secular equations are derived for the considered half-space. The influence of rotation, gravity, fiber volume fraction, and two-temperature on different wave characteristics (phase velocity, attenuation coefficient, specific loss, and frequency shift) is demonstrated graphically considering PZT-5H epoxy material. Numerical simulation indicates that wave propagates at a finite speed in the FRTPC medium in the case of MGT thermoelastic theory, rather than the infinite speed in the classical thermoelasticity model. The present mathematical study may find its application in designing of gyroscopes, rotation sensors, temperature sensors, and other pyro/piezoelectric surface acoustic wave devices.

Sensitivity of Surface Acoustic Wave Sensors Based LiNbO3 128° Y-X and at-Quartz to PM10 and PM2.5

IntroductionParticulate matter (PM) was estimated to cause around 7 million premature deaths worldwide per year according to World Health organization [1]. These particles can cause diseases leading to premature death [2]. Over the last decade, the monitoring of PM became an important issue on a worldwide scale. The miniaturization of the existing bulky systems has also become necessary to reduce their cost. To address this need, a new miniaturized system for PM monitoring was previously developed in our team [3]. It takes advantage of both a 3 Lpm cascade impactor and surface acoustic waves (SAW) sensors to respectively separate and measure particles. The present study aims to compare the sensitivity of two SAW devices. The first exploits Love waves on an AT cut Quartz substrate and the second is based on Rayleigh waves from a LiNbO3 Y-X 128° substrates. The latter presents a high electromechanical coupling factor that could be exploited for the self-cleaning of the device after the measurement. This could allow overcoming the fouling issue faced with impactors that wouldn’t be solved with quartz based sensors which suffer from an insufficient electromechanical coupling. Method In this study we used a dedicated 3 Lpm cascade impactor equipped with SAW delay lines as collecting plate. The Rayleigh wave sensor and the Love wave sensor were designed and fabricated respectively on LiNbO3 Y-X 128° cut and AT-Quartz cut substrates using a conventional photolithography process. The interdigital transducers (IDT) consist of double finger pairs made of 200 nm thick aluminum with a periodicity p=10 µm and a wavelength λ=40 µm. Hence, the working frequency is 125 MHz for the Love mode and 98 MHz for the Rayleigh mode. The propagation of Love wave needs a guiding layer. For that purpose, a silica layer was deposited using sputtering technique with shear velocity lower than the piezoelectric substrates. The region between the two IDTs constitutes the sensing area.Preliminary tests have been performed using candle smoke. As the obtained PM concentrations were unstable and difficult to reproduce, we have developed an experimental set-up bench consisting of a 1m3 chamber, a particle’s generator AGK 2000 and an optical system FIDAS® 100. Thus, sodium chloride (NaCl) was used to produce PM2.5 while PM10 were generated from silicon carbide (SiC) in the 0 to 200 μg/m3 concentration range. When the particles impact on the sensor surface, the velocity of the acoustic waves decreases due to the sensors’ high gravimetric sensitivity. Accordingly, the wave phase velocity shift is measured by monitoring the phase at constant frequency with an open loop interrogation [4]. It’s then correlated to the particles concentration. Results and Conclusions Figure 1 and 2 shows plots of phase derivative dϕ/dt of sensors based AT-Quartz (black) and LiNbO3 (red) with the concentration of PM10 and PM2.5 respectively measured with the optical system FIDAS®. As expected, the sensitivity of the Rayleigh wave sensor based on LiNbO3 is lower than the Love wave sensor based on quartz for both PM10 and PM2.5. The sensor’s sensitivity is estimated by applying a linear fit of the plotted data. The sensitivity of sensors based on quartz is 3.10-4 °/s.μg/m3 for PM 2.5 and 5.10-5 °/s.μg/m3 for PM10. For sensors based on LiNbO3, the sensitivity is 1.10-4 °/s.μg/m3 for PM2.5 and 1.10-5 °/s.μg/m3 for PM10. The feature that the sensors’ response is greater with PM2.5 than with PM10 can be explained by the fact that most adhesion forces are linearly dependent on particle diameter [5] which is often described as the rebound effect. As a result, the smaller particles settle more on the surface of the sensor resulting in a more significant slowdown of the wave. To ensure that each stage is measuring the targeted size range, we took images of the sensors surface at the end of the experiment using a microscope. Figures 3, 4 show the surface of the PM2.5 stage and figures 5, 6 the one of the PM10 stage. One can observe that, as expected, the PM2.5 contain more particles than the PM10 and that the particle sizes correspond well to the ranges [0.3 μm, 2.5 μm] and [2.5 μm, 10 μm]. It has therefore been shown that LiNbO3 sensors, although less sensitive, can also be used for fine particles detection. They still need work to improve their performance and limit the rebound effect, but they remain very promising for the development of self-cleaning systems.

An Analytical Solution for the Problem of Stresses in Magneto-Piezoelectric Thermoelastic Material under the Influence of Rotation

The present paper deals with the study of the wave propagation in a homogeneous transversely isotropic magneto-thermo-piezoelectric cylindrical material, under the influence of rotation, in the context of the linear theory of thermoelasticity. The displacement, electric potential, magnetic potential, electrostatic displacement, and magnetic induction functions are introduced to uncouple the equations of motion, with boundary conditions. After deriving secular equations in closed form and isolated mathematical conditions, the effect of rotation, phase velocity, attenuation coefficient profiles and relative frequency shift on dispersion curves is studied. The study is very helpful in the development of rotation sensors and other piezoelectric devices. The numerical results of the physical quantities have been illustrated graphically.

Sensitivity of Surface Acoustic Wave Sensors Based LiNbO3 128° Y-X and at-Quartz to PM10 and PM2.5

Introduction Particulate matter (PM) was estimated to cause around 7 million premature deaths worldwide per year according to World Health organization [1]. These particles can cause diseases leading to premature death [2]. Over the last decade, the monitoring of PM became an important issue on a worldwide scale. The miniaturization of the existing bulky systems has also become necessary to reduce their cost. To address this need, a new miniaturized system for PM monitoring was previously developed in our team [3]. It takes advantage of both a 3 Lpm cascade impactor and surface acoustic waves (SAW) sensors to respectively separate and measure particles. The present study aims to compare the sensitivity of two SAW devices. The first exploits Love waves on an AT cut Quartz substrate and the second is based on Rayleigh waves from a LiNbO3 Y-X 128° substrates. The latter presents a high electromechanical coupling factor that could be exploited for the self-cleaning of the device after the measurement. This could allow overcoming the fouling issue faced with impactors that wouldn’t be solved with quartz based sensors which suffer from an insufficient electromechanical coupling. Method In this study we used a dedicated 3 Lpm cascade impactor equipped with SAW delay lines as collecting plate. The Rayleigh wave sensor and the Love wave sensor were designed and fabricated respectively on LiNbO3 Y-X 128° cut and AT-Quartz cut substrates using a conventional photolithography process. The interdigital transducers (IDT) consist of double finger pairs made of 200 nm thick aluminum with a periodicity p=10 µm and a wavelength λ=40 µm. Hence, the working frequency is 125 MHz for the Love mode and 98 MHz for the Rayleigh mode. The propagation of Love wave needs a guiding layer. For that purpose, a silica layer was deposited using sputtering technique with shear velocity lower than the piezoelectric substrates. The region between the two IDTs constitutes the sensing area.Preliminary tests have been performed using candle smoke. As the obtained PM concentrations were unstable and difficult to reproduce, we have developed an experimental set-up bench consisting of a 1m3 chamber, a particle’s generator AGK 2000 and an optical system FIDAS® 100. Thus, sodium chloride (NaCl) was used to produce PM2.5 while PM10 were generated from silicon carbide (SiC) in the 0 to 200 μg/m3 concentration range. When the particles impact on the sensor surface, the velocity of the acoustic waves decreases due to the sensors’ high gravimetric sensitivity. Accordingly, the wave phase velocity shift is measured by monitoring the phase at constant frequency with an open loop interrogation [4]. It’s then correlated to the particles concentration. Results and Conclusions Figure 1 and 2 shows plots of phase derivative dϕ/dt of sensors based AT-Quartz (black) and LiNbO3 (red) with the concentration of PM10 and PM2.5 respectively measured with the optical system FIDAS®. As expected, the sensitivity of the Rayleigh wave sensor based on LiNbO3 is lower than the Love wave sensor based on quartz for both PM10 and PM2.5. The sensor’s sensitivity is estimated by applying a linear fit of the plotted data. The sensitivity of sensors based on quartz is 3.10-4 °/s.μg/m3 for PM 2.5 and 5.10-5 °/s.μg/m3 for PM10. For sensors based on LiNbO3, the sensitivity is 1.10-4 °/s.μg/m3 for PM2.5 and 1.10-5 °/s.μg/m3 for PM10. The feature that the sensors’ response is greater with PM2.5 than with PM10 can be explained by the fact that most adhesion forces are linearly dependent on particle diameter [5] which is often described as the rebound effect. As a result, the smaller particles settle more on the surface of the sensor resulting in a more significant slowdown of the wave. To ensure that each stage is measuring the targeted size range, we took images of the sensors surface at the end of the experiment using a microscope. Figures 3, 4 show the surface of the PM2.5 stage and figures 5, 6 the one of the PM10 stage. One can observe that, as expected, the PM2.5 contain more particles than the PM10 and that the particle sizes correspond well to the ranges [0.3 μm, 2.5 μm] and [2.5 μm, 10 μm]. It has therefore been shown that LiNbO3 sensors, although less sensitive, can also be used for fine particles detection. They still need work to improve their performance and limit the rebound effect, but they remain very promising for the development of self-cleaning systems.

Giant Magnetoelastic Coupling in a Love Acoustic Waveguide Based on TbCo2 / Fe Co Nanostructured Film on ST-Cut Quartz

Coupling between dynamic strain and magnetization in ferromagnetic thin films has attracted special consideration as it presents both intriguing fundamental physics problems and technological importance for potential multi-functional devices and information handling. The dynamic strain can be generated by acoustic waves including bulk, surface or guided waves. In this work, we propose the theoretical and experimental investigation of the interaction of pure shear horizontal (SH) wave with a uniaxial multilayered TbCo2/FeCo thin film in a delay line configuration fabricated on Quartz ST-90X cut. We evaluate theoretically the evolution of phase velocity as a function of magnetic field and experimentally the variation of the transmission coefficient. A piezomagnetic model was developed allowing us to calculate the elastic stiffness constants of the multilayer as a function of the applied magnetic field. The model was also implemented for acoustic waves dispersion curves calculation. We show that the evolution of phase velocity is dominated by the C66 elastic stiffness constant variation as expected for the case of shear horizontal surface wave. The fabricated device let us exciting both fundamental and third harmonic shear mode at 410 MHz and 1.2 GHz, respectively. For both modes, the theoretical results corroborate very well the experimental ones. At 1.2 GHz the mode exhibits a maximum phase velocity shift close to 2.5% and an attenuation reaching 500 dB/cm, for a sensitivity as high as 250 ppm/Oe. The reported theoretical model and experimental results are of tremendous interest for the development of advanced devices for magnetic field sensing applications as well as investigating magnon-phonon interaction at a fundamental level.

Computational investigation of plane wave reflections at the open end of subsonic intakes

The reflection of plane waves at the open end of intakes carrying subsonic mean flows are considered in this work. The investigations are conducted with a three-dimensional numerical scheme based on the lattice Boltzmann method. Two different geometry profiles were considered to represent the intake, including a cylindrical bell mouth and a Borda tube. The comparison between numerical and analytical results provided by the low-frequency theory suggested two different traits. For the cylindrical bell mouth, the incoming flow remains potential and the wave reflection is only influenced by the phase velocity shift caused by convection. In such a situation, the available low-frequency theory holds for the entire frequency range of plane wave propagation. Conversely, for sharp geometries, such as the Borda tube, flow separates at the duct's entrance and the wave reflection becomes mostly influenced by the exchange of energy between the flow and the acoustic field. In this case, the numerical results deviate considerably from the theory, even in the low-frequency limit. The mechanisms involving the transfer of rotational kinetic energy from the flow to the acoustic field are discussed and an empirical formula is proposed in terms of reflection coefficient for the entire range of plane wave propagation.

Acoustic Wave Sensors for Liquid Environments

Acoustic wave devices are theoretically investigated in their potential role of technological platform for the development of sensors for liquid environments. In this study, we theoretically studied the propagation of in-plane polarized Lamb modes, Love modes, Shear Horizontal Plate modes along layered structures, aimed at the design of acoustic waveguides suitable to trade-off mass sensitivity and low loss. The phase velocity shift and attenuation due to the presence of a viscous liquid contacting the device surface and to a mass anchored to the sensor surface are calculated for different waveguide structures, confirming that the sensor behavior can be enhanced by a proper choice of the material parameters (i.e., material types, crystallographic orientation, electrical boundary conditions, and thicknesses) of the layered waveguide structure.

The Dynamics of Viscoelastic Layered Systems Studied by Surface Acoustic Wave (SAW) Sensors Operated in a Liquid Phase

We theoretically study a three-layer continuum model of a surface acoustic wave sensor where the two overlayers are allowed to be viscoelastic. This case is particularly important in biosensing, where soft materials submerged in fluids are commonplace. From the general dispersion equation, we calculate the phase velocity shift and the wave attenuation. We show that there is a viscoelastic coupling between the overlayers which results in unintuitive behavior, e.g., the addition of viscous loading to a soft-film sensor can reduce the attenuation.

Soft-film dynamics of SH-SAW sensors in viscous and viscoelastic fluids

We theoretically investigate surface acoustic waves with horizontal polarization (SH-SAWs) propagating in a three-layer system consisting of an elastic substrate and two viscoelastic overlayers. For the limiting case of an acoustically thin middle layer and an infinite top layer, we derive analytical expressions for the phase velocity shift and the wave attenuation. These expressions demonstrate the importance of taking into account the viscoelastic coupling between the two overlayers. Numerical calculations using a combined Maxwell/Voigt scheme confirm our analytical results and also indicate that it is possible for viscoelasticity to cause SH-SAWs to vanish.

Propagation of pore pressure diffusion waves in saturated dual-porosity media (II)

A mechanism has been established for pressure diffusion waves in dual-porosity media. Pressure diffusion waves are heavily damped with relatively low velocities and short wavelengths. The characteristic frequency dominates the attenuation behavior of pressure diffusions and separates wave fields into two asymptotic regimes: relaxed and unrelaxed. Characteristic delay times control the pressure diffusion between the matrix and the fractures. The transition zones in wavelength and attenuation peak shift toward high frequencies when the characteristic delay time decreases. In contrast, the transition zones in both phase and group velocity shift toward low frequencies as the characteristic time of the delay increases. In a spatially dependent diffusivity field, the pressure diffusion waves in dual-porosity media obey an accumulation-depletion law.

Love-Mode MEMS Devices for Sensing Applications in Liquids.

Love-wave-based MEMS devices are theoretically investigated in their potential role as a promising technological platform for the development of acoustic-wave-based sensors for liquid environments. Both single- and bi-layered structures have been investigated and the velocity dispersion curves were calculated for different layer thicknesses, crystallographic orientations, material types and electrical boundary conditions. High velocity materials have been investigated too, enabling device miniaturization, power consumption reduction and integration with the conditioning electronic circuits. The electroacoustic coupling coefficient dispersion curves of the first four Love modes are calculated for four dispersive coupling configurations based on a c-axis tilted ZnO layer on wz-BN substrate. The gravimetric sensitivity of four Love modes travelling at a common velocity of 9318 m/s along different layer thicknesses, and of three Love modes travelling at different velocity along a fixed ZnO layer thickness, are calculated in order to design enhanced-performance sensors. The phase velocity shift and attenuation due to the presence of a viscous liquid contacting the device surface are calculated for different thicknesses of a c-axis inclined ZnO layer onto BN half-space.

Multilayer magnetostrictive structure based surface acoustic wave devices

This study addresses the experimental and theoretical investigations of guided elastic waves propagation in piezo-magnetic multi-layered structure. The structure is composed of a 20×TbCo2(5nm)/FeCo(5nm) nanostructured multi-layer deposited between two Aluminum (Al) Inter-Digitals Transducers forming a surface acoustic wave delay line, on a Y-cut LiNbO3 substrate. We compare the calculated and measured phase velocity variation under the action of the external magnetic field orientation and magnitude. We find quantitative agreement between the measured and modeled phase velocity shift for all external magnetic field configurations (hard axis and easy axis) and for different shape modes of elastic waves at their first and third harmonic operation frequencies. The shear horizontal mode exhibits a maximum phase velocity shift close to 20% for a ratio close to 1 between magneto-elastic film thickness and wavelength.

Surface wave characteristics in a micropolar transversely isotropic halfspace underlying an inviscid liquid layer

The present investigation deals with the propagation of waves in a micropolar transversely isotropic half space with an overlying inviscid fluid layer. Effects of fluid loading and anisotropy on the phase velocity, attenuation coefficient, specific loss and relative frequency shift. Finally, a numerical solution was carried out for aluminium epoxy material and the computer simulated results for the phase velocity, attenuation coefficient, specific loss and relative frequency shift are presented graphically. A particular case for the propagation of Rayleigh waves in a micropolar transversely isotropic half-space is deduced and dispersion curves are plotted for the same as functions of the wave number. An amplitude of displacements and microrotation together with the path of surface particles are also calculated for the propagation of Rayleigh waves in the latter case

Observed near-inertial kinetic energy in the northwestern South China Sea

Based on more than 3 years of moored current-meter records, this study examined seasonal variability of near-inertial kinetic energy (NIKE) as well as all large (greater than one standard deviation from the mean) NIKE events related to storms and eddies in the northwestern South China Sea. The NIKE in the subsurface layer (30-450 m) exhibited obvious seasonal variability with larger values in autumn (herein defined as August, September, and October). All large NIKE events during the observation period were generated by passing storms. Most of the NIKE events had an e-folding timescale longer than 7 d. The phase velocity, vertical wavelength, and frequency shift of these events were examined. The maximum NIKE, induced by typhoon Neoguri, was observed in April 2008. Normal mode analysis suggested that the combined effects of the first four modes determined the vertical distribution of NIKE with higher NIKE below 70 m but lower NIKE from 30 to 70 m. Another near-inertial oscillation event observed in August 2007 had the longest e-folding timescale of 13.5 d. Moreover, the NIKE propagated both upward and downward during this event. A ray-tracing model indicated that the smaller Brunt-Vaisala frequency and the stronger vertical shear of horizontal currents in an anticyclonic eddy and the near-inertial wave with larger horizontal scale facilitated the unusual propagation of the NIKE and the long decay timescale. Although the NIKE originated from wind, the water column structure affected by diverse oceanographic processes contributed substantially to its complex propagation and distribution.

Stoneley wave dispersion in a high permeability sandstone: Perth Basin, Western Australia

There is increasing support for the existence of a relationship between Stoneley wave characteristics and permeability in sandstone formations. We evaluated monopole full waveform sonic data sets acquired in a mudded drill hole at the Mirrabooka Aquifer Storage and Recharge trial site in Perth, Western Australia. To increase the spectral range of the full wave form sonic data the hole was logged three times with transmitter centre frequencies at 1, 3 and 15 KHz. Data were recorded in four receivers spaced at 1ft intervals with the first receiver at 3ft from the transmitter. Stoneley waves were clearly identified in the low frequency range of 1?5 KHz, which is characteristic of Stoneley wave propagation in a slow formation. A semblance slowness technique was used to determine the slowness of Stoneley wave. Slowness values ranged from 950 µs/m (VST = 1050 m/s) for sandstone to 1650 µs/m (VST = 600 m/s) for shaley sediments. Observations of the dependence of phase velocity on frequency were made by using multi filter and phase shift transform techniques. The relationship between Stoneley wave dispersion and fast flow, high permeability pathways, as identified in flow and time lapse induction logging data, was clearly observed in an interval from 330 to 333m below ground level. This high permeability sandstone layer can be identified in dispersion curves by assessing frequency and phase velocity shifts. Our outcomes are significant, as they present the possibility of identifying narrow high permeability layers in wells where full waveform sonic logs have been completed.

Love Wave Characterization of the Shear Modulus Variations of Mesoporous Sensitive Films During Vapor Sorption

Anomalous responses of acoustic humidity sensors coated with mesoporous titania sensitive films have been observed at high humidity levels, due to capillary contraction that alters the film mechanical behavior. As the methods commonly used to assess the elasticity of thin films are difficult to apply during sorption, a dedicated method for the characterization of the variations of the elastic shear modulus of thin films under humidity exposure has been developed. The method combines a Love wave platform with environmental ellipsometric porosimetry (EEP). In the presented approach, EEP measures the thickness of the film and the adsorbed humidity volume fraction under vapor exposure, while the Love wave platform provides the phase velocity shifts induced by water sorption. These parameters then feed an accurate model of Love wave propagation in the multilayered platform for the derivation of the shear modulus of the sensitive film. The method was applied to 100 ± 10 nm thick mesoporous titania films, with 25 ± 1% porosity, under relative humidity exposure in the 3%-95% range. It successfully determined decreases of 39% and 67% of the shear modulus during adsorption and desorption, respectively, from a 3.1 GPa initial value.

Wave propagation in graphene sheets with nonlocal elastic theory via finite element formulation

A nonlocal elastic plate model that accounts for the scale effects is first developed for wave propagations in graphene sheets. Moreover, a finite element model developed from the weak-form of the elastic plate model is reported to fulfill a comprehensive wave study in the sheets and realize an application of the sheets as gas sensors. The applicability of the finite element model is verified by molecular dynamics simulations. The studies show that the nonlocal finite element plate model is indispensable in predicting graphene phonon dispersion relations, especially at wavelengths less than 1nm, when the small-scale effect becomes dominant. Moreover, the nonlocal parameter e0a, a key parameter in the nonlocal model, is calibrated through the verification process. The dependence of the small-scale effect and the width of sheets on the dispersion relation is also investigated, and simulation results show that the phase velocity decreases to an asymptotic value with the width of sheets reaches a sufficiently large size. As an application of the investigation, the potential of graphene sheets as nano-sensors for noble gas atoms is explored by defining and examining an index based on the phase velocity shifts in a graphene sheet attached by gas atoms.

Probing vacuum birefringence by phase-contrast Fourier imaging under fields of high-intensity lasers

In vacuum high-intensity lasers can cause photon-photon interaction via the process of virtual vacuum polarization which may be measured by the phase velocity shift of photons across intense fields. In the optical frequency domain, the photon-photon interaction is polarization-mediated described by the Euler-Heisenberg effective action. This theory predicts the vacuum birefringence or polarization dependence of the phase velocity shift arising from nonlinear properties in quantum electrodynamics (QED). We suggest a method to measure the vacuum birefringence under intense optical laser fields based on the absolute phase velocity shift by phase-contrast Fourier imaging. The method may serve for observing effects even beyond the QED vacuum polarization.

Perturbation of Rayleigh waves in anisotropic media

Herein we consider Rayleigh waves propagating along the traction-free surface of a homogeneous anisotropic elastic half-space. We investigate the perturbation of the phase velocity and of the polarization of Rayleigh waves, i.e., the shift of phase velocity and the shift of polarization of Rayleigh waves from their respective value pertaining to a comparative isotropic state of the elastic medium, as caused by the anisotropic part of the elasticity tensor. With the help of the Stroh formalism, we derive first-order perturbation formulas for these shifts. We also discuss the problem of determining elastic constants of a weakly anisotropic elastic medium by making measurements of Rayleigh waves propagating in all the directions on the traction-free surface.