Pseudo-surface Waves Research Articles

Split-type seismic metamaterials with pseudo-surface wave weakening mechanism

Pseudo surface waves, as a type of propagating wave, are detrimental to the attenuation of seismic Rayleigh waves. A split seismic metamaterial (SSM) that can weaken pseudo surface wave modes and generate ultra wideband gaps of 12.92Hz is proposed. The split configuration of SSM can be obtained by separating the modes of different waves within the energy band curve, which can cause the surface waves inside the sound cone to move outward and weaken the pseudo surface wave modes inside the band gap. Combined with the frequency response curve, it is further demonstrated that the attenuation amplitude of SSM is larger than that of monolithic seismic metamaterials (MSM) within the same bandgap range. Afterwards, by studying the changes in bandgap through structural parameters, the method of a gradient array was used to fuse the characteristic frequency that can generate larger attenuation with the weakened pseudo surface wave mode frequency, resulting in greater attenuation. Finally, it is verified by experiments that SSM can provide ultra-wide low-frequency band gaps while also generating large attenuation accuracy, which provides a practical solution for the application of seismic metamaterials.

Microwave plasma interaction in a printed transmission line for a power limiting application: from surface-wave-sustained to leaky-wave-sustained discharge

The coupling between a microwave signal and a plasma discharge in a suspended microstrip transmission line is analytically studied. Maxwell’s equations are solved in a 2D approximation to get the expressions of the electromagnetic field. The wave propagation in the guiding structure is first explored without plasma, and for several modes and frequencies. A unified characterization of the three different modes that can propagate at the interface between two dielectric media, namely the leaky waves, the pseudo-surface wave and the pure surface wave, is given in terms of of both wave vectors and electromagnetic field magnitude distribution. This analyze allow to conclude that the fundamental mode in this case is a pseudo-surface wave. Thereafter, we focus on the microwave propagation with a uniform plasma inside the guiding structure. In the non collisional limit, it appears that the plasma discharge is sustained by the so-called pure surface wave, whereas in the collisional limit, a leaky wave propagates along the plasma column. Finally, a non-uniform density profile is taken into account in the calculation. The numerical results obtained from the self-consistent simulation of the microwave-plasma coupling, in a previous work, are thus analyzed with the aid of the analytical formulas to identify the microwave coupling involved in our plasma-based microwave power limiter. The computed propagation constant from numerical data confirmed the type of coupling exhibited for a uniform electron density. Furthermore, we highlight the role of the dielectric slab, from which electromagnetic power transfer occurs into the plasma discharge.

Velocimetry of GHz elastic surface waves in quartz and fused silica based on full-field imaging of pump–probe reflectometry

This study reports an imaging method for gigahertz surface acoustic waves in transparent layers using infrared subpicosecond laser pulses in the ablation regime and an optical pump–probe technique. The reflectivity modulations due to the photoelastic effect of generated multimodal surface acoustic waves were imaged by an sCMOS camera illuminated by the time-delayed, frequency-doubled probe pulses. Moving the delay time between 6.0nsto11.5ns, image stacks of wave field propagation were created.Two representative samples were investigated: wafers of isotropic fused silica and anisotropic x-cut quartz. Rayleigh (SAW) and longitudinal dominant high-velocity pseudo-surface acoustic wave (HVPSAW) modes could be observed and tracked along a circular grid around the excitation center, allowing the extraction of angular profiles of the propagation velocity. In quartz, the folding of a PSAW was observed. A finite element simulation was developed to predict the measurement results. The simulation and measurement were in good agreement with a relative error of 2% to 5%.These results show the potential for fast and full-field imaging of laser-generated ultrasonic surface wave modes, which can be utilized for the characterization of thin transparent samples such as semiconductor wafers or optical crystals in the gigahertz frequency range.

Complex dispersion analysis of true and pseudo surface waves propagating in two-dimensional viscoelastic seismic metamaterials

In this paper, the wave characteristics of true surface waves (TSWs) and pseudo surface waves (PSWs) in two-dimensional (2D) seismic metamaterials are explored. The 2D seismic metamaterial is formed by placing periodic concrete pillars on the surface of the soil substrate. The complex dispersion curves of the seismic metamaterial are numerically calculated by the ω–kapproach. The Kelvin–Voigt model is adopted to describe the material viscoelasticity. The results show that not only the TSW modes but also the PSW modes should be taken into account to evaluate the mitigation capacity of the seismic metamaterials. Due to the introduction of material viscoelasticity, the TSWs and PSWs convert from the propagative mode to the evanescent mode. When the PSW modes propagate along the substrate surface, their energy gradually leaks into the bulk of the substrate, leading to their transmission coefficient smaller than that of the TSW modes. Compared to the concrete pillars on the substrate surface, the viscoelasticity of the soil substrate plays a more important role in surface wave reduction. Moreover, the wave propagating length in the seismic metamaterials can be predicted by using complex dispersion relations.

Attenuation of Rayleigh and pseudo surface waves in saturated soil by seismic metamaterials

Seismic metamaterials have received extensive research interest due to their bandgap properties, simplicity in design principles, and stability in response. They have been developed to protect buildings or architectures susceptible to damage from surface elastic waves. In practice, the ground soil is generally a multiphase medium, and the influence of its permeability and viscosity on seismic metamaterials is not yet clear. In this work, we developed a formulation that combines Biot’s theory and Bloch-Floquet theorem to investigate the complex band structures and transmission properties of Rayleigh and pseudo surface waves (PSWs) for pillared and inclusion-embedded seismic metamaterials in saturated soil. It is shown that the ratio of fluid viscosity and permeability η/κ have an impact on the surface wave attenuation and the performances of seismic metamaterials, where the smaller ratio benefits the surface wave broadband attenuation and metamaterials attenuating effects. The complex band structures reveal that inclusion-embedded metamaterials can support the propagation of PSWs having a phase velocity higher than that of the transverse bulk waves. The PSWs are significantly affected by the rubber viscosity due to the mode displacements concentrated in the rubber coatings. The higher viscosity of metamaterials also allows for broadband attenuation of Rayleigh surface waves. The results of this study will present an appropriate way to design viscoelastic seismic metamaterials in saturated soil for low-frequency surface wave attenuation.

Analysis of SAW Temperature Properties in KTiOPO4 Single Crystal

The surface acoustic wave (SAW) properties of potassium titanyl phosphate (KTiOPO4, KTP) single crystal were evaluated by numerical methods. The phase velocity, electromechanical coupling coefficient, power flow deflection angle, and temperature coefficient of delay (TCD) were determined for different crystal cuts of KTP. It was shown that SAW has the electromechanical coupling coefficient of 0.59% and the TCD of 62 ppm/°C on the Z-cut and wave propagation direction along the crystal X + 70°-axis. For the Z-cut and wave propagation direction along the X-axis, the pseudo-surface wave (PSAW) is characterized by the coupling coefficient of 0.46% and the TCD value of 57 ppm/°C. The Bleustein-Gulyaev (BG) wave has the TCD value of 35 ppm/°C and 41 ppm/°C on the Y- and X-cuts of KTP, respectively.

Scanning Electron Microscopy Investigation of Surface Acoustic Wave Propagation in a 41° YX-Cut of a LiNbO3 Crystal/Si Layered Structure

The propagation process of the surface acoustic waves (SAW) and the pseudo-surface acoustic waves (PSAW) in a bonded layered structure of a 41° YX-cut of a LiNbO3 crystal/Si(100) crystal was investigated. The scanning electron microscopy (SEM) method,in the low-energy secondary electrons registration mode, made it possible to visualize the SAW and PSAW in the LiNbO3/Si layered structure. The process of the SAW and PSAW propagation in a LiNbO3/Si layered structure and in a bulk 41° YX-cut of a LiNbO3 crystal were compared. It was demonstrated that the SAW velocities in the layered LiNbO3/Si structure exceed the typical SAW velocities for LiNbO3 and Si single crystals. In the layered structure, the SAW and PSAW velocities were 4062 m/s, 4731 m/s, and 5871 m/s. It was also demonstrated that the PSAW velocities are the same in the LiNbO3/Si layered structure and in the bulk 41° YX-cut of a LiNbO3 crystal.

Propagation and attenuation of Rayleigh and pseudo surface waves in viscoelastic metamaterials

The development of seismic metamaterials has attracted much research interest in the past decade. Efforts have been made by using experimental and theoretical approaches to isolate buildings and structures susceptible to elastic surface wave damage. However, most seismic metamaterials were designed without considering the viscoelastic effect that widely exists in nature. In this work, we investigate the propagation and attenuation of the Rayleigh and pseudo surface waves (PSWs) in two types of viscoelastic seismic metamaterials, namely, pillared and inclusion-embedded metamaterials, by analyzing the complex band structures and transmission spectra. The complex band structure developed in this work reveals for the first time the existence of PSWs and their propagation properties in inclusion-embedded metamaterials at the surface. These PSW modes are hidden in the traditional ω(k) technique, therefore showing the usefulness of the complex band structure approach. Introducing viscosity to the substrate of both types of seismic metamaterials will enhance the attenuation of both the Rayleigh wave and PSW. For inclusion-embedded metamaterials, the viscoelastic effect in the soft coating layer can have a specific influence only on the PSW. PSWs show advantages to minimize the relative attenuating effect in general. The results in this work will open up great possibilities for designing and optimizing seismic metamaterials in practice.

Characterization of a Weyl semimetal using a unique feature of surface plasmon polaritons

We theoretically investigate the decay constant of surface plasmon polaritons in a Weyl semimetal and propose an experimental method for detecting Weyl semimetals. It is revealed that the surface plasmon polariton in a Weyl semimetal exhibits various characteristics depending on the plasmon wave vector. It can be a pure surface wave, a pseudosurface wave that couples with a bulk plasmon, or a generalized surface wave with complex decay constants. Such diverse surface plasmon characteristics are peculiar to Weyl semimetals that obey axion electrodynamics. The results suggest that the measurement of the decay length, the inverse of the decay constant, can be a powerful experimental probe for identifying Weyl semimetals.

Application of the Ritz–Rayleigh method for Lamb waves in extremely anisotropic media

We propose a numerical approach for the calculation of frequency–dispersion curves in a flat anisotropic waveguide based on the Ritz–Rayleigh method, offering several significant benefits over commonly used analytical and numerical models. The problem is linearized using a tailored functional basis based on Legendre polynomials, utilizing all symmetries provided by the problem to reduce the computational demands, which brings significant benefits for an inverse procedure, and thus for material characterization. The approach is completely general in terms of elastic properties and direction of propagation. As an exemplary calculation, frequency–dispersion curves of phase and group velocity are calculated for a (001)-oriented free-standing film of the Ni–Mn–Ga alloy exhibiting a strong cubic anisotropy. In the case of propagation along the [100] direction, the dispersion curves oscillate strongly, creating pairs of symmetric and antisymmetric modes. Taking advantage of the generality of the approach, the curves are also presented for the case of extreme anisotropy. Sets of curves for directions [110] and [1 0.9 0] (i.e., 3∘ off [110]), where the pseudo-surface wave exists, are also calculated. High-frequency asymptotes are shown to correspond with surface and bulk modes propagating along the plate.

Special wave solutions in the theory of waves of a mixed spectrum in a planar gradient bianisotropic nanocrystalline structure

The propagation of surface and pseudosurface waves of a mixed spectrum in a symmetric nanocrystalline film structure with continuously-inhomogeneous anisotropic material characteristics was considered. The substrate and coating of the compositional structure had the same scalar dielectric and magnetic permeabilities. The artificial medium of the waveguide layer was made from a bianisotropic material with an anisotropy of the magneto-dielectric bond, characterized by four tensors of the dielectric, magnetic, and magneto-dielectric permeabilities with nonzero diagonal elements. They depended on spatial coordinates with a biquadratic law. A system of coupled quasi-differential wave equations was obtained toward to the transverse components of the electric and magnetic fields from Maxwell’s equations with taking into account specific material relationships. It had linearly independent solutions, which were represented in the form of generalized series. Recurrence relations were determined for the determination of their terms. Taking into account the continuity of the tangential components of the electric and magnetic fields, a dispersion equation for calculating the transverse wave numbers was found. We obtained the existence of four proper surface and pseudosurface waves with different polarizations, which possess a whole series of fundamentally new characteristics, from the structure of the system of wave equations and their solutions.

Cylindrical Plasma Antenna with Large Longitudinal Density Irregularity

The efficiency of operation of a cylindrical plasma antenna as a function of the degree of longitudinal nonuniformity of the plasma density is examined. The study is based on the method of spectral field expansion into a complete set of functions comprising surface and pseudosurface waves of the plasma column. The system of integrodifferential equations for expansion coefficients determining radiation patterns and the amplitudes of transmitted, reflected, and scattered waves is solved in the case of rapid variation in the plasma density. Dependences of the coefficients of conversion of the surface-wave energy on the plasma-density gradient, the electric length of the section of plasma nonuniformity, and the electric radius of the plasma cylinder are calculated. It is demonstrated by examples that the portion of energy of the surface wave converted into radiation may exceed 50%. It has been found that the radiation patterns are narrow with a single lobe whose maximum is at an angle of several degrees to the direction of propagation of the surface wave. As the plasma-density gradient increases, the lobe width decreases and the lobe itself shifts toward 0°.

Surface waves in a cylindrical borehole through partially-saturated porous solid

Propagation of surface waves is discussed in a cylindrical borehole through a liquid-saturated porous solid of infinite extent. The porous medium is assumed to be a continuum consisting of a solid skeletal with connected void space occupied by a mixture of two immiscible inviscid fluids. This model also represents the partial saturation when liquid fills only a part of the pore space and gas bubbles span the remaining void space. In this isotropic medium, potential functions identify the existence of three dilatational waves coupled with a shear wave. For propagation of plane harmonic waves along the axially-symmetric borehole, these potentials decay into the porous medium. Boundary conditions are chosen to disallow the discharge of liquid into the borehole through its impervious porous walls. A dispersion equation is derived for the propagation of surface waves along the curved walls of no-liquid (all gas) borehole. A numerical example is studied to explore the existence of cylindrical waves in a particular model of the porous sandstone. True surface waves do not propagate along the walls of borehole when the supporting medium is partially saturated. Such waves propagate only beyond a certain frequency when the medium is fully-saturated porous or an elastic one. Dispersion in the velocity of pseudo surface waves is analysed through the changes in consolidation, saturation degree, capillary pressure or porosity.

Radiation from a Plasma Layer with a Strong Longitudinal Irregularity

The efficiency of conversion of the energy of a surface wave into radiation at longitudinal irregularities of a planar plasma layer is studied. The analysis is performed by the spectral expansion of the field in a complete set of surface and pseudosurface waves. The system of integro-differential equations for the coefficients of expansion that determine the amplitudes of the transmitted, reflected, and scattered waves as well as the radiation pattern is solved in the case of a rapid change in the plasma density. The coefficients of transformation of energy into the energy of radiation as functions of the gradient of the plasma density for different values of the electrical length of the region of plasma irregularity and the electric thickness of the plasma layer are found. Examples are demonstrated when the fraction of the energy of the surface wave transformed into radiation reaches 60–70%. Radiation patterns that proved to be highly directional and having one lobe with the maximum at an angle of a few degrees to the direction of propagation of the surface wave are calculated.

A numerical method for predicting Rayleigh surface wave velocity in anisotropic crystals

A numerical method was developed for calculating the Rayleigh Surface Wave (RSW) velocity in arbitrarily oriented single crystals in 360 degrees of propagation. This method relies on the results from modern analysis of RSW behavior with the Stroh formalism to restrict the domain in which to search for velocities by first calculating the limiting velocity. This extension of existing numerical methods also leads to a natural way of determining both the existence of the RSW as well as the possibility of encountering a pseudo-surface wave. Furthermore, the algorithm is applied to the calculation of elastic properties from measurement of the surface wave velocity in multiple different directions on a single crystal sample. The algorithm was tested with crystal symmetries and single crystal elastic moduli from literature. It was found to be very robust and efficient in calculating RSW velocity curves in all cases.

Acoustic Wood anomaly in transmitted diffraction field

In acoustics, the term Wood anomaly, in analogy to the Wood anomaly in optics, has so far referred to the anomalies observed in the specular reflection spectra of acoustic waves perpendicularly incident on periodic surfaces. Inspired by the pioneering work of Jungman et al. on the study of the transmission field of a solid-fluid periodic interface, this work attempts to provide a complete experimental investigation of the transmission fields of a broadband sound pulse transmitted through a periodic liquid-solid interface as well as a periodic solid-liquid interface. At different frequencies, two types of anomalies are observed: a spectral tip and a spectral dip, which correspond, respectively, to the brighter band and the darker band in optical Wood anomalies. The search for their physical origin suggests that the type and location of the observed spectral anomalies are strongly related to the generation and the diffraction of pseudosurface waves on the interface having superimposed periodic corrugations and time-domain windowing in spectral analysis. To compare with the surface waves on a plane surface, the properties of the pseudosurface waves are also investigated through examining their phase and by comparing their amplitudes.

Study of a longitudinally nonuniform plasma layer

Transformation of the energy of surface waves in a plane plasma layer with a longitudinal irregularity of density is studied by the method of spectral decomposition. The total field is represented by an expansion in surface and pseudo-surface waves. A system of integro-differential equation for the coefficients of expansion determining the amplitudes of the transmitted, reflected, and scattered waves is obtained. It is shown that, in some special cases, this system of equations is reduced to a system of ordinary differential equations even if the plasma density rapidly changes. The fraction of the energy of surface waves that transforms into radiation at an acute angle with the layer can reach 50–60%.

Application of Immersion Ultrasonic Testing For Non-Contact Quality Evaluation of Magnetically Impelled Arc Butt Welded Drive Shafts of Motor Vehicles

The article presents contemporary ultrasonic methods that can be applied to evaluate the quality of transmission drive components of motor vehicles. The issues of non-destructive analysis of discontinuities in manufactured drive shafts, consisting currently of thin-walled tubes, were investigated in this study. The driveshaft elements were joined by using innovative method called Magnetically Impelled Arc Butt Welding (MIAB). For many years, a major challenge for engineers working with ultrasonic techniques was joining of thin-walled components (having thickness below 3 mm). In addition of this limitation, the problem of variable geometry of the weld flash on the weld perimeter was highlighted. To reduce the impact of mentioned factors the pseudo-surface waves (also known as lateral waves) have been applied in this study. In order to select optimal parameters of the ultrasonic beam propagation and to understand the physical-acoustic phenomena, the Finite Elements Method modelling was performed. The phenomena of wave transformation on medium boundary and reflections from artificial flaw have been analyzed by numerical modelling. The results of numerical analysis were confirmed by UT experimental research. The manufactured MIAB welded joints were tested with using in-house made experiment set-up. The selected configurations with various shapes and dimensions of samples, and various process parameters have been investigated. The results confirm the usefulness of pseudo-surface ultrasonic waves in UT quality evaluation of MIAB welded elements of drive shafts of motor vehicles.

Theoretical Analysis of SAW Propagation in 3C-SiC/c-AlN

The anisotropic materials as the acoustic wave propagating medium introduce the dependence of the phase velocity on the wave propagation direction, as opposed to the isotropic counterparts; in addition, the profile of the particle displacement components can be quite different, depending on the crystal type and propagation direction. The propagation of surface and bulk acoustic waves (SAWs and BAWs) along the (001), (111) and (110) planes of cubic SiC crystals have been studied. For specific propagation directions in these planes, slight variations in the velocity of the elastic surface waves are found. It was observed that Rayleigh-type, generalized and pseudo-surface waves can propagate at specific directions, thus confirming how the anisotropic behavior of the bare SiC substrate modifies the existence and the field profile of the SAW that propagates at its free surface. Finally, the SAW propagation along AlN/SiC-based multilayered structures is studied for the three SiC planes, different AlN piezoelectric layer thicknesses and electrical boundary conditions.

Propagation of surface waves and surface resonances along cylindrical cavities in materials with any allowed Poisson's ratio – Part I: Clean inner surface

The dynamics of the inner surface of an infinitely long circular‐cylindrical cavity in an isotropic elastic medium is studied in the whole range of the Poisson's ratio including negative values characteristic of auxetic materials. The existence of the unique long‐lived propagation mode (true surface wave, TSW) has been confirmed on the clean surface with the following properties: (i) existence of a low frequency cut‐off for all the azimuthal indices n except for n = 1 (flexural mode), (ii) polarization tending to that of the Rayleigh wave in the short wavelength limit, (iii) Airy phases (inflection points of dispersion curves) for n < 6 that shift towards short wave region when the Poisson's ratio becomes negative. A number of propagation modes with complex frequencies, i.e., with finite life times (surface leaky waves, pseudo surface waves) are found. The torsional leaky mode transforms into the skimming shear‐horizontal wave (Love wave) in the short wavelength limit. An axial–radial leaky mode, similar to the Rayleigh wave but with reverse elliptical polarization turns out a physical solution except for extremely short wavelengths. A strong radial component of the longitudinal resonance occurs at wavelengths comparable to the cavity's radius especially in the incompressible limit.