Quasi-longitudinal Modes Research Articles

A framework for computing directivities for ultrasonic sources in generally anisotropic, multi-layered media

The knowledge of the directivity of ultrasonic sources is an important element in the design of non-destructive evaluation inspection. The commonly used directivity model of piezoelectric devices is the superposition of out-of-plane force monopoles on the stress-free surface of an isotropic elastic half-space. However, this does not cover a growing range of ultrasonic generation scenarios, as new ultrasonic technologies such as laser ultrasound (LU) emerges, and the need for inspection of materials such as carbon fibre reinforced polymers (CFRPs) rises. A directivity calculation framework based on the reciprocity theorem is developed in the current paper, which accommodates various combinations of source types, material properties, and boundary conditions, for example, a localised heating under a surface layer over an anisotropic half-space. The calculation is applicable to materials with weak anisotropy or wave modes that do not have cuspoidal wavefronts, and was validated with finite element models on key representative cases. The analytical solution for LU excitation in a CFRP sample also shows a good fit to the experimentally measured directivity of the quasi-longitudinal wave mode.

Antenna source of radio-frequency emission in ion-proton pulsars

ABSTRACT The growth of a longitudinal or quasi-longitudinal Langmuir mode in the outward-moving beam of ions and protons that forms the open sector of an ion-proton pulsar magnetosphere radiates as an analogue of an end-fed high-impedance horizontal straight-wire antenna an integral number of half-waves in length. The radiation has, broadly, the energy flux, linear polarization, and spectral index that are widely observed: also, the notch phenomenon seen in some integrated pulse profiles occurs naturally. The new field of pulsar observations below 100 MHz may lead to productive tests of the radio emission mechanism.

Analysis of Acousto-Optic Figure of Merit in KGW and KYW Crystals.

Monoclinic potassium rare-earth crystals are known as efficient materials for solid-state lasers and acousto-optic modulators. A number of specific configurations for acousto-optic devices based on those crystals have recently been proposed, but the acousto-optic effect of those crystals has only been analyzed fragmentarily for some interaction directions. In this work, we numerically searched for the global maxima of an acousto-optic figure of merit for isotropic diffraction in KGd(WO4)2 and KY(WO4)2 crystals. It was demonstrated that the global maxima of the acousto-optic figure of merit in those crystals occur in the slow optical mode propagating along the crystal's twofold symmetry axis and in the acoustic wave propagating orthogonally, both for quasi-longitudinal and quasi-shear acoustic modes. The proposed calculation method can be readily used for the optimization of the acousto-optic interaction geometry in crystals with arbitrary symmetry.

Long-wavelength phonon dynamics in incommensurate Bi2Sr2CaCu2O8+δ crystals by Brillouin light scattering spectroscopy

Room temperature phonon dynamics in crystals of the high-Tc superconductor Bi2Sr2CaCu2O(8+delta) were probed using Brillouin light scattering spectroscopy. Eight distinct acoustic modes were observed and identified, including two quasi-longitudinal bulk modes and four quasi-transverse bulk modes. A peak at a frequency shift of ~95 GHz with behaviour reminiscent of an optic phonon was also observed in the spectra. The existence and nature of these modes is a manifestation of the incommensurate structure of Bi2Sr2CaCu2O(8+delta) and suggests that it may be categorized as a so-called composite incommensurate crystal comprised of two weakly interacting sublattices. A mass ratio of m1/m2=0.36 obtained from the two measured quasi-longitudinal acoustic velocities led to sublattice assignments of Bi2Sr2O4 and CaCu2O4. The Brillouin data also places an upper limit of ~10 GHz on the crossover frequency between commensurate and incommensurate phonon dynamics.

Tunable three-dimensional nonreciprocal transmission in a layered nonlinear elastic wave metamaterial by initial stresses

In this work, the three-dimensional (3D) propagation behaviors in the nonlinear phononic crystal and elastic wave metamaterial with initial stresses are investigated. The analytical solutions of the fundamental wave and second harmonic with the quasi-longitudinal (qP) and quasi-shear (qS1 and qS2) modes are derived. Based on the transfer and stiffness matrices, band gaps with initial stresses are obtained by the Bloch theorem. The transmission coefficients are calculated to support the band gap property, and the tunability of the nonreciprocal transmission by the initial stress is discussed. This work is expected to provide a way to tune the nonreciprocal transmission with vector characteristics.

METHOD OF EXCITATION OF QUASI LONGITUDINAL ACOUSTIC WAVES IN LAYERED STRUCTURES

The analysis of methodological possibilities of excitation of quasi-longitudinal (QL) acoustic waves of the megahertz frequency range in layered structures GaN-on-sapphire is studied and carried out. Volume-type transducers polarized by plate thickness are used to generate and detect QL waves. It is concluded that quasilongitudinal modes (QL) can be excited by this method – the so-called Anisimkin (AN) waves, for which the displacement plane is localized in the film plane and the displacement direction is directed along the wave vector.

Microwave Acoustic Attenuation in CTGS Single Crystals.

This article presents a study of special material properties of the single crystalline material Ca3TaGa3Si2O14 (CTGS = Catangasite). The comparatively highly ordered crystal structure and acceptable piezoelectric strength make it a candidate for microacoustic applications under extreme conditions. Obviously, low-loss dynamic behavior is typical for this crystal which consequently enables high-temperature use. As a particular challenge, the behavior at gigahertz frequencies is investigated here. For that, High overtone Bulk Acoustic wave Resonator (HBAR) type measurements in the range of 1-6 GHz are performed. The selection of five distinctive propagation directions for exclusively pure or quasi-longitudinal modes enables to derive the dynamic viscosities from the quality factors of HBAR results. The observed frequency dependences exhibit Akhiezer behavior as the predominant loss mechanism in the cases examined.

Ultrafast light-induced shear strain probed by time-resolved x-ray diffraction: Multiferroic BiFeO3 as a case study

Enabling the light-control of complex systems on ultra-short timescales gives rise to rich physics with promising applications. While crucial, the quantitative determination of both the longitudinal and shear photo-induced strains still remains challenging. Here, by scrutinizing asymmetric Bragg peaks pairs $(\pm h01)$ using picosecond time-resolved X-ray diffraction experiments in BiFeO$_3$, we simultaneously determine the longitudinal and shear strains. The relative amplitude of those strains can be explained only if both thermal and non-thermal processes contribute to the acoustic phonon photogeneration process. Importantly, we also reveal a difference of the dynamical response of the longitudinal strain with respect to the shear one due to an interplay of quasi-longitudinal and quasi-transverse acoustic modes, well reproduced by our model.

Attenuation and Phase Velocity of Elastic Wave in Textured Polycrystals with Ellipsoidal Grains of Arbitrary Crystal Symmetry

This study extends the second-order attenuation (SOA) model for elastic waves in texture-free inhomogeneous cubic polycrystalline materials with equiaxed grains to textured polycrystals with ellipsoidal grains of arbitrary crystal symmetry. In term of this work, one can predict both the scattering-induced attenuation and phase velocity from Rayleigh region (wavelength >> scatter size) to geometric region (wavelength << scatter size) for an arbitrary incident wave mode (quasi-longitudinal, quasi-transverse fast or quasi-transverse slow mode) in a textured polycrystal and examine the impact of crystallographic texture on attenuation and phase velocity dispersion in the whole frequency range. The predicted attenuation results of this work also agree well with the literature on a textured stainless steel polycrystal. Furthermore, an analytical expression for quasi-static phase velocity at an arbitrary wave propagation direction in a textured polycrystal is derived from the SOA model, which can provide an alternative homogenization method for textured polycrystals based on scattering theory. Computational results using triclinic titanium polycrystals with Gaussian orientation distribution function (ODF) are also presented to demonstrate the texture effect on attenuation and phase velocity behaviors and evaluate the applicability and limitation of an existing analytical model based on the Born approximation for textured polycrystals. Finally, quasi-static phase velocities predicted by this work for a textured polycrystalline copper with generalized spherical harmonics form ODF are compared to available velocity bounds in the literature including Hashin–Shtrikman bounds, and a reasonable agreement is found between this work and the literature.

Amorphous SiC/c-ZnO-Based Quasi-Lamb Mode Sensor for Liquid Environments.

The propagation of the quasi-Lamb modes along a-SiC/ZnO thin composite plates was modeled and analysed with the aim to design a sensor able to detect the changes in parameters of a liquid environment, such as added mass and viscosity changes. The modes propagation was modeled by numerically solving the system of coupled electro-mechanical field equations in three media. The mode shape, the power flow, the phase velocity, and the electroacoustic coupling efficiency (K2) of the modes were calculated, specifically addressing the design of enhanced-coupling, microwave frequency sensors for applications in probing the solid/liquid interface. Three modes were identified that have predominant longitudinal polarization, high phase velocity, and quite good K2: the fundamental quasi symmetric mode (qS0) and two higher order quasi-longitudinal modes (qL1 and qL2) with a dominantly longitudinal displacement component in one plate side. The velocity and attenuation of these modes were calculated for different liquid viscosities and added mass, and the gravimetric and viscosity sensitivities of both the phase velocity and attenuation were theoretically calculated. The present study highlights the feasibility of the a-SiC/ZnO acoustic waveguides for the development of high-frequency, integrated-circuit compatible electroacoustic devices suitable for working in a liquid environment.

Quasi longitudinal Lamb acoustic modes along ZnO/Si/ZnO structures

A novel structure consisting of a Si plate sandwiched between two ZnO layers is suggested as propagation medium for Quasi Longitudinal (QL) acoustic Lamb waves. Considering a low-dispersive quasi-longitudinal mode as an example, the phase velocity v, electromechanical coupling constant k2 and mechanical displacements U1, U3 versus plate and ZnO layers thicknesses have been calculated starting from uncoated plate through the same plate with one layer to the plate with two layers onto opposite faces. A remarkable increase in the electromechanical coupling, together with an essential decrease in the vertical displacement U3, at the ZnO surface, have been theoretically demonstrated and experimentally verified for definite combinations of the films/plate thicknesses. This property of the structure is attractive for applications to microwave liquid sensors.

Plane wave propagation in transversely isotropic laser-excited solids

This paper concentrates on the study of body harmonic wave propagation in an anisotropic laser-excited solid in the context of the model based on coupled equations for the displacement and atomic defect concentration fields. The complex secular equations for transversely isotropic solids are derived and discussed. It is found, in general, four types of dispersive waves, namely a quasi-longitudinal (QL), two quasi-transverse (QT) and a quasi-defect wave (N-mode) can propagate in these types of crystals. The different characteristics of waves like phase velocity, attenuation coefficient are obtained and presented graphically. It is demonstrated that there is an appreciable variation in case of the QL mode as compared with QT and N-modes. Some particular cases have also been discussed.

Acoustic metamaterial behavior of three-dimensional periodic architectures assembled by robocasting

Ultrasonic measurements combined with numerical modelling are used to analyze the elastic and acoustic properties of morphologically complex ceramic bodies assembled by the Robocasting technique. It is shown that the micromechanics of the robocast periodic scaffolds leads to several metamaterial-like wave propagation phenomena. Besides the expectable prominent elastic anisotropy and the frequency band structure resulting from the periodicity of the scaffold, a wave-mode mixing is observed that disables the conventional distinguishing between quasi-longitudinal, quasi-shear, and pure shear modes for propagation in the symmetry planes of the structure. This paper proves the capability of Robocasting, as a versatile three-dimensional (3D) printing method, to produce tailored acoustic metamaterials with very low damping and outstandingly strong acoustic anomalies.

Quasi-Linear Polarized Modes in Y-Rotated Piezoelectric GaPO4 Plates

The propagation of both surface and flexural acoustic plate modes along y-rotated x-propagation GaPO4 piezoelectric substrates was studied for several y-cut angles: the phase velocity and coupling coefficient dispersion curves were theoretically calculated for two different electroacoustic coupling configurations. The investigation of the acoustic field profile across the plate thickness revealed the presence of thin plate modes having polarization predominantly oriented along the propagation direction, and hence suitable for operation in liquid environment. These modes include the linearly polarized Anisimkin Jr. and the quasi longitudinal plate modes, AMs and QLs, showing a phase velocity close to that of the longitudinal bulk acoustic wave propagating in the same direction. The temperature coefficient of delay (TCD) of these longitudinal modes was investigated in the −20 to 420 °C temperature range, in order to identify thermally stable or low TCD cuts. The power flow angle, i.e., the angle between the phase and group velocity vectors, was also estimated to evaluate the substrate anisotropy effect on the acoustic wave propagation. The GaPO4 intrinsic properties, such as its resistance to high temperature and its chemical inertness, make it especially attractive for the development of acoustic waves-based sensors for applications in harsh liquid environment.

High P–T Brillouin scattering study of H2O melting to 26 GPa

The properties of solid and liquid phases of H2O at high pressure and temperature remain an active area of research. In this study, Brillouin spectroscopy has been used to determine the temperature dependence of sound velocities in H2O as a function of pressure up to 26 GPa through the phase field of ice VII and into the liquid to a maximum temperature of 1200 K. The Brillouin shift of the quasi-longitudinal acoustic mode moves to lower frequencies upon melting at each pressure. As a test of the method, measurements of the melting of Ar by Brillouin scattering at several pressures show a similar behavior for the acoustic mode, and measured melting points are consistent with previous results. The results of H2O melting are consistent with previously reported melting curves below 20 GPa. The data at higher pressure indicate that ice melts at a higher temperature than a number of previous studies have indicated.

RELATIVISTIC PAIR BEAMS FROM TeV BLAZARS: A SOURCE OF REPROCESSED GeV EMISSION RATHER THAN INTERGALACTIC HEATING

The interaction of TeV photons from blazars with the extragalactic background light produces a relativistic beam of electron-positron pairs streaming through the intergalactic medium (IGM). The fate of the beam energy is uncertain. By means of two- and three-dimensional particle-in-cell simulations, we study the non-linear evolution of dilute ultra-relativistic pair beams propagating through the IGM. We explore a wide range of beam Lorentz factors gamma_b>>1 and beam-to-plasma density ratios alpha<<1, so that our results can be extrapolated to the extreme parameters of blazar-induced beams (gamma_b~10^6 and alpha~10^(-15), for the most powerful blazars). For cold beams, we show that the oblique instability governs the early stages of evolution, but its exponential growth terminates - due to self-heating of the beam in the transverse direction - when only a negligible fraction ~(alpha/gamma_b)^(1/3)~10^(-7) of the beam energy has been transferred to the IGM plasma. Further relaxation of the beam proceeds through quasi-longitudinal modes, until the momentum dispersion in the direction of propagation saturates at DeltaP_{b,parallel}/gamma_b m_e c ~ 0.2. This corresponds to a fraction ~10% of the beam energy being ultimately transferred to the IGM plasma, irrespective of gamma_b or alpha. If the initial dispersion in beam momentum satisfies DeltaP_{b,parallel}/gamma_b m_e c > 0.2 (as typically expected for blazar-induced beams), the fraction of beam energy deposited into the IGM is much smaller than ~10%. It follows that at least ~90% of the beam energy is still available to power the GeV emission produced by inverse Compton up-scattering of the Cosmic Microwave Background by the beam pairs.

Study of phonons in self-assembled InAs quantum dots embedded in an InGaAlAs matrix

We studied phonon modes propagating along the [311] direction in highly ordered, stacked InAs QDs embedded in an InGaAlAs matrix grown on InP(311) substrate by Raman spectroscopy. The Raman spectra showed clear doublets of folded quasi-longitudinal modes which have mixed transverse and longitudinal character. A broad feature observed in the Raman spectra was attributed to superposition of densely folded and/or confined phonon modes that is with agreement with our previous theoretical calculation. The phonon gap was observed and compared with our theoretical calculations.

Mode crossing effects at electron beam–plasma interaction and related phenomena

Mode crossing points are shown to play an important role in interpreting the spatio-temporal plasma wave spectra from satellite and laboratory measurements. Here, the Langmuir wave near the electron plasma frequency is considered and from linear dispersion curve analysis it may cross the whistler wave, the L-wave or the electron-acoustic mode depending on plasma conditions. An essential parameter is the electron cyclotron frequency to plasma frequency ratio, G = Ωe/ωe. The crossing point exists for wave propagation slightly oblique to a background magnetic field and we find that for a broad spectrum of waves excited by an instability, via an energetic beam or background plasma temperature anisotropy, the maximum amplitude of the wave activity appears at the crossing points which can be well separated from the region of maximum linear growth. Within this process the saturated waves act as an ‘antenna’ for other wave modes in the same wave number range. Linear and kinetic simulation analysis are used to demonstrate the frequency splitting at mode crossing points in two relevant examples; unmagnetized beam–plasma instability with Langmuir and electron-acoustic mode crossing in the presence of electron plateau distribution, and beam-excited Langmuir waves in overdense (G < 1) and underdense plasmas (G > 1) with background magnetic field. It is shown that the appearance of amplitude modulations associated with double-peak spectra of the electric field is directly related to the frequency splitting and coupling at mode crossing points. The importance of transitions between quasi-longitudinal wave modes at oblique propagation to transverse modes for the interpretation of beam–plasma interaction phenomena, such as type III radiation, and laboratory experiments is discussed.

The structure of acoustic modes in piezoelectric plates with free and metallized surfaces

By the example of 128°Y,X + 90°-LiNbO3 plates and quasi-longitudinal acoustic modes, the effect of one- and two-sided metallization of plates on the depth profiles of elastic displacements of modes is studied theoretically and experimentally. It is shown that, in the modes with the zero electromechanical coupling coefficient K2 = 0, the elastic displacement profiles for free and metallized plates are the same; while, in the modes with the nonzero coupling K2 ≠ 0, they are noticeably different and correspond to either attraction or repulsion of modes from the metallized surface. Correspondingly, the modes become more or less sensitive to surface loading.

Propagation of the Anisimkin Jr.' and quasi-longitudinal acoustic plate modes in low-symmetry crystals of arbitrary orientation

The Anisimkin Jr. (AN) acoustic plate mode having dominant and depth-independent longitudinal displacement (u(1) >> u(2), u(3); u(1) ≈ constant) is numerically found in tetragonal 4mm Li(2)B(4)O(7) crystal with one of the low-symmetry orientations (Euler angles 89°, 37°, 104°), as an example. The quasi-longitudinal (QL) modes with dominant and depth-dependent longitudinal displacement (u(1) >> u(2), u(3); u(1) ≠ constant) are experimentally detected along several propagation directions Θ in 128°y-LiNbO(3) plate, where Θ = 0°, 30°, 60°, and 90° with respect to the x-axis. Compared with more symmetrical plate materials and orientations, the displacement profiles of the AN and QL modes in lower-symmetry counterparts are qualitatively the same, but their phase profiles are more complicated. Moreover, like any acoustic wave, all plate modes in anisotropic crystals suffer from beam steering, in general. The power flow angles of the modes propagating in a fixed direction are different and depend on the mode order n.