Pseudo-surface Waves Research Articles

Propagation of surface waves and surface resonances along cylindrical cavities in materials with any allowed Poisson's ratio – Part II: Thin‐walled coating

Propagation of infinitely‐lived true surface waves (TSW) and of the evanescent surface resonances (pseudo surface waves, PSW) on the inner surface of a cylindrical cavity in an elastic medium coated with a thin elastic membrane is studied. An analogous flat surface with the same coating is considered as a reference system. The dispersion relations of the true surface waves and of the surface resonances are shown to depend on the interplay between the sound speeds in the substrate and in the covering layer. The short‐wavelength limit of the excitations in the cavity is checked to be consistent with the case of the flat surface. Analytical expressions are obtained for the cut‐offs and for the asymptotic behaviors of the excitations in the long‐wavelength and short wavelength limits. The local surface densities of states (LDOS) as well as the real parts of the Green's functions, i.e., analogues of the reactive power, are calculated. The most eminent anomalies of LDOS, which correspond to the longitudinal resonance, are shown to be located close to the apparently spurious roots of the secular determinant of the surface equations of motion. The roots correspond generally to the total conversion of the longitudinal to transverse bulk waves. These roots show cut‐offs, where the life time of the longitudinal resonance increases to infinity. For still lower wave vectors the maxima of LDOS follow the lines of total conversion transverse‐to‐longitudinal with finite life‐times. The radius dependence of the cut‐off wave vector in the small‐radius limit for a fully symmetric torsional mode is and for a fully symmetric high‐frequency axial–radial TSW follows a 1/a behavior, whereas the analogous dependence for a quasi‐Rayleigh surface wave is proportional to except for a certain range of parameters, where the high‐frequency TSW does not exist.

Room temperature elastic properties of Rh-based alloys studied by surface Brillouin scattering

Platinum metal group alloys are promising materials for use in a new generation of gas turbine engines owing to their excellent high-temperature properties. In the present work, room temperature elastic properties of single crystals of Rh3Nb and Rh3Zr are investigated. Surface Brillouin scattering spectra for a range of wave vector directions on the (001) surface have been acquired in order to determine the angular variation of the velocities of the Rayleigh and pseudo-surface acoustic waves and that of the longitudinal lateral wave (LLW) threshold within the Lamb shoulder. The elastic stiffness constants C11, C12, and C44 of these cubic crystal specimens have been derived using two approaches: the first involving the least-squares fit of the combined measured wave velocity data to calculated values and the second an analytical approach using the Rayleigh velocities in the [100] and [110] directions and LLW velocity in the [100] direction, and extracting the elastic stiffness constants from the secular equations for these velocities. Results from the two methods are in good agreement and are for Rh3Nb, C11 = 368 ± 3, C12 = 186 ± 5, and C44 = 161 ± 3 in GPa; and for Rh3Zr, C11 = 329 ± 4, C12 = 185 ± 6, and C44 = 145 ± 4 in GPa.

Nonexistence of pureS- andP-polarized surface waves at the interface between a perfect dielectric and a real metal

It is known that, at optical frequencies, a simple interface between a perfect dielectric and a real metal can sustain the propagation of surface plasmon polaritons only for P-polarized electromagnetic waves, being S-polarized surface plasmons are prohibited. In this work, we formally show that, strictly speaking, both polarization states are in fact prohibited and that only P-polarized pseudosurface waves are allowed, which is what is encountered in the applications. The existence of such pseudosurface modes allows one to reconcile theory and experimental evidence, but also sets limits for them to be considered as modes bound to the interface.

WAVE REFLECTION IN PIEZOELECTRIC HALF-PLANE

The assumption of quasi-static electric field in the problem of wave reflection in piezoelectric half-plane results in missing an independent electric wave mode at the piezoelectric boundary, which leads to oversimplified solutions of reflected waves in a strong piezoelectric medium if only elastic bulk wave boundary conditions are considered. The paper presents a novel solution to address the issue by using the inhomogeneous wave theory and introducing a virtual reflection wave mode in addition to the elastic bulk wave modes. The virtual wave is assumed to satisfy the Snell's law as well as the piezoelectric boundary condition and can be treated in the same way as the elastic bulk waves. The analysis results show that this virtual wave always propagates along the boundary for any incident angle and can be treated as a pseudo surface wave. The energy transmission analysis reveals that this surface wave transmits zero energy and does not violate the energy conservation between the incident and the reflected elastic bulk waves. In addition, the analysis also reveals an interesting result that the quasi-transverse, not the quasi-longitudinal, incident wave will be fully reflected and no quasi-longitudinal reflected wave will be generated if the incident angle is beyond a critical angle.

X-ray diffraction study of surface acoustic waves and pseudo-surface acoustic waves propagation in La3Ga5.5Ta0.5O14 crystal

X-ray diffraction on the crystal La3Ga5.5Ta0.5O14 modulated by surface acoustic waves (SAW) and pseudo-surface acoustic waves (PSAW) with wavelength of Λ=8 μm was studied using a double axis X-ray diffractometer at the BESSY II synchrotron radiation source. The propagation of SAW and PSAW leads to sinusoidal modulation of the crystal lattice and gives rise to diffraction satellites on the rocking curve, with the intensity and angular divergence between the diffraction satellites depending on the wavelength and amplitude of the crystal lattice acoustic modulation. The analysis of diffraction spectra enables the determination of the amplitude and acoustic wavelengths, and power flow angles of acoustic energy propagation. The investigation of acoustic wave fields showed that PSAW is a flowing back wave which propagates at an angle to the crystal surface.

Surface and pseudo-surface acoustic waves piezoelectrically excited in diamond-based structures

Surface and pseudo-surface acoustic plane waves generated in two- and three-layer AlN/Diamond and AlN/Diamond/γ-TiAl structures by a point electric source are analyzed in the mathematical framework based on the Green's matrix integral representation and guided wave asymptotics derived using the residue technique. The attention is focused on the effect of pseudo-surface-to-surface wave degeneration at certain discrete values of h/λ (h is the thickness of the piezoelectric layer and λ is the wave-length). Earlier such optimal ratios were discovered and experimentally verified for the first pseudo-surface (Sezawa) wave mode in the AlN/Diamond structure. The present research reveals this effect for higher modes as well as examines its manifestation for three-layer structures with different diamond-to-AlN thickness ratios H/h.

Reflection and refraction of plane waves at interface between two piezoelectric media

This paper analyses reflection and refraction of plane waves at a perfect interface between two anisotropic piezoelectric media. The equations of elastic waves, quasi-static electric field, and constitutive relationships for the piezoelectric media are derived. A solution based on the inhomogeneous wave theory is developed to address the inconsistency between the numbers of independent wave modes in the media and the numbers of interfacial boundary conditions to obtain accurate reflection and refraction coefficients in case of strong piezoelectric media, where all the elastic and electric continuity conditions across the interface are satisfied simultaneously. The study shows that there exist independent and zero energy wave modes satisfying the general Snell’s law and propagating along the interface for any incident wave angle. These waves can be treated as pseudo surface waves. It is further found that all the reflection/refraction waves including the pseudo surface waves obey the energy conservation law at the interface boundary. In addition, the analysis also reveals that the reflection and refraction elastic waves can turn into pseudo surface waves at some critical incident angles.

Surface acoustic waves and elastic constants of Cu14%Al4%Ni shape memory alloys studied by Brillouin light scattering

A single crystal Cu14%Al4%Ni shape memory alloy in austenitic phase was studied by Brillouin spectroscopy to analyse angular dispersion of Rayleigh surface waves in the planes (0 0 1) and (1 1 0). Measurements were made at room temperature using a tandem-type Fabry–Perot interferometer (JRS Scientific Instruments). Experimental results permitted determination of three independent elastic constants and anisotropic Young's modulus. In the (1 1 0) plane the pseudo-surface waves were found to occur, which—in the context of the past literature data—is unusual for cubic crystals of anisotropy coefficient higher than one. The elastic tensor components determined were used for simulation of surface phonons by the finite element method. The surface phonon velocities obtained were compared with the experimental results and the results of calculations based on the available analytical expressions for the phonon velocities for high-symmetry directions. Particular attention was paid to the relation between the elastic constants (anisotropy coefficient) and the depth of surface phonon penetration.

Surface and bulk polaritons in a PML-type magnetoelectric multiferroic with canted spins:TE and TM polarization

We present a theory for surface polaritons on ferroelectric–antiferromagnetic materials withcanted spin structure. A small uniform canted moment is allowed, resulting in a weakferromagnetism directed in the plane parallel to the surface. Surface and bulk polariton modesfor a semi-infinite film are calculated for the case of transverse electric (TE) and transversemagnetic (TM) polarization. Example results are presented using parameters appropriate forBaMnF4. We find that the surface modes are non-reciprocal for the TE polarization due to themagnetoelectric interaction, and the non-reciprocity can be controlled by an appliedelectric field. Example results for attenuated total reflection (ATR) are calculated. Themagnetoelectric interaction also gives rise to ‘leaky’ surface modes in the case of TMpolarization. These are pseudo-surface waves that exist in the pass band, and dissipateenergy into the bulk of the material. We show that these pseudo-surface mode frequenciesand properties can be modified by temperature and the application of external electric ormagnetic fields.

Isolated True Surface Wave in a Radiative Band on a Surface of a Stressed Auxetic

We demonstrate that a surface resonance (pseudosurface wave) may transform into a true surface wave, i.e., acquire an infinite lifetime, at a single isolated point within a bulk band (radiative region) in a model of a stressed auxetic material. In contrast with the secluded supersonic elastic surface waves, the one found here does not belong to a dispersion line of true surface waves. Therefore we propose to call it an isolated true surface wave (ITSW). The ITSW manifests itself by a deltalike peak in the local density of states and by anomalies in reflection coefficients. The phenomenon may be useful in redirecting energy and/or information from the bulk to the surface in devices supporting guided acoustic waves.

Ultrafast Laser Pulses to Detect and Generate Fast Thermomechanical Transients in Matter

The use of femtosecond laser pulses to impulsively excite thermal and mechanical transients in matter has led, in the last years, to the development of picosecond acoustics. Recently, the pump-probe approach has been applied to nano-engineered materials to optically generate and detect acoustic waves in the gigahertz-terahertz frequency range. In this paper, we review the latest advances on ultrafast generation and detection of thermal gradients and pseudo-surface acoustic waves in 2-D lattices of metallic nanostructures. Comparing the experimental findings to the numeric analysis of the full thermomechanical problem, these materials emerge as model systems to investigate both the mechanical and thermal energy transfer at the nanoscale. The sensitivity of the technique to the nanostructure mass and shape variations, coupled with the phononic crystal properties of the lattices, opens the way to a variety of applications ranging from hypersonic waveguiding to mass sensors with femtosecond time resolution.

An enhanced algorithm for evaluation of surface waves

A procedure based on the Stroh formalism is presented that yields the approximation for the planar harmonic Green's matrix function for piezoelectric half-space that is valid in the vicinity of the surface, or pseudosurface, wave number. This approximation can be directly exploited in the spectral-theoretical analysis of surface acoustic wave devices. Otherwise, the known characterization of the surface wave supporting substrate can be immediately inferred from it, like the wave velocity, piezoelectric coupling coefficient, the wave damping in the case of leaky pseudosurface waves, and the corresponding surface displacement velocities.

The study of guided waves in surfaces and thin supported films using surface Brillouin scattering and acoustic microscopy

This paper reviews the use of surface Brillouin scattering (SBS) and acoustic microscopy (AM) in studying the surface dynamics of solids in order to obtain information about the near-surface elastic properties of solids and thin supported films. The vibrational modes that are probed by these means include Rayleigh surface and pseudo-surface acoustic waves, longitudinal lateral waves (surface skimming bulk longitudinal waves) and various thin film guided modes, such as Sezawa and Love waves. SBS is the inelastic scattering of light, mediated by thermodynamic fluctuations in the surface elevation and near surface elastic strains. The scattering cross-section is conveniently expressed in terms of Fourier domain elastodynamic Green’s functions. AM depends on the insonification of a surface through a coupling fluid, and the resulting excitation and subsequent decay of the various surface modes. The complex reflectivity of the fluid-loaded surface, and the line and point force surface Green’s functions are invoked in the interpretation of different modalities of AM, yielding much the same information about the surface dynamics. The focus in this paper is on the Green’s function approach. A number of illustrative examples, drawn from the authors’ research, are provided.

Triclinic elastic constants for low albite

The full set of elastic constants for plagioclase end-member phase albite (NaAlSi3O8) is reported for the first time. Velocities of surface acoustic waves (both Rayleigh and pseudo-surface waves) were measured using impulsively stimulated light scattering on polished surfaces having six different orientations (three normal to the Cartesian axes and three lying on diagonals). Data were inverted and results tested using several non-linear optimization techniques. Compliance moduli determined under hydrostatic compression provided additional constraints and reduced covariance in the reported constants. The Cartesian coordinate system associated with the constants (using the $$ {\text{C}}\ifmmode\expandafter\bar\else\expandafter\=\fi{1} $$ unit cell) has the y-axis parallel to the crystal b axis, the x-axis parallel to a* (perpendicular to b and c) and the z-axis consistent with a right-handed coordinate system. The values of the moduli C11, C12, C13, C14, C15, C16, C22, C23, C24, C25, C26, C33, C34, C35, C36, C44, C45, C46, C55, C56, C66 and their 2σ uncertainties (in parentheses) are, respectively, 69.1(0.6), 34.0(0.7), 30.8(0.5), 5.1(0.1), −2.4(0.1), −0.9(0.1), 183.5(2.7), 5.5(2.2), −3.9(0.5), −7.7(0.7), −5.8(0.7), 179.5(2.3), −8.7(0.4), 7.1(0.6), −9.8(0.6), 24.9(0.1), −2.4(0.1), −7.2(0.1), 26.8 (0.2), 0.5(0.1), 33.5(0.2). These constants differ significantly from the previously reported pseudo-monoclinic constants that were based on velocity measurements on polysynthetic twinned crystal aggregates. Differences are consistent with systematic errors in the earlier study associated with sparse data and the presence of cracks and other imperfections.

Surface Wave Propagation in Thin Silver and Aluminium Films

Three kinds of acoustic waves are known: bulk waves, pseudo-surface waves and surface waves. A plane wave section of a constant-frequency surface of a film serves as a hint for the expected nature. Calculations based on slowness curves of films reveal frequency ranges where each type of acoustic waves is predominant. Dispersion curves and displacement acoustic waves are calculated and commented in each frequency interval for different coated materials. Both dispersion and sagittal elliptical displacement are sensitive and depend on diagrams mentioned above. Silver and aluminium thin films having different anisotropy ratios, namely 2.91 and 1.21, are retained for illustration.

Surface wave propagation in an ideal Hall-magnetohydrodynamic plasma jet in flowing environment

The behavior of the Hall-magnetohydrodynamic (Hall-MHD) sausage and kink waves is studied in the presence of steady flow. The influence of the flow both inside and outside the plasma slab is taken into account. The plasma in the environment is considered to be cold and moves with the different flow velocity outside the slab. In the limit of parallel propagation, dispersion relation is derived to discuss the propagation of both the modes. Numerical results for the propagation characteristics are obtained for different Alfvénic Mach number ratios inside and outside the slab. It is found that the dispersion curves for both surface modes, namely, the sausage and kink ones in cold plasma show complexities in their behavior in terms of multivalued portions of the curves. These multivalued portions correspond to the different normalized phase velocities for the same value of Alfvénic Mach number. In contrast to the conventional MHD surface waves which are assumed to be pure surface waves or pseudosurface waves, surface waves are obtained which are bulk waves for very small dimensionless wave numbers, then turn to leaky waves and finally transform to pure surface waves for values of dimensionless wave number greater than one.

A Brillouin scattering study of La0.77Ca0.23MnO3 across the metal–insulator transition

Temperature-dependent Brillouin scattering studies have been carried out onLa0.77Ca0.23MnO3 across the paramagnetic insulator–ferromagnetic metal (I–M) transition ( K). The spectra show modes corresponding to a surface Rayleigh wave(SRW) and a high velocity pseudo-surface wave (HVPSAW) along with bulkacoustic waves (B1 and B2). The Brillouin shifts associated with the SRWand HVPSAW increase, whereas the B1 and B2 frequencies decrease, belowTC.The temperature dependence of the SRW and HVPSAW modes is related to the increase in the elasticconstant C11 across the I–M transition. The decrease in frequency across the I–M transition of the bulkmodes is understood to be due to enhanced self-energy corrections as a result of increasedmagnon–phonon interaction across the I–M transition. Correspondingly, thesemodes show a large increase in the full width at half maximum (FWHM) as thetemperature decreases. We also observe a central peak whose width is maximum atTC.

Rapid and accurate analysis of surface and pseudo-surface waves using adaptive laser ultrasound techniques

A method has been developed to measure the phase velocity of laser generated and detected surface acoustic waves. An optical grating produced by an electronically addressable spatial light modulator (SLM) was imaged onto the sample surface to generate surface acoustic waves whose frequency and wavefront was controlled by the SLM. When the grating period matched the surface acoustic wavelength, the surface wave was strongly excited, thus the wavelength and, thereby the phase velocity was determined. We present results with this method that allows the phase velocity and the angular dispersion of the generalized surface wave as well as the pseudo-surface wave on the (1 0 0) nickel to be measured. Measurements on (1 1 1) silicon single crystals are also presented. The measurement precision is approximately 0.2%. Methods to further improve the measurement precision are also discussed.

Hall-magnetohydrodynamic surface waves in solar wind flow-structures

This paper investigates the parallel propagation of agnetohydrodynamic (MHD) surface waves travelling along an ideal steady plasma slab surrounded by a steady plasma environment in the framework of Hall magnetohydrodynamics. The magnitudes of the ambient magnetic field, plasma density and flow velocity inside and outside the slab are different. Two possible directions of the relative flow velocity (in a frame of reference co-moving with the ambient flow) have been studied. In contrast to the conventional MHD surface waves which are usually assumed to be pure surface or pseudo-surface waves, the Hall-MHD approach makes it necessary to treat the normal MHD slab's modes as generalized surface waves. The latter have to be considered as a superposition of two partial waves, one of which is a pure/pseudo-surface-wave whereas the other constitutive wave is a leaky one. From the two kinds of surface-wave modes that can propagate, notably sausage and kink ones, the dispersion behaviour of the kink mode turns out to be more complicated than that of the sausage mode. In general, the flow increases the waves' phase velocities comparing with their magnitudes in a static Hall-MHD plasma slab. The applicability of the results to real solar wind flow-structures is briefly discussed.

Rapid measurement of surface acoustic wave velocity on single crystals using an all-optical adaptive scanning acoustic microscope

An experimental method has been developed to measure the phase velocity of laser-generated and detected surface acoustic waves. An optical grating produced by a spatial light modulator was imaged onto the sample surface to generate the ultrasound whose frequency and wave front were controlled electrically by tailoring the grating. When the grating period matched the surface acoustic wavelength, strong excition of the surface wave was observed. Thus, the wavelength and, thereby, the phase velocity were determined. We present results with this method that allow the phase velocity and the angular dispersion of the generalized surface wave as well as the pseudosurface wave on the (100) nickel and (111) silicon single crystals to be measured, with the precision of approximately 0.2%. Those factors affecting the measurement precision are discussed.