Solitary surface acoustic waves and bulk solitons in nanosecond and picosecond laser ultrasonics

Recent achievements of nonlinear acoustics concerning the realization of solitons and solitary waves in crystals and their surfaces attained by nanosecond and picosecond laser ultrasonics are discussed and compared. The corresponding pump-probe setups are described, which allow an all-optical contact-free excitation and detection of short strain pulses in the broad frequency range between 10 MHz and about 300 GHz. The formation of solitons in the propagating longitudinal strain pulses is investigated for nonlinear media with intrinsic lattice-based dispersion. The excitation of solitary surface acoustic waves is realized by a geometric film-based dispersion effect. Future developments and potential applications of nonlinear nanosecond and picosecond ultrasonics are discussed.     

Principal surface wave velocities in the point focus acoustic materials signature V(z) of an anisotropic solid

This paper deals with the point focus beam (PFB) acoustic materials signature V(z) of an anisotropic solid, and in particular how it tends to be dominated by a limited number of principal surface rays. These rays are associated with propagation directions in which the Rayleigh wave (RW), pseudo-surface acoustic wave (PSAW) or a lateral wave slowness has an extremum. The phenomenon is interpreted in terms of the complex azimuthally averaged reflectance function of the surface, and also explained on the basis of a ray model. We illustrate the phenomenon with a number of examples, pertaining to the surfaces of single crystal copper and a carbon-fibre epoxy composite. In the case of copper, which has a much larger acoustic impedance than the water couplant, the oscillations in V(z) are dominated by principal RW and PSAW, whereas for the composite there is no RW or pseudo-SAW to be discerned with acoustic microscopy (AM), and V(z) is dominated by principal lateral waves. The utility of PFB AM in the study of anisotropic solids is further elaborated with examples showing how V(z) is sensitive to surface orientation, and how V(z) is affected by the presence of a surface over layer. The phenomena examined in this paper expand the scope for determining materials characteristics, such as elastic constants, crystallographic orientation, residual stress and over layer properties, from PFB V(z) measurements.     

Transmission and scattering properties of acoustic waves in phononic band gap materials

We have developed a formula for studying the transmission and scattering properties of finite-sized phononic band gap (PBG) material. We will show that based on the far field approach the transmission coefficients can be obtained by treating PBG samples as scattering objects. We find that the results agree well with the band structure.     

Imaging of surface acoustic waves

A new experimental method has been devised that directly determines the group velocities of surface acoustic waves. A point source and a point detector are employed to measure the ultrasonic transmission across a solid surface as a continuous function of the propagation direction. Results for single pulses give the times-of-flight for both Rayleigh surface waves (RSW's) and pseudo-surface-waves (PSW's). Calculations and measurements of the group velocities of the surface waves on silicon show some unanticipated behavior: fluid loading qualitiatively changes the group velocity curves for both RSW and PSW. In particular, the RSW branch gains an additional component which we denote here as an induced Rayleigh wave (IRW). If a wave train is employed in the experiment, the analog of phonon focusing is observed for the ultrasonic waves, modified by internal-diffraction effects. Systematic measurements of the wave intensities on silicon as a function of propagation distance are consistent with expected acoustic losses into the surrounding water: the attenuation length of a wave depends on the mode and frequency. A survey of surface-wave images on other crystals is included in this study.     

Detection of surface acoustic waves by scanning tunneling microscopy

A new method for the investigation of ultrasonic waves on surfaces of solids based on scanning tunneling microscopy is presented. A sinusoidal high frequency signal is added to the tip voltage. Hence the tunneling current contains a component whose frequency is the difference of the frequencies of the acoustic wave field and the ac tip voltage. Amplitude and phase of this component carry the full information about the wave field.     

Reflection and mode conversion of surface acoustic waves studied by scanning acoustic force microscopy

We present measurements of the reflection and mode conversion of surface acoustic waves (SAWs) by scanning acoustic force microscopy (SAFM). The SAFM offers a unique combination of high lateral resolution and high sensitivity towards acoustic modes of all polarizations. Since a SAW mixing experiment of two waves can be performed even if the amplitude difference between both waves is 40 dB, wavefields of extremely small amplitudes can be investigated. Using SAFM, the reflection of SAWs from a metallic wedge is investigated with submicron lateral resolution. We are able to identify two reflected wave modes, a Love and a non-coupling Rayleigh mode, by measuring their phase velocities. Received: 4 December 2000 / Accepted: 6 December 2000 / Published online: 9 February 2001     

A finite element model for laser-induced leaky waves at fluid–solid interfaces

The finite element method is firstly used to simulate the laser-induced leaky waves at fluid–solid interfaces. Corresponding models and arithmetic are developed, in that the fluid–solid interactions are described by a coupling matrix and the infinite boundary of fluid domain is modeled by acoustic absorption elements. Typical calculations are executed for air–aluminum plane and cylindrical interfaces. The results are in very good agreements with the experimental signals in available literatures, which verify the correctness of our finite element model for simulating laser-induced leaky wave at fluid–solid interfaces. And some elementary conclusions are obtained for the laser induced leaky waves.     

Ultrasonic resonator with electrical discharge cell for ozone generation

The effect of ultrasound waves in an ultrasonic resonator cell on ozone generation by a hollow needle to plate electrical discharge enhanced by the airflow through the needle is experimentally investigated. It was found that the application of ultrasound waves increases ozone generation for discharge when the needle is negatively biased, and has no effect on ozone generation for the discharge when the needle is biased positively. We try to explain the influence of ultrasound on the discharge mechanisms.     

Numerical Calculation of SAW Propagation Properties at the x-Cut of Ferroelectric PMN-33%PT Single Crystals

Surface acoustic wave （SAW） properties at the x-cut of relaxor-based 0.67Pb（Mg1/3Nb2/3）O3-0.33PbTiO3 （PMN- 33%PT） ferroelectric single crystals are analyzed theoretically when poled along the [001]c cubic direction. It can be found that PMN-33%PT single crystal is a kind of material with a low phase velocity and high electromechanical coupling coefficient, and the single crystal possesses some cuts with zero power flow angle. The results are based on the material parameters at room temperature. The conclusions provide device designers with a few ideal cuts of PMN-33%PT single crystals. Moreover, choosing an optimal cut will dramatically improve the performance of SAW devices, and corresponding results for crystal systems working at other temperatures could also be figured out by employing the method.     

Hysteresis in response of nonlinear bistable interface to continuously varying acoustic loading

In many experimental situations it is an equation of the forced relaxator and not of the forced oscillator that describes a variation in the acoustic field of the interface width (i.e. of a characteristic distance between the surfaces composing the interface). The developed theory predicts that some types of the nonlinear relaxators (depending on the structure of the nonlinear interaction force between the surfaces) exhibit hysteresis in their response to continuous acoustic loading of first increasing and then decreasing amplitude. Nonlinear (unharmonic) variation of the interface width starts at threshold amplitude of the incident sinusoidal acoustic wave, which is higher than threshold amplitude for returning to sinusoidal motion. This dynamic hysteresis (and accompanying it bistability) are possible, in particular, if the dependence of the effective interaction force on the interface width admits two quasi-equilibrium positions of the interface (bistable interface) or if the force itself is hysteretic (hysteretic interface). These theoretical predictions are relevant to some recent experimental observations on the interaction of powerful ultrasonic fields with cracks.     

Ion acoustic shock waves in a relativistic electron-positron-ion plasmas

The Korteweg-de Vries-Burger (KdVB) equation is derived for ion acoustic shock waves in a weakly relativistic electron-positron-ion plasma. Electrons, positrons are considered isothermal and ions are relativistic. The travelling wave solution has been acquired by employing the tangent hyperbolic method. The vivid display of the graphical results is presented and analyzed. It is observed that amplitude and steepness of the shock wave decrease with increase of the relativistic streaming factor, the positron concentration and they increase with the increase of the coefficient of kinematic viscosity and vice versa. It is determined that at low temperature the shock wave propagates, whereas at very high temperature the solitary wave propagates in the system. The results may have relevance in astrophysical plasmas as well as in inertial confinement fusion plasmas.     

Young’s modulus and density of nanocrystalline cubic boron nitride films determined by dispersion of surface acoustic waves

Cubic boron nitride (c-BN) films of 200–420 nm thickness and high phase purity were deposited on silicon (100) substrates by ion-assisted pulsed laser deposition (IA PLD)from a boron nitride target using a KrF-excimer laser, and by plasma-enhanced physical vapor deposition (PE PVD)with a hollow-cathode arc evaporation device. In order to improve the c-BNfilm adhesion, hexagonal boron nitride (h-BN) films with 25–50 nm thickness were used as buffer layers. The density and Young’s modulus of the c-BNfilms were obtained by investigating the dispersion of surface acoustic waves. In data analysis a two-layer model was applied in order to take the influence of the h-BNlayer into consideration. The values for the density vary from 2.95±0.25 g/cm³to 3.35±0.3 g/cm³, and those for the Young’s modulus from 420±40 GPa to 505±30 GPa. The results are compared with literature values reported for nanocrystalline films, polycrystalline disks and single crystal c-BN. Received: 26 March 2001 / Accepted: 29 March 2001 / Published online: 25 July 2001     

Thickness Determination for a Two-Layered Composite of a Film and a Plate by Low-Frequency Ultrasound

We present an ultrasonic method for determining the thickness of a composite consisting of a soft thin film attached to a hard plate substrate, by resonance spectra in the low frequency region, The interrogating waves can be incident only to the two-layered composite from the substrate side. The reflection spectra are obtained by FFT analysis of the compressive pulsed echoes from the composite, and the thicknesses of the film and the substrate are simultaneously inversed by the simulated annealing method from the resonant frequencies knowing other acoustical parameters in prior. The sensitivity of the method to individual thickness, its convergence and stability against experimental noises are studied, Experiment with interrogating wavelength 4 times larger than the film thickness in a sample of a polymer film （0.054mm） on an aluminium plate （6.24mm） verifies the validity of the method. The average relative errors in the measurement of the thicknesses of the film and the substrate are found to be -4.1% and -0.62%, respectively.     

Picosecond X-ray diffraction studies of laser-excited acoustic phonons in InSb

We have employed time-resolved X-ray diffraction with picosecond temporal resolution to measure the time-dependent rocking curves of laser-irradiated asymmetrically cut single InSb crystals. Coherent acoustic phonons were excited in the crystals by irradiation with 800-nm, 100-fs laser pulses at irradiances between 0.25 and 12 mJ/cm². The induced time-dependent strain profiles (corresponding to the coherent phonons) were monitored by diffracting collimated, monochromatic pulses of X-rays from the irradiated crystals. Recording of the diffracted radiation with a fast low-jitter X-ray streak camera resulted in an overall temporal resolution of better than 2 ps. The strain associated with the coherent phonons modifies the rocking curve of the crystal in a time-dependent manner, and the rocking curve is recorded by keeping the angle of incidence of the X-rays upon the crystal fixed, but varying the energy of the incident X-rays around a central energy of 8.453 keV (corresponding to the peak of the rocking curve of the unperturbed crystal). The observed time-dependent diffraction from the irradiated crystals is in reasonable agreement with simulations over a wide range of energies from the unperturbed rocking-curve peak. Received: 22 March 2002 / Revised version: 25 March 2002 / Published online: 6 June 2002     

Perturbation Analysis on Guided Waves in a Fluid-Filled Borehole Surrounded by a Cubic Crystal Anisotropic Medium

The perturbation method is employed to analyse the guided waves in a borehole surrounded by a cubic crystal medium for the first time. The cubic crystal medium is regarded as a reference unperturbed isotropic state added to the perturbation. The dispersion characteristics of Stoneley wave, pseudo-Rayleigh wave, flexural wave, and screw wave are investigated in detail. It is found that dispersion of the guided waves excited by monopole and dipole sources does not depend on the azimuth of the source, whereas the dispersion of screw wave excited by quadrupole source is significantly related to the azimuth of the source. Screw waves propagated along different azimuth in the borehole can be split. This is different from screw waves in transversely isotropic media （hexagonal crystal）, which have been widely studied.     

Guided Waves in a Multi-Layered Cylindrical Elastic Solid Medium

We investigate the guided waves in a multi-layered cylindrical elastic solid medium. The dispersion function of guided waves is usually complex and the dispersion curves of all modes are not conveniently obtained. Here we present an effective method to obtain the dispersion curves of all modes. First, the dispersion function of the guided waves is transformed into a real function. The dispersion curves are then calculated for all the modes of the guided waves by the bisection method. The modes with the orders n = 0, 1, and 2 are analysed in two- and three-layer media. The existence condition of Stoneley wave is discussed. The modes of the guided waves are also investigated in a two-layer medium, in which the velocity of shear wave in the outer layer is less than that in the inner layer.     

Determination of Thickness of an Inaccessible Thin Film under a Multilayered System from Natural Frequencies

We investigate the relationship between natural frequencies of a multilayered system of different elastic materials and the thickness of the undermost thin film. The natural frequencies are numerically calculated from the reflection coefficient of a sample system of ＂steel-epoxy resin-aluminium-thin polymer＂ with normal incidence. Strain energy ratio is defined and calculated to give the physics explanation why some frequencies are sensitive to thickness of the thin film in certain range. Experiments of three specimens indicate that the measured natural frequencies agree well with the theoretical ones. It is found in our experiments that the ratio of the lowest film thickness to wavelength is about 1/5. The average relative errors for the inverted polymer film thicknesses are found to be 11.8%, -4.8% and -1.3%, respectively.     

Symmetric and Anti-Symmetric Lamb Waves in a Two-Dimensional Phononic Crystal Plate

It is weft known that Lamb waves in a plate with a mirror plane can be separated into two uncoupled sets： symmetric and anti-symmetric modes. Based on this property, we present a revised plane wave expansion method （PWE） to calculate the band structure of a phononie crystal （PC） plate with a mirror plane. The developed PWE method can be used to calculate the band structure of symmetric and anti-symmetric modes separately, by which the depending relationship between the partial acoustic band gap （PABG）, which belongs to the symmetric and anti-symmetric modes alternatively, and the position of the scatterers can be determined. As an example of its application, the band structure of the Lamb modes in a two-dimensional PC plate with two layers of void circular inclusions is investigated. The results show that the band structure for the symmetric and anti-symmetric modes can be changed by the position of the scatterers drastically, and larger PABGs will be opened when the scatterers are inserted into the area of the plate, where the elastic potential energy is concentrated.     

Flat superlens by using negative refraction in two-dimensional phononic crystals

We experimentally and theoretically demonstrated a flat superlens by negative refraction imaging for acoustic waves in a two-dimensional phononic crystal. The sample consists of a square array of steel cylinders immersed in water. The dispersion surfaces at the first band for this sample are nearly circular around point M in the first Brillouin zone, which makes the index of the negative refraction for the phononic crystal sample be well defined for all angles of incidence. Both the observed negative refraction behavior and imaging effect are in excellent agreement with numerical simulations by the Multiple Scattering Theory method.     

Laser Generation of Surface Waves on Cylinder with a Slow Coating

An analytical model of acoustic field excited by a pulsed-laser line source on a coated cylinder is presented. Surface wave dispersive behaviours for a cylinder with a slow coating are analysed and compared with that of a bare cylinder. Based on this analysis, the laser-generated transient response of the perturbed Rayleigh wave and the higher modes of steel cylinder with a zinc coating are calculated from the model using residue theory and FFT technique. The theoretical result from the superposed waveform of the perturbed Rayleigh wave and higher modes agree well with the waveform obtained in experiment. The results show that the model and numerical method provide a useful technique for quantitatively characterizing coating parameters of coated cylinder by the laser generated surface waves.