Changes In Phase Velocity Research Articles

Understanding wave characteristics via linear superposition of retarded fields

The Feynman–Schwartz method of linearly superposing retarded fields to understand the origin of the refractive index is generalized to an obliquely incident electromagnetic wave interacting with a planar medium. Different integral equations for the wave field in the medium are obtained for the TE-state and the TM-state of wave polarization. The two states of polarization are shown to satisfy the same differential equation for the spatial variation of the fields and thus they have the same dispersion relation (or the index of refraction) and change of phase velocity upon penetration into the medium. The integral equations are also used to deduce the well-known reflection and transmission coefficients in various cases.

Microstructural and Electrical Characterization of Barium Strontium Titanatebased Solid Solution Thin Films Deposited on Ceramic Substrates by Pulsed Laser Deposition

AbstractFerroelectrics are multicomponent materials with a wealth of interesting and useful properties, such as piezoelectricity. The dielectric constant of the BSTO ferroelectrics can be changed by applying an electric field. Variable dielectric constant results in a change in phase velocity in the device allowing it to be tuned in real time for a particular application. The microstructure of the film influences the electronic properties which in turn influences the performance of the film. Ba0.6Sr0.4Ti1-y(A 3+, B5+)yO3 thin films, of nominal thickness of 0.65 μm, were synthesized initially at substrate temperatures of 400°C, and subsequently annealed to 750°C, on LaAlO3 (100) substrates, previously coated with LaSrCoO conductive buffer layer, using the pulsed laser deposition technique. The microstructural and physical characteristics of the postannealed thin films have been studied using x-ray diffraction, scanning electron microscopy, and nano indentation and are reported. Results of capacitance measurements are used to obtain dielectric constant and tunability in the paraelectric (T>Tc) regime.

Group velocity of solitons

It is shown that, in addition to the well-known phase accumulation of a traveling soliton, which may be interpreted as a change of phase velocity as a result of the Kerr nonlinearity, there is a change in the speed of travel of the envelope, the group velocity. This analysis is extended to dispersion-managed solitons, for which it is shown that the discrepancy between phase- and group-velocity changes is generally smaller.

Viscosity Measurement of Nematic Liquid Crystal Using Shear Horizontal Wave Propagation in Liquid Crystal Cell

Propagation characteristics of a shear horizontal (SH) wave in a cell structure containing a nematic liquid crystal layer are described on the basis of numerical analysis and experimental results. The SH wave propagation is described by the numerical analysis result for the nematic liquid crystal as an anisotropic liquid, considering the director angle of the liquid crystal. The temperature dependence of effective viscosities of a typical nematic liquid crystal N-(p-methoxybenzylidene)-p'butylaniline)] (MBBA) is evaluated from the measurement of the phase velocity change of the SH wave in the liquid crystal cell.

Measurement of the anomalous phase velocity of ballistic light in a random medium by use of a novel interferometer

Ballistic light, i.e., radiation that propagates undeflected through a turbid medium, undergoes a small change in phase velocity and exhibits unusual dispersion because of its wave nature. We use a novel highly sensitive differential phase optical interferometer to study these previously unmeasurable phenomena. We find that ballistic propagation can be classified into three regimes based on the wavelength-to-size ratio. In the regime in which the scatterer size is comparable with the wavelength, there is an anomalous phase-velocity increase as a result of adding scatterers of higher refractive index. We also observe an anomaly in the relative phase velocity, where red light is slowed more than blue light even though the added scatterers are made of material with normal dispersion.

Surface Acoustoelectric Waves in a Piezoelectric–High-Temperature Granular Superconductor Layered Structure

Interactions of surface acoustoelectric waves with a granular high-temperature superconducting medium are studied. Dispersion equations describing the characteristics of surface acoustoelectric waves are derived for piezoelectrics of 4 and 6mm and 3m symmetry. It is shown that at a temperature above the critical point an attenuation jump and a sudden change in the phase velocity of surface acoustoelectric waves are observed. This effect increases with increase in the electromechanical coupling coefficient and decrease in the thickness of the high-temperature superconducting film. The results obtained can be used in designing frequency selectors and transient photodetectors.

Ultrasonic Monitoring of Material Degradation in FRP Composites

This research uses laser ultrasonic techniques to monitor a (directly measurable) ultrasonic property—frequency-dependent Rayleigh wave velocity (material dispersion)—and then relates changes in this acoustic property to changes in the material's properties (such as stiffness) that characterize damage. The subject material system is a thick, glass-reinforced, vinylester (thermosetting) fiber-reinforced polymer (FRP) composite. Laser ultrasonics is an ideal methodology to monitor changes in the Rayleigh phase (or group) velocity of this material because of its high fidelity, broad bandwidth, point source/receiver, and noncontact nature. The experimental procedure consists of measuring a series of transient elastic waveforms in a thick FRP specimen and then operating on these waveforms with the 2D fast Fourier transform to develop the dispersion relationship for that specimen. Material degradation (damage) is introduced into these specimens with environmental aging, and the dispersion curves are used to quantitatively track changes in material properties as a function of degradation.

Phase Sensitive Pump-Probe Spectroscopy Using a Michelson-Type Interferometer

Time-resolved phase sensitive pump-probe spectroscopy using a Michelson-type interferometer has been carried out. In this experiment, we obtain information on the time-resolved amplitude and phase of probe pulses by measuring cross-correlations between probe pulses and reference pulses. This method was demonstrated in an experiment on dye molecules, hexamethylindotricarbocyanine iodide, in ethylene glycol at room temperature. The experimental results indicated the time evolution of the phase and the increase in peak velocity of the probe pulse. These phenomena can be explained by phase velocity change and group velocity change due to the pump pulse. A simulation based on a two-level Bloch model for the dye molecules reproduced the experimental results quite well.

Changes of the acoustic modal phase velocity, group velocity, and interference distance in an eddy

In this paper, by using the modal dispersion equation with the phase-integral approximation, and considering an eddy (or water mass) as a sound channel disturbance, the effects of the undisturbed channel, cold-core eddy, and warm-core eddy on the acoustic propagation characteristics are discussed. According to the solutions of the dispersion equation, the relation is obtained between the modal phase velocity (Cn), group velocity (Un), and interference distance (Ln), and the eddy intensity. When the plane wave (with an incident angle α) travels toward the center of a warm-core eddy (disturbed intensity BM), ‘‘double channel phenomenon’’ will take place in case of sin2<th>α<BM<2(1−cos<th>α), and then the modal phase velocity and interference distance will have anomalous changes. The interference distance of normal mode has a minimum. The larger the number of modes and the higher the source frequency, then the more obvious the ‘‘hollow case’’ for interference distance. However, for any cold-core eddy, the modal phase velocity or the interference distance will be monotonically changed.

Modeling of linear pressure fields in sonochemical reactors considering an inhomogeneous density distribution of cavitation bubbles

Although a lot of experimental work was done on the investigation of chemical effects of power ultrasound, only very few efforts were directed towards engineering aspects, like optimum design and scale-up of sonochemical reactors. This paper deals with the calculation of acoustic fields and energy density distributions in sonochemical reactors with an inhomogeneous distribution of cavitation bubbles, which are a basis for the design of sonochemical reactors of various geometrical shapes. The time-dependent wave equation applied to a damped wave propagation represents the basis of our theory. A new model is presented for the numerical calculation of three-dimensional pressure fields in liquids taking into account an inhomogeneous distribution of wave parameters due to the presence of the cavitation bubbles. Compared to a single-phase fluid, gas bubbles in a liquid lead to a heavy change of phase velocity and sound attenuation. These changes are calculated for every time step and volume element of the reactor. Employing this technique, one should be able to calculate the pressure field in a sonochemical reactor with a sufficient accuracy which serves to predict the spatial distribution of cavitation events.

Analysis of Surface Acoustic Wave Grating Waveguides Considering Velocity Dispersion Caused by Reflectivity

Conventional surface acoustic wave (SAW) grating waveguide analyses ignore the changes in phase velocity in the grating region. In reality, velocity dispersion is caused by the reflectivity of finger electrodes, and phase velocity changes near the stop band. In this paper, a new approximate analytical model of a SAW grating waveguide is proposed. This model considers the dispersion of phase velocity, by placing a wave number along waveguide of a transverse mode in such a way that it becomes a solution of the coupling-of-modes (COM) theory. The results of the new model differ from those of conventional analyses. The frequency characteristics of 2-port resonators on 36.5°Y-X quartz and 45°X-Z Li2B4O7 are measured. Calculations using this new model show good agreement with measurements in terms of resonance frequencies and response levels, while those using conventional analyses vary largely. The adequacy of this model is confirmed by the experimental results.

SAW diagnostics of GaAs surface structure

Surface acoustic waves (SAW) are very sensitive to the properties of crystal surfaces, so they find an application in crystal surface diagnostics. In this work GaAs (1 1 1) semi-insulating samples had SAW transducers formed as Al thin-film interdigital structures that operated at a central frequency of 65 MHz. SAW parameters (amplitude and phase variations of the SAW output signals) were measured during irradiation of the GaAs surface from a light source. The results indicate that SAW propagation is sensitive not only to the state of the natural oxide layers covering the GaAs surface, including oxide composition, surface morphology etc., but also to the crystalline state of the GaAs surface itself, particularly to the presence of stress deformations within the GaAs. These deformations are most likely due to a modification of the oxide layer that changes the SAW maximum velocity direction, as indicated by changes in the SAW phase velocity.

Direct measurement of ultrasonic dispersion using a broadband transmission technique

A broadband, through-transmission technique is described that measures directly the change in phase velocity with frequency without first measuring the absolute phase velocity at different frequencies. The method only requires the measurement of the specimen's thickness and recording of two pulses: one without and one with the specimen inserted between the transmitting and receiving transducers. From the two pulses, the dispersion as well as the attenuation can be determined using Fourier analysis without phase unwrapping. Experimental results of two specimens show an excellent agreement between the measured dispersion and the dispersion determined from the measured attenuation using a time causal model. This agreement verifies the model as well as demonstrates the accuracy and precision of the proposed method.

Broadband measurements of phase velocity in Albunex suspensions.

The phase velocities in suspensions of Albunex, an ultrasound contrast agent, are determined using the technique of broadband phase spectroscopy. In these suspensions, phase velocities were measured as a function of Albunex concentration in Isoton II (buffered saline). The dispersion over the measurement bandwidth (1-15 MHz) grew with increasing Albunex concentration, exhibiting a 221-m/s change (17% increase) in phase velocity between 1.0 and 3.8 MHz at the highest concentration reported (32 microL Albunex/8 mL Isoton). The dispersion behavior of the Albunex suspensions is described using a model of encapsulated gas bubbles. The influence of the dispersion in Albunex on broadband pulses is discussed, as well as the potential impact this dispersion may have on the formation of ultrasonic images of the heart.

Modeling of Three-Dimensional Linear Pressure Fields in Sonochemical Reactors with Homogeneous and Inhomogeneous Density Distributions of Cavitation Bubbles

A new model is presented for the numerical calculation of pressure fields in liquids with an inhomogeneous distribution of cavitation bubbles. To calculate the pressure field in a homogeneous single-phase fluid, the Helmholtz integral and the Kirchhoff integral are solved numerically. The Helmholtz integral equation and the Kirchhoff integral are used for the calculation of the acoustic field in a homogeneous fluid for all kinds of transducers of various shapes. The first term of the integral equation embodies a simple superposition of the pressure fields of several point sources, which serves to simulate a harmonic vibrating surface, while the Kirchhoff integral calculates the pressure field which emerges from the boundaries. With a new technique the three-dimensional time-independent pressure field is calculated gradually in the beam direction. With this procedure one is able to combine the Helmholtz integral with a wave propagation in liquids with inhomogeneous distributions of cavitation bubbles. Compared to a single-phase fluid, gas bubbles in a liquid lead to a heavy change of phase velocity and sound attenuation. These changes are determined and considered for every step in the beam direction. With this technique, one should be able to calculate the pressure field in a sonochemical reactor with a sufficient approximation which serves to predict the spatial distribution of cavitation events. These events are related to the yield of chemical reactions.

Liquid Viscosity Measurement Using Plate Mode Shear Horizontal Waves on a Piezoelectric Ceramic Thin Plate

Numerical analysis results of the propagation characteristics of multiple mode shear horizontal (SH) waves along a piezoelectric ceramic thin plate with liquid loading on one of two boundary surfaces are described. The fractional phase velocity changes for S0, A0 and S1 mode SH waves have linear dependences on the square root of liquid viscosity under the electrically shorted boundary condition of both surfaces of the substrate. The mechanical displacement in the liquid layer decays exponentially with the distance from the substrate-liquid interface. The existing depth of the displacement in the liquid layer increases with liquid viscosity in the form of a linear relationship to the square root of liquid viscosity. The measurement of liquid viscosity using two modes of SH waves is carried out. The measured results for water solutions of glycerol using S0 and A0 mode SH waves show linear dependences between the fractional velocity change and the square root of liquid viscosity, and are consistent with the theoretical values.

Developmental changes in flow-wave propagation velocity in embryonic chick vascular system.

We analyzed flow-wave propagation velocity in the early embryonic vascular system and its responses to acute alterations in circulating blood volume. Two 20-MHz pulsed Doppler velocimeters were positioned along the arterial system in stage 18 (n = 12), 21 (n = 10), and 24 (n = 11) chick embryos. Distance between the two measurement sites was measured by video-microscopy. Phase velocity was calculated using Fourier transform up to the fourth harmonics. Wave-front velocity was also calculated by threshold technique. In a subset of embryos at stage 24 (n = 10), circulating blood volume was acutely altered to change stroke volume. Mean phase velocity increased from 42.9 +/- 3.3 to 95.8 +/- 7.5 cm/s from stage 18 to 24 (P < 0.05 by analysis of variance), whereas wave-front velocity increased from 52.8 +/- 2.4 to 72.2 +/- 5.2 cm/s. Stroke volume and mean aortic pressure paralleled the changes in mean phase velocity and wave-front velocity in normal development and in response to changes in circulating blood volume. Thus developmental changes in wave-propagation velocity were consistent with changes in the size of the vascular system, pressure range, and elastic properties of the arterial wall during systemic vasculogenesis in the embryo.

Bounds on phase velocity changes of plane waves in elastic media due to changes in elastic moduli

By using the normality of the acoustic tensor for homogeneous, linearly elastic media, bounds are obtained for the changes in plane wave phase velocities due to changes in the elastic moduli of the medium. The bounds, which hold for arbitrary propagation directions and arbitrary changes in elastic moduli are then specialized to the cases where a single modulus is varied holding all the rest constant. Three dimensional bounding surfaces are derived and graphically presented for the possible changes in phase velocity (actually, square of phase velocity times mass density) of any given mode while propagating in any direction due to the changes in a specific elastic modulus. The results of this paper can be used in analytical developments wherever a need exists to place bounds on possible changes in a solution due to changes in elastic moduli, such as in the reconstruction of elastic moduli from phase or group velocity information. 1997 Elsevier Science Ltd.

Acoustoelasticity in cracked solids

SUMMARY A new model that accounts for the stress dependence of the phase velocity of elastodynamic waves propagating in a cracked solid under compression is presented. The phase velocities of longitudinal and shear waves are derived from the effective elastic properties of a cracked solid, which are evaluated within the framework of Kachanov’s approach. Following Kachanov, the extra-compliance tensor of the cracked solid is related to the crack compliances, which display a marked non-linear behaviour when subjected to a compressive load. Such non-linear behaviour is shown to be derived from the elastic interaction between the contacting crack faces under compression. This work does not address the effect of mutual interaction among cracks and the generation of higher harmonics due to the medium non-linearity. Numerical examples are presented that illustrate the phase velocity changes occurring in a solid with a random distribution of parallel cracks as a function of an external compressive load. A distinctive feature of the acoustoelastic effect in solids with large parallel fractures and in solids with distributions of aligned microcracks is also illustrated.

Elastic wave sensing system

A sensing system detects elastic waves propagated along a sensing path in a sheet to detect a characteristic of material contacting the other side of the sheet. An acoustic load applied between transducers discriminates characteristics in diverse environments. Different systems detect density, stiffness, presence, degree of coupling, thickness, or fill height of the material, with applications to areas as diverse as aircraft wing ice measurement, storage tank fill height detection, and mass flow detection. In one preferred embodiment a protective housing covers and protects the first side of the sheet over a region of the sheet encompassing the sensing path, and may secure transducers in defined positions. The housing preferably defines a closed reservoir that is temporarily filled to determine a normative measurement such as transit time or change in phase velocity. The normative measurement provides an empirical calibration that, in turn, allows a final parameter or a detection threshold to be precisely determined.