Surface scattering in media with time and spatial dispersion

Scattering of scalar and vector waves from a randomly rough interface between media, in which several types of waves (modes) exist due to the time and spatial dispersion, has been studied in the Kirchhoff approximation. As a wave of a certain type is reflected from the interface, it transforms into other modes not only in the diffusive fields but in the coherent components as well. We have calculated the mean (coherent) field and the angular diagram of the diffusively scattered intensity. It is shown that the coherent components of the waves generated on reflection (cross-modes) propagate in directions that are different from the specular one. The dispersion gives rise to the frequency dependence of the scattering diagram even in the geometric-optics approximation.     

纤锌矿氮化物量子阱中光学声子模的三元混晶效应

本文先比较了几种常用方法(修正的无规元素等位移模型、虚晶近似和简化相干势近似等)对纤锌矿三元混晶体声子频率的拟合结果,再选用与实验数据接近的拟合方法,结合介电连续和单轴晶体模型导出含纤锌矿三元混晶In_xGa_1－xN和Al_xGa_1－xN单量子阱各类光学声子模的色散关系,进一步分析了声子模随组分的变化. 结果表明,修正的无规元素等位移模型对单模性纤锌矿     

Surface waves between metallic films and truncated photonic crystals observed with reflectance spectroscopy

We have analyzed and demonstrated surface-wave excitations, by propagating waves in air, at the interface between a truncated photonic crystal (PC) and a silver film in the near-infrared. The truncated PC was fabricated with several unit cells of alternating SiO(2) and Si(3)N(4) layers. The dispersion relation of surface waves was calculated using the supercell method. A Fourier-transform infrared spectrometer measured the spectral reflectance of the fabricated sample at different incidence angles. An angle-resolved laser scatterometer measured the reflectance as a function of the incidence angle at the wavelength of 891 nm. The agreement between the resonance conditions obtained from experiments and the calculated dispersion relation manifests that surface waves at the PC-Ag interface may be utilized to build coherent thermal-emission sources.     

Spatial dispersion in metamaterials with negative dielectric permittivity and its effect on surface waves

The effect of spatial dispersion on the electromagnetic properties of a metamaterial consisting of a three-dimensional mesh of crossing metallic wires is reported. The effective dielectric permittivity tensor epsilon(ij)(omega, k) of the wire mesh is calculated in the limit of small wavenumbers. The procedure for extracting the spatial dispersion from the omega versus k dependence for electromagnetic waves propagating in the bulk of the metamaterial is developed. These propagating modes are identified as similar to the longitudinal (plasmon) and transverse (photon) waves in a plasma. Spatial dispersion is found to have the most dramatic effect on the surface waves that exist at the wire mesh-vacuum interface.     

Excitation mechanisms and dispersion characteristics of guided waves in multilayered cylindrical solid media

This paper first reviews a method of simulating the propagation characteristics of guided waves in multilayered coaxial cylindrical elastic solid media. Secondly, this method is used to investigate the properties of the guided waves for the ultrasonic long-range non-destructive evaluation techniques for rockbolts. To do so, the special case of non-leaky guided modes in open waveguides is considered. The method explains how the complex dispersion function is converted into a real function: hence the bisection technique can be employed to search for all the real roots. The model is used to (i) characterize the low dispersion range and anomalous dispersion of normal and Stoneley modes and (ii) analyze the excitation mechanisms of guided waves from axisymmetric and non-axisymmetric acoustic sources. The results are used to select suitable excitation frequency ranges associated with dominant modes with large amplitudes, low dispersion, and distinguishable propagation velocities to reduce signal distortion. The results suggest the lowest order flexural mode, excited by a radial force source, has potential to be used in practice. Also, the highly dispersive Stoneley mode propagating along a cylindrical interface is defined and distinguished from the normal mode using two properties, velocity high-frequency asymptotes and amplitude distributions along the radial direction.     

Propagation characteristics of guided waves in a rod surrounded by an infinite solid medium

The dispersion and excitation characteristics of the guided waves in a rod surrounded by an infinite solid medium (cladding) are investigated. First, the bisection technique is employed to find all the roots of the dispersion function on the basis of theoretical analysis and to obtain the complex phase and group velocity dispersion curves of the guided modes. Second, according to their different dispersion characteristics, the guided modes are divided into two categories: normal modes and Stoneley modes. And it is concluded that the normal modes merely exist in the “hard cladding” model in which the cladding’s shear velocity is larger than the rod’s; while the Stoneley modes in cylindrical interface are highly dispersive and merely exist in the model whose acoustical parameters satisfied the existence condition of the Stoneley waves. Third, the seldom discussed issue, the excitation mechanisms of the guided waves, excited by three source models: symmetric point source, axial and radial force sources, are simulated respectively. Attention is paid on the dominant mode which has better excitation sensitivity and the suitable excitation frequency range. Moreover, the propagation characteristics of the Stoneley modes, ignored in previous references, are analyzed and compared with those of the normal modes.     

Dispersion of interface waves in sediments with power-law shear speed profiles. II. Experimental observations and seismo-acoustic inversions.

The propagation of seismic interface waves is investigated in soft marine sediments in which the density is constant, the shear modulus is small, and the profile of shear speed c(s) versus depth z is of the power-law form c(s) (z) = c0z(v), in which c0 and v are constants (0< v < 1). Both the phase speed V and the group speed U of interface waves scale with frequency as f(v/(v -1)) and they obey the simple relation U= (1 - v) V. These relations are derived in a simple way using ray theory and the WKB method; a companion paper [O. A. Godin and D. M. F. Chapman, J. Acoust. Soc. Am. 110, 1890 (2001)] rigorously derives the same result from the solutions to the equations of motion. The frequency scaling is shown to exist in experimental data sets of interface wave phase speed and group speed. Approximate analytical formulas for the dispersion relations (phase and group speed versus frequency) enable direct inversion of the profile parameters c0 and v from the experimental data. In cases for which there is multi-mode dispersion data, the water-sediment density ratio can be determined as well. The theory applies to vertically polarized (P-SV) modes as well as to horizontally polarized (SH) modes (that is, Love waves).     

Parallel velocity shear driven electrostatic waves in a very dense nonuniform magnetoplasma

It is shown that the parallel (magnetic field-aligned) velocity shear can drive the low-frequency (in comparison with the ion gyrofrequency) electrostatic (LF-ES) waves in an ultracold super-dense nonuniform magnetoplasma. By using an electron density response arising from the balance between the electrostatic and quantum Bohm forces, as well as the ion density response deduced from the continuity and momentum equations, a wave equation for the LF-ES waves is derived. In the local approximation, a new dispersion relation is obtained by Fourier transforming the wave equation. The dispersion relation reveals an oscillatory instability of dispersive drift-like modes in super-dense quantum magnetoplasmas.     

Evolution of the polarization of electromagnetic waves in weakly anisotropic inhomogeneous media — a comparison of quasi-isotropic approximations of the geometrical optics method and the Stokes vector formalism

The main methods describing polarization of electromagnetic waves in weakly anisotropic inhomogeneous media are reviewed: the quasi-isotropic approximation (QIA) of geometrical optics method that deals with coupled equations for electromagnetic field components, and the Stokes vector formalism (SVF), dealing with Stokes vector components, which are quadratic in electromagnetic field intensity. The equation for the Stokes vector evolution is shown to be derived directly from QIA, whereas the inverse cannot be true. Derivation of SVF from QIA establishes a deep unity of these two approaches, which happen to be equivalent up to total phase. It is pointed out that in contrast to QIA, the Stokes vector cannot be applied for a polarization analysis of the superposition of coherent electromagnetic beams. Additionally, the ability of QIA to describe a normal modes conversion in inhomogeneous media is emphasized. Presented at 9-th International Workshop on Nonlinear Optics Applications, NOA 2007, May 17–20, 2007, Świnoujście, Poland     

Surface electromagnetic waves at the interface between dissipative porous nanocomposite and hypercrystal under different temperatures

In the current paper the properties of surface plasmon polaritons as well as hybrid polarized surface electromagnetic waves at the plane interface of a porous semiconductor nanomaterial and a hypercrystal are studied theoretically and numerically. The nanomaterial, as well as the hypercrystal, is made of n-type doped indium antimonide (n-InSb) semiconductor layers. The losses which inherent to the semiconductor materials are taken into account. To describe the properties of the constituent semiconductor layers the approximate analytical temperature models for concentration and mobility of conduction electrons are applied. This allows to consider the effect of electron scattering on the properties of supported electromagnetic modes in the wide frequency range. The contacting materials are considered in the subwavelength approximation when it is possible to introduce the effective permittivity components. It is shown that taking into account dissipation processes in the semiconductor constituent layers result in the appearance of additional surface modes branches, changes in the surface waves penetration depth, frequency and angular existence domains.     

On the instability of electrostatic waves in a nonuniform electron–positron magnetoplasma

The dispersion properties of three-dimensional electrostatic waves in a nonuniform electron–positron (EP) magnetoplasma are analyzed. A new dispersion relation is derived by use of the electron and positron density responses arising from the electron and positron continuity and Poisson equations. In the local approximation, the dispersion relation admits two wave modes with different velocities. The growth rates of various modes are illustrated both analytically and numerically. Considering the temperature gradients produces a linearly stable transverse mode. The growth rate of the slow mode instability due to the density inhomogeneity only is the highest one, though it appears at higher thermal energy. The angle of the wave propagation affects drastically on the instability features in each case. The applications of the present analysis are briefly discussed.     

The propagation of in-plane P-SV waves in a layered elastic plate with periodic interface cracks: exact versus spring boundary conditions

The propagation of in-plane (P-SV) waves in a symmetrically three-layered thick plate with a periodic array of interface cracks is investigated. The exact dispersion relation is derived based on an integral equation approach and Floquet's theorem. The interface cracks can be a model for interface damage, but a much simpler model is a recently developed spring boundary condition. This boundary condition is used for the thick plate and also in the derivation of plate equations with the help of power series expansions in the thickness coordinate. For low frequencies (cracks small compared to the wavelength) the three approaches give more or less coinciding dispersion curves, and this is a confirmation that the spring boundary condition is a reasonable approximation at low frequencies.     

Resonant transmission of acoustic waves through an elastic plate quasiperiodically corrugated on surfaces

In this work, we study the resonant transmission of acoustic waves through a plate with quasiperiodic surface corrugations. The transmission spectrum shows peculiar transmission peaks, which cannot be simply attributed to the coherent diffraction as recognized previously in structured hard plates (without sustaining internal modes), whereas come from the resonant excitation of the coupled Stoneley surface modes in the elastic plate. The excitation frequencies can be determined by the geometrical structure factor of the quasiperiodic lattice, combining with the dispersion relation of the surface modes.     

Characterization of mechanical properties of a hollow cylinder with zero group velocity Lamb modes

Hollow cylinders used in the industry must be regularly inspected. Elastic guided waves, similar to Lamb modes in a plate, can propagate in the axial direction or around the circumference. They are sensitive to geometrical and mechanical parameters of the cylindrical shell. The objective of this paper is to show that zero group velocity (ZGV) Lamb modes can be used to bring out anisotropy and to measure elastic constants of the material. This study provides experimental and numerical investigations on a Zirconium alloy tube extensively used by the nuclear industry in reactor core components. A non-contact method, based on laser ultrasound techniques and ZGV Lamb modes, demonstrates that the difference observed between axial and circumferential guided waves cannot be explained by an isotropic model. Then, a transverse isotropic model is used for the Zircaloy tube. Four of the five elastic constants are directly extracted from ZGV resonance frequencies. The last one is deduced from the measured dispersion spectra. With this complete set of constants, a good agreement is obtained between theoretical and experimental dispersion curves for both axially and circumferentially propagating guided waves.     

Time-harmonic torsional waves in a composite cylinder with an imperfect interface

In this paper, the propagation of time-harmonic torsional waves in composite elastic cylinders is investigated. An imperfect interface is considered where tractions are continuous across the interface and the displacement jump is proportional to the stress acting on the interface. A frequency equation is derived for the rod and dispersion curves of normalized frequency as a function of normalized wave number for elastic bimaterials with varying values for the interface constant F are presented. The analysis is shown to recover the dispersion curves for a bimaterial rod with a perfect (welded) interface (F = 0), and has the correct limiting behavior for large F. It is shown that the modes, at any given frequency, are orthogonal, and it is outlined how the problem of reflection of a torsional mode by a planar defect (such as a circumferential crack) can be treated.     

Effect of tensor g-factor on the spectrum of eigen modes in magnetoactive plasma

The influence of the tensorial nature of the gyromagnetic coupling on a spectrum of eigen modes in magnetoactive plasma is studied. A dispersion equation for waves propagating in such a medium is obtained in the approximation of frigid hydrodynamics.     

The peculiarities of coupled electromagnetic and magnetoelastic waves in antiferromagnets

A spectrum of coupled electromagnetic, spin and elastic waves in a two-sublattice antiferromagnet with weak ferromagnetism is theoretically investigated. The influence of the g-factor anisotropy and the transverse and longitudinal relaxation in magnetic subsystem on the spectrum of coupled waves is considered. The most changes of dispersion laws occurred in long-wavelength approximation and near the spin reorientation point, then the vectors of ferromagnetism and antiferromagnetism reoriented onto another crystallographic axis. It is shown that the magnetoelastic, the Dzyaloshinsky and the dipole interactions, the anisotropy of g-factor, the external magnetic field and the longitudinal susceptibility determine the activation of quasiferromagnetic waves. The dispersion laws of quasielectromagnetic and quasielastic waves can change from linear dependence to square. At large damping in magnetic subsystem, one from these modes can become the pure relaxation one.     

Surface and interface Bleustein-Gulyaev waves along symmetry directions of cubic crystals

We have studied the dispersion relation of surface and interface Bleustein-Gulyaev waves along symmetry directions of the (001) and (110) surfaces and interfaces of cubic crystals by using an extension of the surface Green function matching method recently developed. We have shown, for the first time to our knowledge, in a general way that along the [001] direction on (001) metallized and non-metallized surfaces the Bleustein-Gulyaev mode does not exist. On the other hand for the [110] direction on the (110) surfaces, metallized or not, the Bleustein-Gulyaev mode always exists. For metallized (110) surfaces the dispersion relation is obtained in closed form, whereas for non-metallized (110) surfaces we obtain the dispersion relation as a simple equation which must be solved numerically. We have obtained the existence condition for the Bleustein-Gulyaev modes in these cases. The velocities of the Bleustein-Gulyaev modes for ZnS, ZnSe, ZnTe and GaAs are given, when they exist. The same analysis has been applied to the study of the dispersion relation of interface Bleustein-Gulyaev mode, and a brief discussion is given.     

SH wave propagation in a piezoelectric/piezomagnetic plate with an imperfect magnetoelectroelastic interface

In this paper, we investigate the SH wave propagation in a layered piezoelectric (PE) and piezomagnetic (PM) plate with an imperfect magnetoelectroelastic interface. A linear magnetoelectroelastic spring model is used to describe the weakness of the imperfect interface. On the basis of this model, dispersion curves and mode shapes of the SH waves are computed. In particular, a PZT-5A/CoFe₂O₄ composite plate is considered in the numerical examples to calculate the dispersion curves and the mode shapes for different combinations of the magnetic, electrical and elastic spring constants. The effects of the layer thickness ratio and the electric-magnetic boundary conditions on the dispersion curves are discussed in details. Our results show that for a general weak bonding case, the high modes of the dispersion curves are not monotonous in the range of small wave numbers. With the layer thickness ratio increasing, the wave velocities of the SH waves increase. The electric boundary conditions mainly determine the dispersion curves of the SH waves in the case of a small layer thickness ratio, i.e. a large thickness of the PE layer. The present results have relevant applications in the nondestructive testing and evaluation of the layered PE/PM plate-like wave devices.     

Transport properties of random media composed of core-shell spheres

With the energy-density coherent potential approximation method, a series of calculations concerning the contribution from the morphology and dispersion of random media composed of core-shell spheres on the transport properties of random media are conducted in terms of the scattering-cross-section efficiency factor, mean free path, velocity of electromagnetic energy, and diffusion coefficient. It is found that the core layer introduces more complicated resonant modes which lead to diverse possibilities to sharply decrease the transport of light within random media.