Acceleration waves in elastic dielectrics with polarization gradient effects

In this paper the propagation of acceleration waves arbitrary form propagating into a deformed eleastic dielectric with polarization effect is investigated. An acceleration wave is defined as a second order propagating surface of discontinuity on which the position vector, the polarization vector and Maxwell potential, and their first order derivatives with respect to time and space coordinates are continuous while the second order derivatives of these quantities may suffer jumps but are continuous everywhere else. By computing the jumps of the balance equations on the singular surface, implicit equations for wave speeds corresponding to non-zero amplitudes of the acceleration wave are obtained. It is noteworthy that the second order derivatives of Maxwell potential are also continuous across the acceleration wave.The same equation for wave speeds are also derived for isotropic elastic dielectrics. The wave speeds for longitudinal and transverse waves are obtained in explicit forms and the conditions of existence for real wave speeds are investigated.     

Diffraction of horizontally polarized ultrasonic plane waves on a periodically corrugated solid-liquid interface for normal incidence and Brewster angle incidence

The theory, and the use at normal incidence, of shear-vertically polarized waves (with polarization vector in the plane containing the incident wave vector and the normal on the interface) using the mode conversion method has been tackled by others. Here we develop the theory for shear-horizontally polarized incident waves (with polarization vector perpendicular to both the normal on the interface and the incoming wave vector). We take into account normal incidence as well as oblique incidence. For normal incidence, we discover the generation of Love waves. If oblique incidence is considered, we discover the existence of a Brewster angle of incidence, comparable with the Brewster angle in optics, in which a diffraction grating can be used as a polarization filter.     

Corrugation-type instability of the free motion of 180° domain walls in uniaxial ferromagnets

Investigation of the spectrum of oscillations of a 180° domain wall (DW) freely moving in a uniaxial ferromagnet shows that the one-dimensional structure becomes unstable with respect to surface distortions in the region of negative effective mass (negative differential mobility). The upper critical value of the perturbation wave vector, above which the DW corrugation is not developed and the wave vector of a perturbation mode with the maximum increment are determined.     

Stress-wave displacement polarizations and aftenuation in unidirectional composites: Theory and experiment

The wave propagation mechanism of changes in displacement polarizations was studied in unidirectional graphite/epoxy composite materials. Change in Displacements can be large enough to cause a transition in the mode or displacement polarizations from longitudinal to transverse. These unusual mode transitions are a result of the peculiar elastic anisotropy observed in only a few crystals and unidirectional graphite/epoxy composities at high-fiber volume fractions Theoretical calculation of these mode transitions were compared with experimental measurements Mode transitions occur when the wave vector orientation is varied from 51.9° to 74.4° in unidirectional samples of T300/5208 graphite/epoxy composite with a 0.6°-fiber volume fraction. Energy flux deviation and particle displacement directions and amplitudes also were compared with theory. To show this mode transition, an attenuation study was performed. The attenuation coefficient, measured in units of reciprocal time, does not appear to depend on the wave vector orientation and the wave type (quasi-transverse and quasi-longitudinal waves) at 5-MHZ frequency. But the attenuation coefficient, expressed in units of reciprocal length, does depend on the wave type and the wave vector orientation because the wave velocity is included in the calculation of this coefficient. Previous studies have focused on how anisotropy and attenuation influence the stress wave speed (eigenvalues), but in this study we focused more on how the same parameters influence the displacement polarizations (eigenvectors) of the same propagating waves. Because eigenvalues and their corresponding eigenvectors are both solutions of the same eigenvalue problem, more attention should be given to measurement of the eigenvectors.     

A complete solution in elastodynamics

Summary In the context of classical elastodynamics, complete representations for the displacement vector and the stress tensor are obtained in terms of a single vector obeying a wave equation. The connection between these representations and other known representations is exhibited.     

Scattering of a plane wave by an anisotropic ferrite-coated conducting sphere

On the basis of the three-dimensional spherical vector wave functions in ferrite anisotropic media, and the fact that the first and second spherical vector wave functions in ferrite anisotropic media satisfy the same differential equations, the electromagnetic fields in homogeneous ferrite anisotropic media can be expressed as the addition of the first and second spherical vector wave functions in ferrite anisotropic media. Applying the continue boundary condition of the tangential component of electromagnetic fields in the interface between the ferrite anisotropic medium and free space, and the tangential electric field vanishing in the interface of the conducting sphere, the expansion coefficients of electromagnetic fields in terms of spherical vector wave function in ferrite medium and the scattering fields in free space can be derived. The theoretical analysis and numerical result show that when the radius of a conducting sphere approaches zero, the present method can be reduced to that of the homogeneous ferrite anisotropic sphere. The present method can be applied to the analyses of related microwave devices, antennas and the character of radar targets.     

Electron-photon drag in a superlattice under the action of a strong electric field

An expression for the current that appears due to the charge carrier drag by a monochromatic electromagnetic wave propagating along a semiconductor superlattice (SL) is obtained for the case when the electric field vector of the wave is parallel to the SL vector and a constant bias electric field is applied along the SL axis. The dependence of the drag current on the bais electric field strength has a nonmonotonic (resonant) character and shows that the drag effect changes sign at a sufficiently large bias field strength.     

The energy band model for bismuth: Resolution of a theoretical discrepancy

The Lax two-band model contains a term linear in wave vector which is missing in the Abrikosov-Falkovsky model. It is shown that this term is recovered if the Abrikosov-Falkovsky development is carried to second order. It is argued from the results of energy band calculations and from experiment that the term in question is as important as the term second order in wave vector which was introduced by Cohen and by Abrikosov and Falkovsky. From a study of cyclotron resonance and de Haas-van Alphen effect it is concluded which second-order terms in the general Cohen model must be kept in order to obtain agreement with experiment.     

Energy flux characteristics of inhomogeneous waves in anisotropic thermoviscoelastic media

This study aims to calculate the wave-field characteristics of four attenuating waves in anisotropic thermoviscoelastic medium. An energy balance equation relates the complex-valued energy flux vector to the time-averaged densities of kinetic energy, strain energy and dissipated energy of plane harmonic waves in the medium. A complex slowness vector defines the inhomogeneous propagation of an attenuating wave in the medium. This slowness vector is specified with the phase velocity and the two non-dimensional attenuation parameters of the wave. One of the attenuation parameter defines the inhomogeneity strength of the wave as a measure of its deviation from homogeneous propagation. The phase velocity, attenuation parameters, polarizations of particles, propagation direction are combined to define the group velocity, ray direction and quality factor of attenuation of an inhomogeneous wave in the medium. Numerical examples are considered to study the variations of these characteristics of energy flux with propagation direction and inhomogeneity strength for each of the four attenuating waves in the medium. The effects of anisotropic symmetries are analyzed on the velocities of waves. The decay-rate of energy densities is exhibited with offset in the propagation-attenuation plane.     

Polarization ellipse and Stokes parameters in geometric algebra

In this paper, we use geometric algebra to describe the polarization ellipse and Stokes parameters. We show that a solution to Maxwell's equation is a product of a complex basis vector in Jackson and a linear combination of plane wave functions. We convert both the amplitudes and the wave function arguments from complex scalars to complex vectors. This conversion allows us to separate the electric field vector and the imaginary magnetic field vector, because exponentials of imaginary scalars convert vectors to imaginary vectors and vice versa, while exponentials of imaginary vectors only rotate the vector or imaginary vector they are multiplied to. We convert this expression for polarized light into two other representations: the Cartesian representation and the rotated ellipse representation. We compute the conversion relations among the representation parameters and their corresponding Stokes parameters. And finally, we propose a set of geometric relations between the electric and magnetic fields that satisfy an equation similar to the Poincaré sphere equation.     

Gap modes of one-dimensional photonic crystal surface waves

The finite-difference time-domain method is employed for the analysis of coupling of the surface modes of two truncated one-dimensional photonic crystals separated by a gap. The wave vector, field distributions, and existence conditions of the coupled surface modes are investigated. The wave vector of symmetric gap modes increases with decreasing gap width, while that of antisymmetric modes decreases-exactly opposite of the situation for surface plasmons on metallic half-spaces separated by a dielectric gap. Photonic crystal gap modes could easily and effectively be used as nondissipating gap-mode waveguides.     

Propagation of inhomogeneous plane waves in anisotropic viscoelastic media

A new technique is explained to study the propagation of inhomogeneous waves in a general anisotropic medium. The harmonic plane waves are considered in a viscoelastic anisotropic medium. The complex slowness vector is decomposed into propagation vector and attenuation vector for the given directions of propagation and attenuation of waves in an unbounded medium. The attenuation is further separated into the contributions from homogeneous and inhomogeneous waves. A non-dimensional inhomogeneity parameter is defined to represent the deviation of an inhomogeneous wave from its homogeneous version. Such a partition of slowness vector of a plane wave is obtained with the help of an algebraic method for solving a cubic equation and a numerical method for solving a real transcendental equation. Derived specifications enable to study the 3D propagation of inhomogeneous plane waves in a viscoelastic medium of arbitrary anisotropy. The whole procedure is wave-specific and obtains the propagation characteristics for each of the three inhomogeneous waves in the anisotropic medium. Numerical examples analyze the variations in propagation characteristics of each of the three waves with propagation direction and inhomogeneity strength.     

Can a Travelling Electromagnetic Wave be Present in a Layered Medium?

Abstract

The problem of the presence of a travelling electromagnetic wave in an inhomogeneous medium is addressed. An argument is presented in favour of the option that the Poynting vector determines whether the wave is travelling or not. A strict harmonic solution to the Maxwell equations in a plane stratified medium is shown not to be a travelling wave. This solution can be decomposed into two travelling fields which separately do not satisfy the Maxwell equations and which are identified as the transmitted and return fields. The direction of the Poynting vector for the transmitted field satisfies the generalized Snell's law. The reflectance of a layer of such a medium is calculated and shown to be zero for some incidence angles. Phases of the two travelling fields are considered and shown to be different from those of geometric optics.     

Symmetries of cross-polarization diffraction coefficients of gratings

In a recent paper [J. Opt. Soc. Am. A 16, 1108 (1999)] Logofatu et al. demonstrated by experimental and numerical evidence that the 0th-order cross-polarization (s to p and p to s) reflection coefficients of isotropic, symmetrical, surface-relief gratings in conical mount are identical. Here an analytical proof is given to show that the observed identity is merely a manifestation of the electromagnetic reciprocity theorem for the 0th-order diffraction of symmetrical gratings. The above result is further generalized to bianisotropic gratings, to the 0th-order cross-polarization transmission coefficients, and to the mth-order reflection and transmission coefficients when the wave vector of the incident plane wave and the negative of the wave vector of the mth reflected order are symmetrical with respect to the plane perpendicular to the grating grooves.     

Point force excitation of a thick-walled elastic infinite pipe with an embedded inhomogeneity

The propagation of elastic waves in thick-walled pipe with an embedded inhomogeneity is considered. The pipe is excited by a point force applied on its surface and the time harmonic problem is solved using the null field approach, a method whose main characteristics are surface integral representations and expansions in spherical and cylindrical vector wave functions. Entering in the expression for the scattered field are the transition matrix for the cavity, the reflection matrices for the inner and outer surfaces of the pipe, the transformation functions between the spherical and cylindrical vector wave functions and also the translation for the cylindrical waves. Numerical examples, both in the frequency and time domain, are presented for a spherical cavity and an open circular crack.     

Non-diffractive Vector Bessel Beams

Abstract

The non-diffractive vector Bessel beams of an arbitrary order are examined as both the solution to the vector Helmholtz wave equation and the superposition of vector components of the angular spectrum. The transverse and longitudinal intensity components of the vector Bessel beams are analysed for the radial, azimuthal, circular and linear polarizations. The radially and azimuthally polarized beams are assumed to be formed by the axicon polarizers used with the initially unpolarized or linearly polarized light. Conditions in which the linearly polarized Bessel beams can be approximated by the scalar solutions to the wave equation are also discussed.     

Variational solution for modal wave-front projection functions of minimum-error norm.

Common wave-front sensors such as the Hartmann or curvature sensor provide measurements of the local gradient or Laplacian of the wave front. The expression of wave fronts in terms of a set of orthogonal basis functions thus generally leads to a linear wave-front-estimation problem in which modal cross coupling occurs. Auxiliary vector functions may be derived that effectively restore the orthogonality of the problem and enable the modes of a wave front to be independently and directly projected from slope measurements. By using variational methods, we derive the necessary and sufficient condition for these auxiliary vector functions to have minimum-error norm. For the specific case of a slope-based sensor and a basis set comprising the Zernike circular polynomials, these functions are precisely the Gavrielides functions.     

Flow structure in three-dimensional waves on a vertically falling liquid film

We have simultaneously measured the velocity vector and film thickness fields in three-dimensional (3D) waves formed upon the decay of regular 2D waves on a liquid film flowing down a vertical plate. Velocity fields at various distances from the plate surface in various regions of a 3D wave are constructed. It is shown that the liquid flow in the wave has a complex structure with regions of backflow and spanwise streams, which mainly occur under the main crest of the wave.     

Simulation of wind velocity time histories on long span structures modeled as non-Gaussian stochastic waves

A methodology is proposed for efficient and accurate modeling and simulation of correlated non-Gaussian wind velocity time histories along long-span structures at an arbitrarily large number of points. Currently, the most common approach is to model wind velocities as discrete components of a stochastic vector process, characterized by a Cross-Spectral Density Matrix (CSDM). To generate sample functions of the vector process, the Spectral Representation Method is one of the most commonly used, involving a Cholesky decomposition of the CSDM. However, it is a well-documented problem that as the length of the structure – and consequently the size of the vector process – increases, this Cholesky decomposition breaks down numerically. This paper extends a methodology introduced by the second and fourth authors to model wind velocities as a Gaussian stochastic wave (continuous in both space and time) by considering the stochastic wave to be non-Gaussian. The non-Gaussian wave is characterized by its frequency–wavenumber (FK) spectrum and marginal probability density function (PDF). This allows the non-Gaussian wind velocities to be modeled at a virtually infinite number of points along the length of the structure. The compatibility of the FK spectrum and marginal PDF according to translation process theory is secured using an extension of the Iterative Translation Approximation Method introduced by the second and third authors, where the underlying Gaussian FK spectrum is upgraded iteratively using the directly computed (through translation process theory) non-Gaussian FK spectrum. After a small number of computationally extremely efficient iterations, the underlying Gaussian FK spectrum is established and generation of non-Gaussian sample functions of the stochastic wave is straightforward without the need of iterations. Numerical examples are provided demonstrating that the simulated non-Gaussian wave samples exhibit the desired spectral and marginal PDF characteristics.     

振动控制研究中的小波包降噪处理

在土木结构振动控制研究中,通常采用人工地震波或实测地震波进行输入,这些地震波往往受到椒盐噪声、脉冲噪声、高斯噪声等多种高频噪声的干扰,影响了振动控制研究的效果.提出一种小波包降噪的处理方法,用以降低高频噪声干扰和简化地震波有效特征向量提取.把实测地震波与降噪处理的地震波应用在一般结构主动控制理论研究中,运用LQR控制算法,通过编制计算机程序进行仿真分析.分析结果表明:地震波经降噪处理前后主动控制地震响应变化非常小,控制系统对于实测地震波的干扰成分具有良好的鲁棒性.