各向异性超常材料中倒退波的传播研究

研究了完全各向异性超常材料中的倒退波传播现象,得到了在材料本征轴和传输轴成任意角度情形下倒退波形成的条件,分析了超常材料的介电张量和磁导率张量、电磁波的偏振方式对倒退波形成和传播的影响. 在此基础上,进一步分析了几种不同色散曲线关系的各向异性超常材料中倒退波的产生情况,获得了电磁波波矢和坡印亭矢量(能流)夹角的具体表达式和倒退波传播的一般性结论. 此外,还研究了近零介电常数超常材料中倒退波的传播特性,发现在此类超常材料中倒退波只能是完美倒退波. 关键词： 超常材料 负折射 倒退波 各向异性     

The anisotropy of the basic characteristics of Lamb waves in a (001)-Bi<Subscript>12</Subscript>SiO<Subscript>20</Subscript> piezoelectric crystal

The orientation dependences of the phase velocity, the effective electromechanical coupling coefficient, and the angle between the wave normal and the energy flux vector are numerically calculated for zeroand first-order Lamb waves propagating in the (001) basal plane of a Bi₁₂SiO₂₀ cubic piezoelectric crystal. It is shown that the anisotropies of these modes are different and depend on the plate thickness h and the wavelength λ. For h/λ < 1, the mode anisotropy can exceed the anisotropy of the corresponding characteristics of surface acoustic waves propagating in the same plane; for h/λ > 1, it approximately coincides with the SAW anisotropy for all the characteristics.     

Diffraction gratings of isotropic negative-phase velocity materials

Diffraction of electromagnetic plane waves by the gratings made by periodically corrugating the exposed planar boundaries of homogeneous, isotropic, linear dielectric-magnetic half-spaces is examined. The phase velocity vector in the diffracting material can be either co-parallel or anti-parallel to the time-averaged Poynting vector, thereby allowing for the material to be classified as of either the positive- or the negative-phase velocity (PPV or NPV) type. Three methods used for analyzing dielectric gratings — the Rayleigh-hypothesis method, a perturbative approach, and the C formalism — are extended here to encompass NPV gratings by a careful consideration of field representation inside the refracting half-space. Corrugations of both symmetric as well as asymmetric shapes are studied, as also the diversity of grating response to the linear polarization states of the incident plane wave. The replacement of PPV grating by its NPV analog affects only nonspecular diffraction efficiencies when the corrugations are shallow, and the effect on specular diffraction efficiencies intensifies as the corrugations deepen. Whether the type of the refracting material is NPV or PPV is shown to affect surface wave propagation as well as resonant excitation of surface waves.     

Double pulse quasi-collinear high harmonic generation scheme as a tool for X-ray laser plasma gain probing

We calculate the field distribution based on the vector diffraction theory for a superposition of spirally phase shifted radially polarized beams. Twisted longitudinally polarized field is found in the focal region. The total intensity as well as the polarization components rotates around the beam axis near the focus. Calculation of the Poynting vector at the focal plane shows that the electromagnetic energy is redistributed between different polarization components. Nonzero value of transverse components of the Poynting vector implies the transverse flow of the energy in the focal region.     

Cherenkov radiation emitted by a vortex into an anisotropic dielectric

The fields produced by a Josephson vortex moving in a sandwich placed into an anisotropic dielectric are investigated. When the vortex velocity exceeds the velocity of light in the direction of the normal to the sandwich surface, Cherenkov emission of electromagnetic waves propagating from the sandwich to the bulk of the dielectric takes place. The Poynting vector of outgoing waves is determined. It is shown that the radiation directivity considerably depends on the degree of anisotropy in the permittivity. The radiation loss power of the vortex is determined, and the relation between the transport current and the vortex velocity is established.     

Wave anisotropy of shear viscosity and elasticity

The paper presents the theory of shear wave propagation in a “soft solid” material possessing anisotropy of elastic and dissipative properties. The theory is developed mainly for understanding the nature of the low-frequency acoustic characteristics of skeletal muscles, which carry important diagnostic information on the functional state of muscles and their pathologies. It is shown that the shear elasticity of muscles is determined by two independent moduli. The dissipative properties are determined by the fourth-rank viscosity tensor, which also has two independent components. The propagation velocity and attenuation of shear waves in muscle depend on the relative orientation of three vectors: the wave vector, the polarization vector, and the direction of muscle fiber. For one of the many experiments where attention was distinctly focused on the vector character of the wave process, it was possible to make a comparison with the theory, estimate the elasticity moduli, and obtain agreement with the angular dependence of the wave propagation velocity predicted by the theory.     

The anisotropy of elastic waves in a tellurium crystal

For acoustic waves propagating in an acoustooptic tellurium crystal, the dependence of their polarization on the propagation direction with respect to the crystal axes is discussed. The characteristic features of waves propagating in the crystal are considered; these features manifest themselves in an excess of the phase velocity of shear acoustic modes over the velocity of longitudinal modes. The change in the wave type from quasi-longitudinal to quasi-transverse as a result of the variation in the propagation direction of ultrasound is investigated. It is shown that such a behavior of bulk acoustic waves is caused by the specific relation between the elastic moduli, which differs from the corresponding relations observed in other acoustooptic materials.     

对称平面单轴晶体金属波导的模式场(1)

由于平面各向异性介质金属波导的重要应用,本文讨论了光在对称平面单轴晶体金属波导(波导层是单轴晶体,两个波导界面均为金属)内的传输特性.对于晶体光轴位于波导界面法方向与传输方向构成的平面内的特殊波导结构,利用麦克斯韦方程组并结合单轴晶体的性质,精确解出了波导模式场.结果表明:1)此种特殊结构波导内存在横电波(TE)和横磁波(TM);2)TM波的坡印廷矢量与波矢方向不在一条直线上;3)波导层为负单轴晶体时波导主模是TE波主模,而波导层为正单轴晶体时波导主模是TM波主模.     

Conical refraction of elastic waves in absorbing crystals

The absorption-induced acoustic-axis splitting in a viscoelastic crystal with an arbitrary anisotropy is considered. It is shown that after “switching on” absorption, the linear vector polarization field in the vicinity of the initial degeneracy point having an orientation singularity with the Poincaré index n = ±1/2, transforms to a planar distribution of ellipses with two singularities n = ±1/4 corresponding to new axes. The local geometry of the slowness surface of elastic waves is studied in the vicinity of new degeneracy points and a self-intersection line connecting them. The absorption-induced transformation of the classical picture of conical refraction is studied. The ellipticity of waves at the edge of the self-intersection wedge in a narrow interval of propagation directions drastically changes from circular at the wedge ends to linear in the middle of the wedge. For the wave normal directed to an arbitrary point of this wedge, during movement of the displacement vector over the corresponding polarization ellipse, the wave ray velocity s runs over the same cone describing refraction in a crystal without absorption. In this case, the end of the vector moves along a universal ellipse whose plane is orthogonal to the acoustic axis for zero absorption. The areal velocity of this movement differs from the angular velocity of the displacement vector on the polarization ellipse only by a constant factor, being delayed by π/2 in phase. When the wave normal is localized at the edge of the wedge in its central region, the movement of vector s along the universal ellipse becomes drastically nonuniform and the refraction transforms from conical to wedge-like.     

Optical properties of strongly anisotropic metamaterials

We study the behavior of wave propagation in strongly anisotropic metamaterials with different principal dielectric constants. Analytical expressions of the dispersion relation, Poynting vector, and group velocity are derived theoretically. The light propagation properties for TM and TE waves in these metamaterials are explored, in which the backward wave, negative refraction, phase-compensation effects, and far-field propagation wave carrying subwavelength information are discussed. These theoretical results are supported by numerical simulation.     

Dispersion and attenuation of surface acoustic waves of shear horizontal polarization on a free surface of a hexagonal crystal with a structurally damaged isotropic surface layer

The phase velocity dispersion and the inverse attenuation length of surface acoustic waves of shear horizontal polarization propagating along a free flat (smooth) surface of a hexagonal crystal (Z cut) in the presence of a thin (compared to the wavelength) structurally damaged surface layer are found in the analytical form. It is shown that, in the long-wavelength limit (the wavelength is large compared to the characteristic size of layer inhomogeneities), which is of the greatest interest to experimenters, the change in the phase velocity dispersion and the change in the inverse attenuation length are proportional to the third and sixth powers of the wave frequency, respectively. The inverse attenuation length is numerically calculated.     

Numerical analysis of propagation characteristics of electromagnetic wave in lossy left-handed material media

The propagation characteristics of electromagnetic wave in lossy left-handed materials (LHM) are studied using finite-difference time-domain (FDTD) method base on auxiliary differential equation (ADE) technology. The LHM medium is realized with lossy Drude models for both the negative electric permittivity and the negative magnetic permeability. The discretized ADE-FDTD equations are derived in detail. The incident wave used in the simulation is a multiple cycle m-n-m pulses source. The term of Poynting's vector E_xH_y was calculated. These numerical results demonstrate conclusively that the phase velocity direction of electromagnetic wave propagation and the direction of the Poynting vectors are anti-parallel in LHM. The amplitude of electric field is reduced with the enhancive distance of LHM slab. It is also demonstrated that the energy of electromagnetic wave in the LHM slab is obviously attenuated, and the attenuation of energy becomes stronger with the angular plasma frequency ω_p increasing. These results indicate that LHM stealth is effective in theory, and reasonable selection of the large negative index of refraction can greatly enhance its effectiveness.     

Scattering of elastic waves by multiple elastic circular cylinders with imperfect interface

In the current paper a general method is presented for the rigorous solution for the scattering of elastic waves by a cluster of elastic circular cylinders of infinite length. The interface separating the cylinder from the surrounding media is considered to be homogeneous imperfect. Specifically, the tractions are continuous but the displacements are discontinuous and proportional in terms of interface stiffness parameters to their respective traction components. Using the exact theory of multipole expansion, analytic solutions for the scattered and internal fields excited by an incident plane P-wave, an incident cylindrical P-wave and an incident plane SV-wave are derived.

Numerical results for directivity patterns and scattering cross-sections are presented for a finite hexagonal array of elastic circular inclusions with imperfect interface. The results show that the sequence of maxima and minima in the curves of scattered cross-sections becomes more undistinguishable as the interface becomes more imperfect. Also, the results reveal that large low-frequency peaks of the scattered cross-sections, which correspond to resonance scattering, can be observed for both the low-velocity and high-velocity elastic cylinders with extremely imperfect interface while the small high-frequency peaks of the scattered cross-sections can appear for low-velocity elastic cylinders with relatively perfect interface. Furthermore, the results clearly show that the interaction effects between cylinders cannot be ignored for an incident plane SV-wave as compared to an incident plane P-wave. More importantly is the fact that the reciprocity relations, which hold for elastic wave scattering by a single cylinder, no longer apply for elastic wave scattering by multiple cylinders.     

The coexistence of TE-TM surface waves in uniaxially anisotropic left-handed materials

We investigate theoretically the characteristics of surface waves in uniaxially anisotropic left-handed materials. The constraints for the existence of TE and TM polarized surface waves in uniaxially anisotropic left-handed materials are identified. We discuss mainly whether TE and TM polarized surface modes may coexist in the same frequency domain at the interface between one isotropic regular medium and another uniaxially anisotropic left-handed medium. It is shown that the answer to the coexistence of TE and TM surface modes is really positive. The Poynting vector and the density of energy associated with surface modes are calculated. Depending on the system parameters either TE or TM surface modes has the time averaged Poynting vector directed opposite or same to the mode phase velocity. In the presence of anisotropy, negative refraction does not need to be left-handed. We show that the characteristics of surface waves in uniaxially anisotropic left-handed media are significantly different from that in isotropic left-handed media.     

Fabric dependence of quasi-waves in anisotropic porous media

Assessment of bone loss and osteoporosis by ultrasound systems is based on the speed of sound and broadband ultrasound attenuation of a single wave. However, the existence of a second wave in cancellous bone has been reported and its existence is an unequivocal signature of poroelastic media. To account for the fact that ultrasound is sensitive to microarchitecture as well as bone mineral density (BMD), a fabric-dependent anisotropic poroelastic wave propagation theory was recently developed for pure wave modes propagating along a plane of symmetry in an anisotropic medium. Key to this development was the inclusion of the fabric tensor--a quantitative stereological measure of the degree of structural anisotropy of bone--into the linear poroelasticity theory. In the present study, this framework is extended to the propagation of mixed wave modes along an arbitrary direction in anisotropic porous media called quasi-waves. It was found that differences between phase and group velocities are due to the anisotropy of the bone microarchitecture, and that the experimental wave velocities are more accurately predicted by the poroelastic model when the fabric tensor variable is taken into account. This poroelastic wave propagation theory represents an alternative for bone quality assessment beyond BMD.     

Scattering of elastic waves by multiple elastic circular cylinders with imperfect interface

In the current paper a general method is presented for the rigorous solution for the scattering of elastic waves by a cluster of elastic circular cylinders of infinite length. The interface separating the cylinder from the surrounding media is considered to be homogeneous imperfect. Specifically, the tractions are continuous but the displacements are discontinuous and proportional in terms of interface stiffness parameters to their respective traction components. Using the exact theory of multipole expansion, analytic solutions for the scattered and internal fields excited by an incident plane P-wave, an incident cylindrical P-wave and an incident plane SV-wave are derived.

Numerical results for directivity patterns and scattering cross-sections are presented for a finite hexagonal array of elastic circular inclusions with imperfect interface. The results show that the sequence of maxima and minima in the curves of scattered cross-sections becomes more undistinguishable as the interface becomes more imperfect. Also, the results reveal that large low-frequency peaks of the scattered cross-sections, which correspond to resonance scattering, can be observed for both the low-velocity and high-velocity elastic cylinders with extremely imperfect interface while the small high-frequency peaks of the scattered cross-sections can appear for low-velocity elastic cylinders with relatively perfect interface. Furthermore, the results clearly show that the interaction effects between cylinders cannot be ignored for an incident plane SV-wave as compared to an incident plane P-wave. More importantly is the fact that the reciprocity relations, which hold for elastic wave scattering by a single cylinder, no longer apply for elastic wave scattering by multiple cylinders.     

Anfachung und Dämpfung magneto-akustischer Wellen in MHD-Kanälen und ihr Einfluß auf die mittlere Stromdichte und die mittlere Hall-Feldstärke

Magneto-acoustic waves generated by fluctuations in the Hall parameter, the electric conductivity and the stream velocity are theoretically investigated in a weakly ionized plasma streaming across a strong external magnetic field and bearing a current flowing perpendicular to both magnetic field and stream velocity. The investigations hold for seeded rare gas plasmas at any degree of seed ionization but are resticted to waves propagating in parallel or antiparallel direction to the current density vector and in parallel or antiparallel direction to the stream velocity vector and to wave lengths which are small in comparsion to the interaction length which occurs as a characteristic wave length. The influence of these waves on the mean current density and the mean Hall field intensity is calculated in case of small amplitudes and low degree of seed ionization up to second order terms. Omitting Ohmic heating the dispersion equation can be solved exactly. A phase shift exists between the fluctuations in gas density and gas velocity. The phase velocity and the amplification rate depend on the wave length. Typical results are represented in a diagram. For both types of waves the phase velocity slightly rises with increasing wave length, while the amplification rate decreases. Waves propagating in opposite direction to the current density vector are amplified, if the electron velocity exceeds a critical value. They reduce the mean current density and the mean Hall field intensity. Waves propagating in opposite direction to the stream velocity vector are also amplified except for very high degrees of seed ionization. The threshold current density is greater than that for the waves of the first type approximately by the Hall parameter as factor. At extremely high degree of seed ionization the phase velocity is directed opposite to the direction occuring at weakly ionized seed. Waves of the second type decrease the mean current density, but increase the mean Hall field intensity.     

Surface waves propagating around the periphery of a piezoelectric cylinder of hexagonal symmetry with time dependent elastic stiffness

Acoustic surface waves propagating around the periphery of a piezoelectric cylinder of hexagonal symmetry are investigated. A co-axial structure with a piezoelectric insulator as the inner cylinder and electric conductor as the outer cylinder is considered. The dispersion equation is derived and solved under certain approximations assuming the elastic stiffness to be time dependent as in Voigt's model of viscoelasticity. The final expressions for the mechanical displacement component and electric potential are obtained. Ultimately some important parameters of such waves as group velocity, Poynting vector and power flow components have also been determined.I am grateful to Dr. A. K. Pal for his helpful suggestions in the preparation of the paper.     

Energy-momentum four-vector on a wavefront

We first discuss the synchronous and asynchronous interpretations of relativistic dynamics, and then prove that the synchronous formulation makes it possible to define in the limitvc the energy-momentum four-vector of a classical field on a wavefront propagating with the velocity of light. It is also shown that except for plane waves, the Poynting vector is not the energy flow vector of the electromagnetic field.     

光脉冲通过含有色散与增益型缺陷的一维光子晶体的传播

研究了光脉冲通过含有色散和增益型缺陷的一维光子晶体的传播行为.缺陷的色散与增益性质用Lorentz振子模型描述.随着振子强度的变化，脉冲峰的传播呈现极慢光速和超光速的传播行为，但能量速度小于真空中的光速c.脉冲峰的超前与落后是各Fourier分量在介质中获得了不同的相移和幅度改变后重新相干叠加的结果. 关键词： 光子晶体 缺陷 光脉冲传播 能量速度