A note on Snell laws for electromagnetic plane waves in lossy media

Based on Maxwell's equations and Ohm's law, we rederived the Snell laws for reflection and transmission of harmonic inhomogeneous plane electromagnetic (EM) waves propagating through planar lossy interfaces. The present results are new, simple and exact and they recover the ordinary Snell laws in the case of lossless media. Besides, these results show that the wave propagation direction strongly depends on the polarization state of the EM wave and the lossy media can behave as a polarizing device. Moreover, we verify that in low frequency regime these traveling waves do not exhibit total internal reflection at interfaces between two adjacent lossy media.     

A General Framework for Localization of Classical Waves: I. Inhomogeneous Media and Defect Eigenmodes

We introduce a general framework for studying the localization of classical waves in inhomogeneous media, which encompasses acoustic waves with position dependent compressibility and mass density, elastic waves with position dependent Lamé moduli and mass density, and electromagnetic waves with position dependent magnetic permeability and dielectric constant. We also allow for anisotropy. We develop mathematical methods to study wave localization in inhomogeneous media. We show localization for local perturbations (defects) of media with a spectral gap, and study midgap eigenmodes.     

非均匀波导中的声聚焦

理论研究了声波在非均匀波导中的空间聚焦问题,利用多模态导纳法构建波导内任意位置处声压与入射声压在模态域的映射关系,计算使声波聚焦于空间某位置时的最佳入射波,并画出了相应的聚焦声场.研究了三种非均匀情况:水平变截面波导、含散射体波导以及声速垂直变化波导.结果表明,当输入最佳入射波时,在非均匀波导中可以产生良好的单点或多点声聚焦效果,声波的聚焦过程充分地利用了波导结构及介质非均匀性对声波的散射作用.     

Visual characteristics of inhomogeneous acoustic waves

Experimentally obtained visualizations of propagating inhomogeneous acoustic waves driven by zero-order antisymmetric Lamb waves (flexural waves) in water are presented. The inhomogeneous waves are visualized by optical holographic interferometry. A series of photographs show the evolution in time of instantaneous acoustic pressure distributions associated with propagating inhomogeneous waves. The photographs reveal characteristic features of flexurally driven inhomogeneous waves such as transversely attenuated wavefronts oriented perpendicularly to the plate boundary and a phase propagation velocity along the boundary approximately equal to the plate wave velocity (250 meters/second). Effects due to the dispersive nature of the flexural plate waves are also noted in the photographic series. Features distinguishing these subsonic, inhomogeneous surface waves (also called trapped or evanescent waves) from the leaky, lateral or head wave and also from incompressible fluid motions associated with low frequency vibrations of fluid loaded plates are identified. The relevance of inhomogeneous acoustic waves driven by subsonic flexural waves to practical sound-structure interaction problems is discussed.     

非均匀可激发介质中的稀密螺旋波

在非均匀可激发介质中,采用Barkley模型数值模拟了稀螺旋波和密螺旋波, 并对二者的动力学行为随参数的变化进行了研究. 结果发现:稀螺旋波的旋转频率随参数b的增加迅速减小,之后趋于饱和, 显示出不同于密螺旋波的行为;两种螺旋波的周期和波长随参数ε 和非均匀区域尺寸R的增加而增加,相对稀螺旋波而言,密螺旋波的性质对R的依赖更为敏感; 稀螺旋波端点的波速随R的增加而减小,与密螺旋波波速变化趋势相反. 另外,由于非均匀区域的影响,当ε 或b 超过某一临界值时,螺旋波臂上出现缺陷点.     

Reflection–refraction of attenuated waves at the interface between a thermo-poroelastic medium and a thermoelastic medium

Phenomenon of reflection and refraction is considered at the plane interface between a thermoelastic medium and thermo-poroelastic medium. Both the media are isotropic and behave dissipative to wave propagation. Incident wave in thermo-poroelastic medium is considered inhomogeneous with deviation allowed between the directions of propagation and maximum attenuation. For this incidence, four attenuated waves reflect back in thermo-poroelastic medium and three waves refract to the continuing thermoelastic medium. Each of these reflected/refracted waves is inhomogeneous and propagates with a phase shift. The propagation characteristics (velocity, attenuation, inhomogeneity, phase shift, amplitude, energy) of reflected and refracted waves are calculated as functions of propagation direction and inhomogeneity of the incident wave. Variations in these propagation characteristics with the incident direction are illustrated through a numerical example.     

多可激性障碍下的螺旋波动力学

在许多实际可激系统中局部不均匀是广泛存在的, 它们是螺旋波形成以及动力学行为改变的重要因素. 本文研究了可激性障碍对螺旋波动力学行为的影响. 研究表明, 在障碍区域内可激性参数大于区域外情况下障碍会对其附近的螺旋波波头有吸引作用, 多局部障碍共存时吸引行为不仅依赖障碍分布, 而且依赖障碍的大小以及区域内可激性参数的具体取值. 通过抑制变量小值区域的变化分析了这些行为发生的原因. 在障碍区域内可激性参数小于区域外情况下障碍对其近邻的螺旋波波头有排斥作用, 排斥后波头的运动依赖初始螺旋波是刚性旋转的还是漫游的. 多局部障碍共存时排斥作用对螺旋波动力学行为的改变依赖障碍的分布、大小与区域内可激性参数的具体取值以及初始螺旋波的类型. 关键词： 螺旋波 时空混沌 可激性障碍     

Theoretical model of phase exclusion conditions for the sum-frequency wave produced by a nonlinear acoustic source

A theoretical model of the sum-frequency wave field produced by a nonlinear acoustic source with three-frequency pumping is reported. The model allows for the dissipation and diffraction of the Gaussian beam. The sum-frequency wave is represented within the second-order approximation as a superposition of two synchronous copropagating waves with equal frequencies. It is shown that the spatial and amplitude-phase characteristics of the sum-frequency wave are affected not only by the amplitude-phase relations in the pumping spectrum, but also by the diffraction-caused variations in amplitudes and phases of the primary waves. This dependence is most clearly seen under the phase exclusion conditions, when the generation of the sum-frequency wave is actually suppressed (excluded) owing to the appropriate choice of the amplitude and phase pumping spectra. The theoretical results are found to agree well with experimental data. The possible practical applications of the phase exclusion conditions are as follows: inspection of inhomogeneous media, detection of objects near interfaces, reduction of nonlinear attenuation, acoustic measurements, etc.     

非线性偶极-交换表面自旋波的包络孤立子解

介绍了非线性表面自旋波理论研究的新进展 ,并对前人的理论做了推广 ,针对具有非均匀交换各向异性的偶极 交换铁磁介质的非线性表面自旋波的性质和行为进行了较为系统的理论研究. The new progress in the theoretical investigation on nonlinear surface spin waves is reviewed, and the theory mentioned above is generalized. A relatively systematical investigation on the behaviors and properties of the nonlinear surface spin waves in dipole-exchange ferromagnetic media with inhomogeneous exchange anisotropy is developed.     

Wave refraction in negative-index media: always positive and very inhomogeneous

We present the first treatment of the refraction of physical electromagnetic waves in newly developed negative index media (NIM), also known as left-handed media (LHM). The NIM dispersion relation implies that group fronts refract positively even when phase fronts refract negatively. This difference results in rapidly dispersing, very inhomogeneous waves. In fact, causality and finite signal speed always prevent negative wave signal (not phase) refraction. Earlier interpretations of phase refraction as "negative light refraction" and "light focusing by plane slabs" are therefore incorrect, and published NIM experiments can be explained without invoking negative signal refraction.     

Spatial Investigations of Point-Radiated Fields above the Electron Cyclotron Frequency in an Inhomogeneous Magnetized Plasma

Spatial behaviors of mode-converted electron Bernstein waves at the upper hybrid layer in an inhomogeneous magnetized plasma are investigated experimentally and theoretically when the radiated source is located outside the upper hybrid layer. The theoretical spatial field patterns in two dimensions which include the mode-converted cyclotron harmonic wave radiated from a point source are found to be in near accord with the experimental results.     

Analysis of plasma sheath propagation attenuation based on ray tracing

Based on the complex Snell's law of lossy media, a ray tracing method is proposed to study the propagation attenuation characteristics of electromagnetic (EM) waves in plasma sheaths. The plasma sheath is modelled as layered media. This method considers the complex ray characteristics of inhomogeneous plane EM waves, tracks the propagation rays of EM waves in each layer of media, and calculates the propagation attenuation of EM waves in each layer of media according to the propagation direction of the complex rays. The attenuation during numerical cumulative propagation is the total attenuation of EM waves through the plasma sheath. By comparing the results with that obtained from the WKB method, the accuracy of the ray tracing algorithm is proved. The results of the propagation attenuation of a blunt cone model are calculated by the proposed method, and the effects of different parameters on the EM wave propagation attenuation in the plasma sheath are analysed at different heights, velocities, incident angles, and incident positions. Studying the propagation characteristics of EM waves in the plasma sheath is of importance in application for radar target tracking, blackout communication, and other issues.     

Fast compressional wave attenuation and dispersion due to conversion scattering into slow shear waves in randomly heterogeneous porous media

Within the viscosity-extended Biot framework of wave propagation in porous media, the existence of a slow shear wave mode with non-vanishing velocity is predicted. It is a highly diffusive shear mode wherein the two constituent phases essentially undergo out-of-phase shear motions (slow shear wave). In order to elucidate the interaction of this wave mode with propagating wave fields in an inhomogeneous medium the process of conversion scattering from fast compressional waves into slow shear waves is analyzed using the method of statistical smoothing in randomly heterogeneous poroelastic media. The result is a complex wave number of a coherent plane compressional wave propagating in a dynamic-equivalent homogeneous medium. Analysis of the results shows that the conversion scattering process draws energy from the propagating wave and therefore leads to attenuation and phase velocity dispersion. Attenuation and dispersion characteristics are typical for a relaxation process, in this case shear stress relaxation. The mechanism of conversion scattering into the slow shear wave is associated with the development of viscous boundary layers in the transition from the viscosity-dominated to inertial regime in a macroscopically homogeneous poroelastic solid.     

Exact self-similar wave solutions for the generalized (3 + 1)-dimensional cubic–quintic nonlinear Schröinger equation with distributed coefficients

In this paper, a similarity transformation is presented to reduce the generalized (3 + 1)-dimensional cubic–quintic nonlinear Schrödinger equation with distributed coefficients to the related constant-coefficients one. Then a number of spatiotemporal self-similar wave solutions are constructed. Under the specific choice of the dispersion, cubic and quintic nonlinearities, phase modulation and the gain/loss, we investigate the dynamical behaviors of those spatiotemporal self-similar waves in an inhomogeneous optical fiber media.     

Stochastic processes in a nonlinear Kerr-like ordered liquid

A special case of the problem determined by laser-induced instabilities (at cw input) in wave interactions with inhomogeneous anisotropic media with high threshold nonlinearity under condition of energy competition and exchange between waves with orthogonal polarizations is examined.     

Dynamics of solitons under random perturbations

The dynamics of solitons is investigated in media with randomly inhomogeneous and fluctuating parameters. Some exact results of the theory of nonlinear stochastic waves are given. An analysis is made of various approximate approaches, e.g. of the mean field method and the Born approximation. Special attention is paid to the perturbation technique based on the inverse scattering transform and to the construction of the most adequate stochastic perturbation theory for solitons. The described formalism is used to investigate the evolution of nonlinear wave (soliton) parameters, and the statistical characteristics of radiation generated by solitons in fluctuating media are analysed also. The same approach makes it possible to take into account the simultaneous effect of random and regular (e.g., friction) perturbations on the dynamics of solitons. Examples are given of situations arising when one describes nonlinear waves in real physical systems.     

A Green's function method for surface acoustic waves in functionally graded materials

Acoustic wave propagation in anisotropic media with one-dimensional inhomogeneity is discussed. Using a Green's function approach, the wave equation with inhomogeneous variation of elastic property and mass density is transformed into an integral equation, which is then solved numerically. The method is applied to find the dispersion relation of surface acoustic waves for a medium with continuously or discontinuously varying elastic property and mass density profiles.     

On a theory of surface waves in a smoothly inhomogeneous plasma in an external magnetic field

A theory of surface waves in a magnetoactive plasma with smooth boundaries has been developed. A dispersion equation for surface waves has been derived for a linear law of density change at the plasma boundary. The frequencies of surface waves and their collisionless damping rates have been determined. A generalization to an arbitrary density profile at the plasma boundary is given. The collisions have been taken into account, and the application of the Landau rule in the theory of surface wave damping in a spatially inhomogeneous magnetoactive collisional plasma has been clarified.     

Inhomogeneous relativistic electron beam interaction with inhomogeneous warm plasma

The interaction of inhomogeneous relativistic electron beam with inhomogeneous bounded warm plasma, which leads to amplification of waves, is analyzed. It is shown that due to the resonant increase in wave’s field with a decrease in the plasma permittivity to zero, the power absorbed by plasma is finite and depends on the plasma thermal velocity. The relativistic electron beam not only amplifies waves in plasma but also provides efficient absorption of these waves by plasma.