Electromagnetic waves in isotropic and gyrotropic media

Maxwell’s equations are considered for waves in transparent inhomogeneous anisotropic and gyrotropic media with time dispersion. A uniaxial inhomogeneous crystal is taken for an anisotropic medium and an isotropic heterogeneous medium in a constant electric field for a gyrotropic medium. The solutions for flat-layered and cylindrical media are presented in terms of Hertz potentials. __________ Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 3, pp. 82–86, March, 2008.     

平面波在横向各向同性均匀介质中的传播

导出均匀各向异性介质当中具有横向各向同性性质的一类介质中平面波的严格解,给出了慢度曲面的三维分布图形,研究了属于这类介质的单向纤维增强复合材料中声波的传播规律。平面波的特征用慢度矢量、波矢量、偏振矢量和群速度等物理量来刻画.由于引入了描述介质各向异性特性的方向矢量,各物理量最终以与座标系无关的形式来表达,因而具有普遍的适用性。     

分层介质中面波的能量分布

在三维情况下研究了分层介质中Rayleigh和Love面波的能量分布问题,分析了多层介质中柱面面波的能量传播特性.面波是声源与介质分界面相互作用的结果,其能流密度随深度增加很快衰减,但在一定深度处出现极大和极小值.通过数值分析发现只有当径向距离较大时,面波能量传播的速度才等于其群速度.文中还考查了频率、深度、介质层状结构等参数对能量分布的影响.     

Polarization effects during the interaction of counterpropagating waves in isotropic resonant media

Using the method of nonlinear polarization spectroscopy in the oppositely propagating laser beams of different power at a wavelength of 3.39 μm, we study, both theoretically and experimentally, the mechanisms of the formation of dichroism and birefringence during the interaction of arbitrarily polarized fields of resonant radiation with gaseous methane under conditions of low pressure of the gas in the cell and saturation of the operating transition F ₂ ⁽²⁾ by the field of a strong wave. Spectral forms of the polarization resonances of the test-wave intensity at the output of the polarization spectrometer are studied experimentally. Based on the vector theory of light interaction with matter, we present an exhaustive theoretical interpretation of the experimental data on the dependence of the polarization state of a weak wave on the intensity of a linearly or circularly polarized high-power counterpropagating wave. A new technique of measuring the induced nonlinear anisotropy for test-field waves and the macroscopic parameters of the resonant gas is developed. __________ Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 50, No. 1, pp. 72–93, January 2007.     

Energy propagation for dispersive waves in dissipative media

University of Bologna, Italy. Published in Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 36, No. 7, pp. 650–664, July, 1993.     

Hierarchical model for the scale-dependent velocity of waves in random media

Elastic waves of short wavelength propagating through the upper layer of the Earth appear to move faster at large separations of source and receiver than at short separations. Existing perturbation theories predict a linear increase of the velocity shift with increasing separation and cannot describe the saturation of the velocity shift at large separations that is seen in computer simulations. We point out that this nonperturbative problem can be solved using a model developed originally for the study of directed polymers. The saturation velocity is found to scale with the four-thirds power of the root-mean-square amplitude of the velocity fluctuations, in good agreement with the computer simulations.     

多孔介质BISQ模型中的慢纵波

着重研究了多孔介质BISQ模型中慢纵波的基本特性.给出了BISQ模型下慢纵波速度 和衰减的低频近似公式.与Biot理论对比，BISQ模型中慢纵波的衰减随频率降低急剧增大， 且随喷射流长度的减小而增加；相速度随喷射流长度的减小而增加，其低频极限值不是零； 孔隙流体位移与固相骨架位移之比的幅值随喷射流长度的增加而减小，其相位特点与Biot模 型预测的不同；在流体与孔隙介质的边界上可产生更大的渗流.为对比，同时也给出快纵波 的行为.依据BISQ模型可推断：非黏滞流体饱和孔隙介质中不存在喷射流机理；BISQ模型中 关键词： 多孔介质 喷射流 慢纵波 动力协调     

横向各向同性固体中圆柱状散射体对水平偏振剪切波的散射

给出横向各向同性介质中SH波的标量波动方程,并通过简单的坐标变换,将其化为标准的Helmholtz方程.建立了求解散射问题的积分方程,利用边界单元方法数值计算了横向各向同性固体中圆柱状空洞及刚性散射体对SH波的散射场分布。重点分析了各向异性对空洞散射体散射场指向性的影响.     

Charge-density waves and isotropic metals

Fermi-surface instability leading to charge density waves is a common malady in anisotropic metals, and there is now evidence that it also infects isotropic ones.     

Finite-amplitude waves in isotropic elastic plates

The propagation of finite-amplitude waves in a homogeneous, isotropic, stress-free elastic plate is investigated theoretically. Geometric and weak material non-linearities are included, and perturbation is used to obtain solutions of the non-linear equations of motion for harmonic generation in the waveguide. Solutions for the second-harmonic, sum, and difference-frequency components are obtained via modal decomposition. Ordinary differential equations for the modal amplitudes in the expansion of the second-order solution are obtained using a reciprocity relation. There are no restrictions on the modes or frequencies of the primary waves. Two conditions for internal resonance are quantified: phase matching, and transfer of power from the primary to the secondary wave.     

On the theory of scattering of electromagnetic waves in media with space-time velocity fluctuations

We express the effective permittivity tensor for a medium that is, on the average, motionless and nonstationary. It is shown that fast time pulsations of velocity lead to an increase in the average wave field and in the propagation velocity of an electromagnetic wave. Using a computer, we compare the surfaces of the frequency spectra of the strength of the scattered field for the Gaussian and diffusion components of the solenoidal velocity field. Dips are shown to emerge in the frequency spectrum that corresponds to the diffusion correlation function as the velocity pulsation increases.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 39, No. 9, pp. 1091–1095, September, 1996.     

Acoustic-elastodynamic interaction in isotropic fractal media

This research explores the acoustic-elastodynamic interaction in isotropic fractal media. The analysis discusses the direct coupling of two constitutive models under dynamic loading: a continuous solid and an isotropic fractal medium. We consider two situations where in the first, the fractal medium is enclosed within a thin spherical shell (interior problem), while in the second, the fractal medium extends infinitely outside the shell (exterior problem). The two problems are simulated analytically, and the exact solution for the shell displacement is expressed in closed form in the Laplace domain. The formulation of the radiation condition for infinite fractal media is essential to derive the exterior problem’s solution. This study represents a meaningful idealization of real-application problems involving the interaction of multi-constitutive media, e.g. the human brain, whereby fractal features affect the response of this body under various excitations.     

Electromagnetic wave refraction on the interface of absorptive and transparent isotropic media and non-resonant excitation of surface waves

New formulae for the angles of refraction at the interface of the absorbing/transparent isotropic media are derived from Maxwell's equations. Using the time-averaged Poynting vector for the direction of the beam of light, the noncoincidence of incidence and refraction planes is predicted for the mixed polarization of incident wave. The angle between the refracted beam and incidence plane is especially large for the condition of non-resonant excitation of surface electromagnetic waves at a flat interface of absorptive-transparent media.