The wave flow effect on a plane boundary between vacuum and an optical medium with a quasi-zero refractive index

A boundary problem in which a plane electromagnetic wave is reflected and refracted at a plane boundary of a semi-infinite optical medium with a quasi-zero refractive index has been solved. Such a medium has a random refractive index taking values in an interval from zero to some finite value less than unity. It means that the concept of a sharp interface between two media loses its meaning, the boundary of the medium becomes inhomogeneous, and laws of reflection and refraction of light become non-Fresnelian. Formulas for non-Fresnelian amplitudes of reflection and refraction have been derived. It is shown that a surface wave arises near the boundary of a medium with a quasi-zero refractive index. The wave propagates both on the inside and outside of the boundary.     

Resonance compression of an acoustic beam in a crystal

The resonance excitation of an intense acoustic beam in a crystal is described for a special geometry of pump-wave reflection from the crystal surface. The resonance appears in the vicinity of the total internal reflection angle under the condition that the wave field in a compressed reflected beam propagating almost parallel to the surface is close to the volume eigenmode satisfying the free boundary condition. Criteria for the existence of such modes are considered in detail. Conversion conditions are analyzed under which a “parasitic” reflected wave of the same branch as the incident wave is absent and entire energy from the incident wave falls within a narrow intense acoustic beam of another branch. It is shown that, when the surface is chosen parallel to the crystal symmetry plane, the conversion criterion is reduced to the sole condition on the elastic moduli of the medium. Analysis is performed by analytic and numerical methods for skew cuts of monoclinic, rhombic, trigonal, and hexagonal crystals, when the boundary is the symmetry plane, while the sagittal plane has no symmetry. A number of crystals are found in which resonance excitation is very close to conversion.     

Reflection of spin and spin-elastic waves at the interface of a ferromagnetic half-space

This paper considers the reflection of pure spin and spin-elastic (or magneto-elastic) waves at the interface of a ferromagnetic half-space and a vacuum. For pure spin waves two cases are considered, with exchange effects, and without. It is shown that when exchange effects are taken into account, volume spin waves in the ferromagnetic half space incident at the boundary with the vacuum generate a reflected volume spin wave, and an accompanying compound surface wave propagating along the boundary and consisting of two partial inhomogeneous spin waves in the ferromagnetic half-space and a partial magneto-static inhomogeneous surface wave in the vacuum. When exchange effects are neglected the incident wave generates only a reflected volume wave in the ferromagnetic half-space.

Reflection and transmission of spin-elastic (or magneto-elastic) waves has been considered only in the case of the absence of exchange effects. An incident volume wave generates a volume spin-elastic reflected wave and one inhomogeneous magneto-static accompanying surface wave.

Excitations of the magnetic field are not transmitted into the vacuum in both cases when the exchange effect is neglected. In all cases the reflection of a spin wave has the character of a full internal reflection.     

圆形活塞声源的有限振幅反射波

本文研究了圆形活塞声源的有限振幅声波的反射。应用像源法计算已产生的谐波本身在边界上的反射,将它们看成是反射边界上振动的新声源所产生的辐射场,再应用弱冲击理论来计算这部分场自己产生的谐波场。在水池中作了二阶谐波的反射实验,反射界面是水池壁。结果表明,谐波声压随距离的平均衰减规律与理论符合得很好。实验还表明,反射谐波场沿纵向距离以及与它相垂直的横断面上有强烈的干涉现象,而纵向相干长度比横向相干长度大一个数量级。通过理论估计,认为这种现象是由于反射壁的有限厚度、它的两个平面之间有一个很小的角度以及发射波束有一定的宽度所造成的。这样估算出来的两个相干长度与实验符合。 关键词：     

Acousto-optic study of the unusual cases of reflection of bulk elastic waves in a paratellurite crystal

The propagation and reflection of bulk ultrasonic waves in a paratellurite crystal have been investigated by the acousto-optic method. Simultaneous excitation of two acoustic waves by one piezoelectric transducer has been observed in a cell of complex, specially chosen configuration. Maximally efficient conversion of the energy of a quasi-longitudinal wave into a single reflected quasi-shear wave with a walkoff angle 72° is implemented for the reflection from a free crystal boundary. The wave beam compression by a factor of 7 is observed for this reflection. A reflection (close to backward) of waves with an angle of spatial separation of the incident and reflected beams equal to 8° is also implemented. The acousto-optic figure of merit values of the medium are calculated for arbitrary propagation and polarization directions of the interacting light and ultrasonic waves. Possible applications of the effects studied in acousto-optics and acoustoelectronics are indicated.     

Resonance excitation of intense acoustic beams in crystals of different syngonies

The resonance excitation of an intense elastic wave in a crystal, arising under conditions of the nonspecular reflection of an incident pump wave is described for a crystal geometry close to a cut that allows the existence of a bulk eigenwave satisfying the free boundary condition. It is shown that choosing a crystal surface parallel to the plane of symmetry optimizes reflection resonance due to the coincidence of the excited wave’s intensity maximum and the reflected (parasite) wave’s intensity minimum in the same geometry of reflection. Parameters of resonance are given for a number of crystals with monoclinic, orthorhombic, and hexagonal syngonies.     

REFLECTION OF PLANE WAVES BY THE FREE BOUNDARY OF A POROUS ELASTIC HALF-SPACE

In the present paper, we study reflection of inclined incident plane waves from a free boundary of the half-space in which the material is described by constitutive equations valid for elastic solids with voids. Both the cases of the transverse and longitudinal incident waves are considered, and it is shown that only the transverse one can propagate in the solid without attenuation, after having been reflected from the free boundary surface. The reflection coefficient and the amplitude of the surface oscillations are expressed in explicit form. The general results are demonstrated for several hypothetical porous materials, and it is shown that the reflection coefficient and the vibration amplitude are typically less than in classical media without voids. However, for relatively large transverse wave speed and high porosity, free boundary oscillation can exceed the classical one.     

Particle-in-Cell Simulation of the Reflection of a Korteweg-de Vries Solitary Wave and an Envelope Solitary Wave at a Solid Boundary

Reflections of a Korteweg-de Vries(KdV) solitary wave and an envelope solitary wave are studied by using the particle-in-cell simulation method.Defining the phase shift of the reflected solitary wave,we notice that there is a phase shift of the reflected KdV solitary wave,while there is no phase shift for an envelope solitary wave.It is also noted that the reflection of a KdV solitary wave at a solid boundary is equivalent to the head-on collision between two identical amplitude solitary waves.     

Uniform asymptotics of the wave diffracted by a cone of arbitrary cross section

In this paper, inspired by V. A. Borovikov’s pioneering work, we study a wave diffracted by a convex cone of arbitrary cross section. Our analysis is focused on the shadow boundary of the wave reflected by the cone surface, where geometric optics yields nonphysical weak singularity. The uniform asymptotic expansion constructed here, which is expressed in terms of the parabolic cylinder functions, is regular at the geometric shadow boundary. Outside the penumbra region, it perfectly matches the ray expansions of the reflected wave, yielding in addition a regular spherical wave, would-be scattered by the cone vertex. Dedicated to the memory of Vladimir Borovikov     

Reflection and transmission phenomena of waves propagating between an isotropic medium and an arbitrarily oriented anisotropic medium

We theoretically analyze waves propagating between an isotropic medium and an anisotropic medium. Closely examining the boundary condition reveals that the phenomenon of nonsymmetrical reflection occurs when the wave propagates from an anisotropic to an isotropic medium. Calculating the reflection of thin films requires correcting the phase change in each reflected trip in the Airy formula. Analytical results of measurement of the elliptical surface of a wave-vector distribution in an anisotropic medium indicate that reflection and transmission still occur when the reflected and the refracted angles are larger than 90 degrees .     

周期镶嵌亥姆霍兹共鸣腔平板的声全背向反射

研究斜入射声波在周期镶嵌亥姆霍兹共鸣器的刚性界面上的反射行为。共鸣器间的空间周期间隔d和入射声波的波长λ相当,且大于共振腔尺寸,因此可被视为具有集总参数的声学元件。理论分析和数值计算均表明,当入射波频率和方向既满足布拉格共振条件又同时满足亥姆霍兹共振条件时,在通常的反射方向上反射声波消失,反射波逆入射方向传播,引起与常规反射全然不同的全背向反射。     

Electrooptic reflection with surface plasmons

Electrooptic reflection with surface plasmons is studied both experimentally and theoretically. An attenuated total reflection (ATR) geometry is used in which a quartz electrooptic crystal onto which a thin Ag film has been evaporated is contacted to the hypotenuse face of a high-index prism. Modulation in the ATR of an He–Ne beam near the angle for surface plasmon excitation is observed when a low-frequency electric field is applied to the quartz crystal. Experiments have been done with both single and multiple boundary surface waves. The angular spectra show phase reversal structure due to the interference of the modulated reflected wave with the ATR wave. The modulated reflectance is calculated directly from a well-known solution to the boundary value problem in nonlinear optics. Good quantitative agreement with the observations is obtained.     

Quantum superarrivals and information transfer through a time-varying boundary

The time-dependent Schrödinger equation is solved numerically for the case of a Gaussian wave packet incident on a time-varying potential barrier. The time evolving reflection and transmission probabilities of the wave packet are computed for several different time-dependent boundary conditions obtained by reducing or increasing the height of the potential barrier. We show that in the case when the barrier height is reduced to zero, a time interval is found during which the reflection probability is larger (superarrivals) compared to the unperturbed case. We further show that the transmission probability exhibits superarrivals when the barrier is raised from zero to a finite value of its height. Superarrivals could be understood by ascribing the features of a real physical field to the Schrödinger wave function which acts as a carrier through which a disturbance, resulting from the boundary condition being perturbed, prpagates from the barrier to the detectors measuring reflected and transmitted probabilities. The speed of propagation of this effect depends upon the rate of reducing or raising the barrier height, thus suggesting an application for secure information transfer using superarrivals.     

Vectorial laws of refraction and reflection using the cross product and dot product

We demonstrate that published vectorial laws of reflection and refraction of light based solely on the cross product do not, in general, uniquely determine the direction of the reflected and refracted waves without additional information. This is because the cross product does not have a unique inverse operation, which is explained in this Letter in linear algebra terms. However, a vector is in fact uniquely determined if both the cross product (vector product) and dot product (scalar product) with a known vector are specified, which can be written as a single equation with a left-invertible matrix. It is thus possible to amend the vectorial laws of reflection and refraction to incorporate both the cross and dot products for a complete specification with unique solution. This enables highly efficient, unambiguous computation of reflected and refracted wave vectors from the incident wave and surface normal.     

单轴晶体内表面入射e光线的双反射

基于光线遵从的Fermat原理,从几何学的角度讨论和分析了在单轴晶体中入射的e光线在界面上的双反射,得到了确定光线反射方向的一般公式,并对几种特殊情况进行了讨论.指出了上述结果与由电磁波的边界条件计算所得结果是一致的.     

表面垂直裂痕诱发瑞利波散射的数值分析

激光激发的声表面波为材料表面缺陷的检测提供了有力的工具.针对含缺陷材料在模型边界上的复杂性,建立了基于平面应变的有限元模型并选取了相同厚度但含有不同深度的表面裂痕的单层铝板进行了对比计算,得到了声表面波经过不同深度的表面裂痕时产生的反射及透射信号波形的时域特征.进而引入了基于Wigner-Ville分布理论的时-频分析方法计算裂痕前、后散射的瞬态表面波的能量在时间-频率平面内分布的情形.结果显示：声表面波接近中心频率的某一频率成分在经过深度小于其中心波长的表面缺陷时,随着裂痕深度的增加,对应于该频率的反射系数呈现单调递增的趋势;而透射系数呈现递减的特征,这一结果可以为激光超声检测表面缺陷提供一种定量的表征手段.     

Plasmons and polaritons in a semi-infinite plasma and a plasma slab

Plasmon and polariton modes are derived for an ideal semi-infinite (half-space) plasma and an ideal plasma slab by using a general, unifying procedure, based on equations of motion, Maxwell's equations and suitable boundary conditions. Known results are re-obtained in much a more direct manner and new ones are derived. The approach consists of representing the charge disturbances by a displacement field in the positions of the moving particles (electrons). The dielectric response and the electron energy loss are computed. The surface contribution to the energy loss exhibits an oscillatory behaviour in the transient regime near the surfaces. The propagation of an electromagnetic wave in these plasmas is treated by using the retarded electromagnetic potentials. The resulting integral equations are solved and the reflected and refracted waves are computed, as well as the reflection coefficient. For the slab we compute also the transmitted wave and the transmission coefficient. Generalized Fresnel's relations are thereby obtained for any incidence angle and polarization. Bulk and surface plasmon-polariton modes are identified. As it is well known, the field inside the plasma is either damped (evanescent) or propagating (transparency regime), and the reflection coefficient for a semi-infinite plasma exhibits an abrupt enhancement on passing from the propagating regime to the damped one (total reflection). Similarly, apart from characteristic oscillations, the reflection and transmission coefficients for a plasma slab exhibit an appreciable enhancement in the damped regime.     

Resonant excitation of intense acoustic waves in crystals

The resonant excitation of an intense elastic wave through nonspecular reflection of a special pump wave in a crystal is described. The choice of the plane and angle of incidence is dictated by the requirement that the excited reflected wave be close to the bulk eigenmode with its energy flow along a free boundary. The resonance parameters have been found for a medium with an arbitrary anisotropy. General relations are concretized for monoclinic, rhombic, and hexagonal systems. A criterion is formulated for an optimal selection of crystals in which the resonant reflection is close to the conversion one, when almost all of the energy from the incident beam of the pump wave falls into the near-surface narrow high-intensity reflected beam. Estimates and illustrations are given for such crystals as an example. The intensity of the reflected beam increases with its narrowing, but its diffraction divergence also increases with this narrowing. Nevertheless, the intensity of the beam can be increased by a factor of 5–10 at sufficiently high frequencies while keeping its divergence at an acceptable level. Amplification by two orders of magnitude can be achieved by compressing the beam in two dimensions through its double reflection.     

Enhanced backscattering of waves reflected from a very rough surface formed by a system of open flat waveguides

A plane wave reflection from a statistically rough surface, which consists of a system of open flat waveguides, is considered in the physical optics approximation. It is shown that for sufficiently deep waveguides the backscattered field is comparable to the specularly reflected field.     

Dispersion of Electromagnetic Waves in a Periodic Ferromagnet-Dielectric Structure

The special features of normal TE mode propagation in a periodic ferromagnet-dielectric structure are investigated. The magnetizing field is parallel to the boundary between the media and perpendicular to the mode propagation direction. The matrix of the structure period transformation, dispersion relation, and energy reflection coefficient are derived by solving the boundary problem for the normal wave incidence on a semi-infinite periodic medium. It is demonstrated that the reflected wave spectrum and characteristics can be controlled by an external field. __________ Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 5, pp. 69–75, May, 2005.