General solution of the coupled-wave equations of acousto-optics

The basic problem of the diffraction of an optical plane wave by an acoustic plane wave in an anisotropic homogeneous medium is considered. The acousto-optical interaction is considered indifferently of the isotropic or of the birefringent type. Coupled-wave equations are obtained rigorously and cast into an eigenvalue value problem. A general solution is obtained for the diffraction efficiency of diffracted orders, for any interaction length and diffraction regime. The theory includes the Bragg regime, the Raman-Nath regime, and all intermediate situations in the same formulation. The method of solution is both exact and computationally efficient. It is similar in character to the rigorous coupled-wave analysis of Moharam and Gaylord but differs by the choice of basis functions adapted to propagating rather than static gratings. Examples are given for acousto-optical interaction in paratellurite, TeO2.     

Asymptotics of a right-angled impedance wedge

The asymptotics of the wave field scattered by a right-angled impedance wedge is considered. The exact complex Sommerfeld-type integral solution for the problem of the diffraction of a plane wave by a right-angled impedance wedge is transformed into a new representation. This new representation is in a form suitable for the asymptotic behaviour to be derived across the specular and shadow boundaries where the usual diffraction coefficient becomes infinite.     

半圆柱型沉积盆地对SH波散射的数值分析

该文实现了一种半无限域SH波散射问题的数值分析方法。采用传递矩阵法得到SH波斜入射时的自由场,将其作为输入;采用集中质量显式有限元方法计算区域内节点的位移;采用透射人工边界计算人工边界点的位移;通过编写的FORTRAN程序实现计算过程。运用该方法对均匀半空间内半圆柱型沉积盆地在SH波入射下的散射进行了分析,与Trifunac M D的解析解进行了对比,验证了该文方法的有效性,分析了不同入射角对地表位移和位移谱放大系数的影响。最后,对成层半空间内半圆柱型沉积盆地在SH波入射下的散射进行了分析。相对于解析方法而言,该方法可以考虑更为复杂地形情况。     

The solution of a mixed boundary value problem in the theory of diffraction

Summary An exact solution is obtained for the problem of the diffraction of a cylindrical sound wave by an absorbent semi-infinite plane. The two faces of the half-plane have different impedance boundary conditions. The problem which is solved is a mathematical model for a noise barrier whose surface is treated with two different acoustically absorbent materials.The usual Wiener-Hopf method (which is the standard technique for solving half-plane problems) has to be modified to give a solution to the present mixed boundary value problem.     

Diffraction of elastic waves by an elliptic crack—II

A recently developed integral equation technique is used to obtain a low frequency solution for the diffraction of a plane compressional or shear wave by an elliptic crack embedded in an elastic medium. The mixed boundary value problem is reduced to a coupled system of integro-differential equations. A formal power series solution for the coupled system of integro-differential equations is developed. Attention is focussed on the farfield scattered amplitudes and the dynamic stress intensity factor. The limiting values when the ellipse degenerates into a circle agree with those of a circular crack.     

Impact response of a finite crack in an orthotropic piezoelectric ceramic

Summary The transient dynamic stress intensity factor and dynamic energy release rate were determined for a cracked piezoelectric ceramic under normal impact in this study. A plane step pulse strikes the crack and stress wave diffraction takes place. Laplace and Fourier transforms are employed to reduce the transient problem to the solution of a pair of dual integral equations in the Laplace transform plane. The solution of the dual integral equations is then expressed in terms of a Fredholm integral equation of the second kind. A numerical Laplace inversion technique is used to compute the values of the dynamic stress intensity factor and the dynamic energy release rate for some piezoelectric ceramics, and the results are graphed to display the electroelastic interactions.     

Half-plane diffraction in a case of oblique incidence

Abstract

The classical problem of half-plane diffraction is examined in a particular case of oblique incidence. A scalar solution to the problem is proposed using boundary diffraction wave theory and some limitations of the solution are discussed.     

Plane wave diffraction by a perfectly transparent half-plane

The exact solution is found for plane wave diffraction by an arbitrary phase step. The analysis is performed by using the Huygens-Fresnel principle and the superposition integral, where every secondary wave was identified with the surface element field of the actual electromagnetic wave. The dependence of the total field structure on the height of the phase step is analyzed. The formation algorithm is demonstrated for the primary wave component of the edge diffraction, which has a singular nature and determines nearly all physical properties of this phenomenon.     

Scale transformation of Maxwell's equations and scattering by an elliptic cylinder

A scale transformation that converts an ellipse into a circle has been suggested in the literature as a method for eliminating the need to evaluate the conventional Mathieu function solution for scattering by an elliptic cylinder. This suggestion is tested by examining the wave equation in the scaled coordinate system and by evaluating the scattering from a thin ellipse for conditions where it is expected that an approximate solution can be obtained using the scalar theory single-slit approximation. It is found that, for a plane electromagnetic wave normally incident on a thin perfectly conducting ellipse, the position of the first minimum in the diffraction pattern, relative to the central axis, differs by approximately a factor of 7 between the single-slit and the scaled theory approach to the problem. The examination of the scaled wave equation and the scattering calculation suggests that, because the scale transformation generates an anisotropic medium, the use of a uniform medium solution in the scaled coordinate system is not appropriate.     

二维金属光栅的矢量模式研究

用矢量模式场来描述二维金属光栅各层中的电磁场。由边界条件,推导出模式场方程组;借助反射透射系数阵递推算法,得出了方程组的解。这种矢量模式方法物理概念清晰且稳定收敛,可以处理任意偏振态平面波入射到二维亚波长金属光栅中的衍射问题。     

Broadband quasi-total autocollimation cross-polarization wave transformation

The problem of diffraction of plane E-and H-polarized waves on a chiral layer supported on a periodic reflective grating composed of rectangular metal rods is solved using the methods of reexpansion and generalized scattering matrices. The diffraction on this structure is accompanied by quasi-total autocollimation cross-polarization wave transformation in a broad frequency band.     

Diffraction of electromagnetic waves by a multielement diffraction grating

A rigorously posed electrodynamical problem of diffraction of a plane wave by a multielement diffraction grating that consists of cylindrical screens with arbitrary curvature is solved by the method of integral equations. We construct an integral representation of the Green function of the problem under consideration which gives a significant increase in the accuracy of calculations and investigate the phenomenon of resonance propagation of an electromagnetic wave along the axis of a two-layer grating irradiated with aE-polarized wave which propagates along the normal to the grating.Karpenko Physicomechanical Institute, Ukrainian Academy of Sciences, L'viv. Translated from Fiziko-Khimicheskaya Mekhanika Materialov, Vol. 31, No. 2, pp. 87–98, March – April, 1995.     

An intermediate range solution to a diffraction problem with impedance conditions

An intermediate range solution for the problem of plane wave diffraction by a finite plate with impedance boundaries is presented. Initially, the problem is expressed in terms of two Wiener–Hopf equations with the help of Fourier transform and the boundary conditions in the transformed domain. The consideration of the intermediate range approximation in terms of source position renders integrals that are generally elusive to tackle because of the presence of branch points. These integrals are evaluated by invoking a modified stationary phase method, thereby a field valid over an intermediate range is calculated. The graphical analysis is preformed for various parameters of physical interest for both intermediate and far-field solutions.     

Analytical solution of the Takagi equations for X-ray backscattering from a cylindrically bent crystal

An approximate analytical solution of the system of Takagi equations for the amplitudes of diffracted and transmitted waves is obtained for the backscattering of a plane X-ray wave from an elastically bent crystal. In the case of diffraction in the reverse direction (strict backscattering), the obtained solution is exact.     

Stress field in a crack on the interface of materials irradiated with SH-waves

On the basis of the solution of the problem of diffraction of a field of plane SH-waves on a crack located on the interface of materials obtained by the authors earlier, we deduce asymptotic expressions for the stress intensity factors at the crack tips. The dependences of the stress intensity factors on the dimensionless crack length, the angle of incidence of the plane wave, and the mechanical and physical properties of the materials are investigated. The possibility of appearance of singularities of the stress intensity factors near the remote crack tip (relative to the source of radiation) for the tangential and critical angles of irradiation is demonstrated. It is shown that, for the critical angles of incidence, these singularities can appear only in perfect materials and that, in the presence of losses, the increase in the stress intensity factors is bounded. It is also demonstrated that the indicated effects are caused by the diffraction interaction of SH-waves with the crack tips. __________ Translated from Fizyko-Khimichna Mekhanika Materialiv, Vol. 43, No. 4, pp. 18–30, July–August, 2007.     

A computational inverse diffraction grating problem

Consider the diffraction of a time-harmonic plane wave incident on a perfectly reflecting periodic surface. A continuation method on the wavenumber is developed for the inverse diffraction grating problem, which reconstructs the grating profile from measured reflected waves a constant distance away from the structure. Numerical examples are presented to show the validity and efficiency of the proposed method.     

Alternative interpretation of the edge-diffraction phenomenon

An alternative interpretation of the phenomenon of edge diffraction is proposed according to a new separation of the Fresnel function. The subfields are investigated in the problem of diffraction of a plane wave by a perfectly conducting half-plane, and the results are compared numerically with other interpretations.     

Wave Theory for a Converging Spherical Incident Wave in an Infinite-aperture System

Abstract

Weyl's formula describes the decomposition of a monochromatic spherical wave into an angular spectrum of plane waves. In this paper, explicit formulae for the separate contributions of homogeneous and inhomogeneous plane waves are given, and the results used to obtain an exact solution to the half-space boundary-value problem for the focusing of a converging spherical incident wave in an infinite-aperture system.     

Diffraction of electromagnetic waves on two spheres: Application to designing antennas for space vehicles

Designing the antenna systems for space vehicles employing electrojet thrusters has to be based on a strict solution of the problem of electromagnetic wave diffraction on two bodies. Here, the problem of diffraction on two spherical surfaces is strictly solved in terms of the scalar field potentials. A method for the transformation of wave amplitudes upon a shift of the spherical coordinate system is proposed. The results of numerical calculations are presented.     

Electromagnetic wave propagation in a plane dielectric layer under critical conditions

An exact solution to the problem of a plane wave propagation in a plane-stratified dielectric layer of arbitrary thickness is studied. An approach based on self-consistent finite differences is suggested, replacing the layer by a stack of homogeneous sublayers of variable thickness matched to the local behavior of the permittivity profile. For the region around zero permittivity, it is predicted that small perturbations of the physical parameters of the problem cause qualitative and quantitative changes in the solution. The conditions for the excitation of a surface wave are formulated. Computed data for the wave are presented.