Scattering of a plane electromagnetic wave by an infinite wedge with a truncated circular cylinder coated coaxially with a magnetodielectric layer

We formulate and solve the problem of scattering of a plane electromagnetic wave by an infinite, perfectly conducting wedge with a truncated, perfectly conducting circular cylinder which is coated coaxially with a magnetodielectric layer and located along the wedge edge. The rigorous solution is obtained and reduced to a system of linear algebraic equations of the second kind for unknown coefficients of Fourier expansions of the scattered field. The results of calculating the scattered field in the far zone with a specified accuracy are presented for the case of an H-polarized wave. It is shown that for certain values of the electric radius of the cylinder, the backscattering cross section of such a structure has pronounced maxima.     

Acoustic scattering by a circular cylinder parallel with another of small radius

The scattering of a plane acoustic wave by an infinite penetrable or impenetrable circular cylinder, parallel with another one, also penetrable or impenetrable, of acoustically small radius, is considered. The method of separation of variables, in conjunction with translational addition theorems for cylindrical wave functions, is used. Analytical expressions are obtained for the scattered pressure field and the various scattering cross sections, for normal incidence. Numerical results are given for penetrable and impenetrable cylinders.     

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.     

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.     

Scattering from a coated nihility circular cylinder placed in chiral metamaterial

The scattering of electromagnetic plane wave from a coated nihility circular cylinder placed in chiral metamaterial is investigated. The nihility cylinder is coated with chiral or chiral-nihility metamaterial and the medium hosting the coated cylinder is also considered as chiral or chiral-nihility metamaterial. The vector wave equation is used to find out the solution for the fields scattered from the concentric chiral ciruclar cylinders immersed in chiral metamaterial. Inner chiral cylinder is reduced to nihility cylinder taking permittivity and permeability approaching to zero with chirality parameter equal to zero. Coated perfect electric conductor (PEC)/perfect magnetic conductor (PMC) are obtained by taking very large value of permittivity/permeability of the inner cylinder. Numerical results for fields reflected from coated nihility cylinder are compared with those obtained for coated PEC/PMC cylinder. Our results for the special case of dielectric coated nihility/PEC cylinders in free space are shown to be in agreement with already published results thus validating the scheme of analysis.     

Three-Dimensional Scattering of an Incident Plane Shear Horizontal Guided Wave by a Partly through-Thickness Hole in a Plate

We investigate the three-dimensional(3D) scattering problem of an incident plane shear horizontal wave by a partly through-thickness hole in an isotropic plate,in which the Lamb wave modes are also included due to the mode conversions by the scattering obstacle in the 3D problem.An analytical model is presented such that the wave fields are expanded in all of propagating and evanescent SH modes and Lamb modes,and the scattered far-fields of three fundamental guided wave modes are analyzed numerically for different sizes of the holes and frequencies.The numerical results are verified by comparing with those obtained by using the approximate Poisson/Mindlin plate model for small hole radius and low frequency.It is also found that the scattering patterns are different from those of the SO wave incidence.Our work is useful for quantitative evaluation of the plate-like structure by ultrasonic guided waves.     

Acoustic scattering by an elastic elliptic cylinder in water: numerical results and experiments

The acoustic scattering from an elastic elliptic cylinder immersed in water and excited by a normally incident plane wave is considered in this paper. The purpose is to determine, theoretically and experimentally, the pressure scattered by this cylinder. A model based on the theory of elasticity is described briefly. It consists in carrying out expansions in Fourier series of the expressions relating to the conditions of continuity (displacements and constraints) at the surface of cylinder. These expressions form a system of equations. The resolution of this system enables us to obtain the scattering coefficient, then the pressure scattered by the cylinder. The numerical results obtained from this model are compared with experimental results obtained by means of an experimental short-pulse method presented in the literature. An good agreement between the results is noted.     

The projection approximation versus an exact solution for X-ray phase contrast imaging, with a plane wave scattered by a dielectric cylinder

We show that exact solutions for an X-ray plane wave scattered by a dielectric cylinder with radius large compared to the radiation wavelength, give almost the same intensity fringes as seen when using the projection approximation (PA) to simulate propagation based phase contrast imaging. The characteristic Argand plane Cornu spiral and hypocycloid from the complex wavefield beyond the cylinder was observed to agree with the PA simulations. Asymptotic approximations to the exact analytical solution simplify to the projection approximation at the centre of the cylinder. The projection approximation underestimates observed fringes at a propagation distance comparable with the cylinder radius, but converges to the exact solution at larger propagation distances. This demonstrates that the complex ray approach of the projection approximation is insufficient, in comparison to the exact approach, when the propagation distances are sufficiently small.     

Electromagnetic scattering from a two dimensional perfect electromagnetic conductor (PEMC) strip and PEMC strip grating simulated by circular cylinders

Electromagnetic scattering of an incident plane wave from a rectangular strip and strip grating, are presented semi-analytically. The strip and strip grating are simulated by joining parallel perfect electromagnetic conductor (PEMC) circular cylinders and are illuminated by a TM_z incident plane wave. The PEMC medium does not allow electromagnetic energy to enter. An interface of this medium serves as an ideal boundary to the electromagnetic field. The solution is based on the application of the boundary conditions on the surface of each cylinder in terms of its local coordinate system. The technique is used to predict the scattered field pattern of PEMC strip and PEMC strip grating.     

Diffraction and scattering of TM plane waves from a binary periodic random surface

This paper deals with the diffraction and scattering of a TM plane wave from a binary periodic random surface generated by a stationary binary sequence using the stochastic functional approach. The scattered wave is represented by a product of an exponential phase factor and a periodic stationary process. Such a periodic stationary process is regarded as a stochastic functional of the binary sequence and is expressed by an orthogonal binary functional expansion with band-limited binary kernels. Then, hierarchical equations for the binary kernels are derived from the boundary condition without approximation. We point out that binary kernels obtained by a single scattering approximation diverge unphysically when the periodic random surface is zero on average, thus the effects of multiple scattering should be taken into account. The expressions of such binary kernels are obtained using the multiply renormalizing approximation. Then, statistical properties such as differential scattering cross-section and the optical theorem are numerically calculated with the first two order binary kernels and illustrated in the figures. It is found that the incoherent Wood's anomaly appears in the angular distribution of scattering even when the surface has zero average.     

具有轨道角动量光束入射下的单球粒子散射研究

根据广义Mie理论,研究了具有轨道角动量拉盖尔-高斯光束（LGB）的空间传输特性以及单粒子散射特性.在单体球粒子对高斯光束散射研究的基础上,分析了在自由空间不同传输距离LGB光束的光强分布情况,在不考虑散射和波束相移关系的情况下,将LGB作为入射高斯光束,通过对波束入射时的散射衰减截面求解得到波束因子,利用矢量球谐函数对入射高斯波束进行展开,从而研究了单球粒子在在轴条件下对具轨道角动量高斯波束入射的散射问题.通过数值计算,讨论了散射强度及角分布在不同波束宽度情况下对其散射特性的影响,并与平面波的情况做了对比.结果表明,当波束束腰半径较小时,束腰半径对衰减率的影响较大,而当束腰半径远大于粒子半径时,接近于平面波的情况. 关键词： 广义Mie理论 轨道角动量 Laguerre-Gauss光束 单球粒子     

修正一阶Born近似改进水中弱散射目标的散射声场预报

在推导Fourier衍射定理中运用一阶Born近似时忽略了弱散射体内外的波数差异,使散射声场方向特性的预报产生较大误差,针对这一问题,对一阶Born近似进行修正。考虑散射体内外波数差异引起的幅度和相位误差,通过调整频域采样圆弧半径并移动圆心位置得到了修正的一阶Born近似解。由于更准确地反映了目标与周围水介质的声学性质,有效提高了散射声场的预报精度。根据修正的Born近似计算了弱散射条件下无限长圆柱目标的散射远场指向性,结果与严格解相吻合,对其它形状截面的柱状目标也得到了合理的计算结果。      

Application of the mutual-interaction method to a class of two-scatterer systems: I. Two discrete scatterers

In a recent paper we developed a formalism that fully accommodates the mutual interactions among scatterers separable by parallel planes. The total fields propagating away from these planes are the unknowns of a system of difference equations. Each scatterer is characterized by a scattering function that expresses the scattered wave amplitude as a function of the incident and scattered wavevectors for a unit-amplitude plane wave scattered from the object in isolation. This function can be derived completely from the scattered far field with the help of analytic continuation. For a two-scatterer system the mutual-interaction equations reduce to a single Fredholm integral equation of the second kind. It turns out that analytic solutions are tractable for those scattering functions that are Dirac deltas or a sum of products of separable functions of the incident and scattered wavevectors. Scattering functions for planes and isotropic scatterers, as well as electric and magnetic dipoles all possess this property and are considered. The exact scattering functions agree with results obtained by analytic continuation. This paper consists of two parts. Part I derives analytic solutions for two discrete scatterers (isotropic scatterers. electric dipoles, magnetic dipoles). Part II is devoted to scattering from an object (isotropic or dipole scatterer) near an interface separating two semi-infinite uniforn-media. Because the results in this paper are exact, the effects of near-field interactions can be assessed. The forms of the scattering solutions can be adapted to objects that are both radiating and scattering.     

Wave diffraction by a concave statistically rough surface

We consider a statistically rough impedance surface that is concave on average in contrast to a plane. Backscattering from such a surface is considered based on the small perturbation theory method. The diffraction problem is divided into two parts which are considered separately: the problem of scattering by small roughness (assumed to be local) and the propagation of incident and scattered fields over a smooth large-scale concave surface. In contrast to the 'two-scale' scattering model, the zero-order unperturbed wavefield is not assumed to be specularly reflected from the local tangent plane to the smooth surface, but it is a solution of a corresponding diffraction problem. Two particular cases of smooth surfaces are considered: first, the inner surface of a concave cylinder with a constant radius and finite angular pattern, and second, a compound surface that consists of a coupled half-plane and the cylindrical surface mentioned above. In a geometrical optics limit and with propagation at low grazing angles, the analytical results for a zero-order (unperturbed) field are obtained for these two cases in the form of a series over multiple specular reflected fields. It is shown that these non-local processes lead to the essential increase in the backscattering cross section in comparison with the two-scale model and tangent-plane approach.     

Application of the mutual-interaction method to a class of two-scatterer systems: I. Two discrete scatterers

Abstract

In a recent paper we developed a formalism that fully accommodates the mutual interactions among scatterers separable by parallel planes. The total fields propagating away from these planes are the unknowns of a system of difference equations. Each scatterer is characterized by a scattering function that expresses the scattered wave amplitude as a function of the incident and scattered wavevectors for a unit-amplitude plane wave scattered from the object in isolation. This function can be derived completely from the scattered far field with the help of analytic continuation. For a two-scatterer system the mutual-interaction equations reduce to a single Fredholm integral equation of the second kind. It turns out that analytic solutions are tractable for those scattering functions that are Dirac deltas or a sum of products of separable functions of the incident and scattered wavevectors. Scattering functions for planes and isotropic scatterers, as well as electric and magnetic dipoles all possess this property and are considered. The exact scattering functions agree with results obtained by analytic continuation. This paper consists of two parts. Part I derives analytic solutions for two discrete scatterers (isotropic scatterers. electric dipoles, magnetic dipoles). Part II is devoted to scattering from an object (isotropic or dipole scatterer) near an interface separating two semi-infinite uniforn-media. Because the results in this paper are exact, the effects of near-field interactions can be assessed. The forms of the scattering solutions can be adapted to objects that are both radiating and scattering.     

Wave diffraction by a concave statistically rough surface

Abstract

We consider a statistically rough impedance surface that is concave on average in contrast to a plane. Backscattering from such a surface is considered based on the small perturbation theory method. The diffraction problem is divided into two parts which are considered separately: the problem of scattering by small roughness (assumed to be local) and the propagation of incident and scattered fields over a smooth large-scale concave surface. In contrast to the ‘two-scale’ scattering model, the zero-order unperturbed wavefield is not assumed to be specularly reflected from the local tangent plane to the smooth surface, but it is a solution of a corresponding diffraction problem. Two particular cases of smooth surfaces are considered: first, the inner surface of a concave cylinder with a constant radius and finite angular pattern, and second, a compound surface that consists of a coupled half-plane and the cylindrical surface mentioned above. In a geometrical optics limit and with propagation at low grazing angles, the analytical results for a zero-order (unperturbed) field are obtained for these two cases in the form of a series over multiple specular reflected fields. It is shown that these non-local processes lead to the essential increase in the backscattering cross section in comparison with the two-scale model and tangent-plane approach.     

Fast prediction of scattered sound field based on Fourier diffraction theory under second-order born approximation

The directional pattern of sound waves scattered from an object insonified by a plane wave can be efficiently predicted using the Fourier diffraction theorem (FDT). This is achieved by sampling a circle in the discrete Fourier transform of the object/medium distribution. However, the FDT-based approach under the first-order Born approximation is only applicable to weak scattering. To improve the prediction accuracy and expand the method’s scope of applications, we introduce a second-order correction term to the solution, which is obtained by taking the first-order scattered waves as secondary incident sources, and calculate the “scattering” in the same way as in the first-order FDT-based approach. Adding the resulting correction term to the directional pattern based on the first-order Born approximation, the second-order prediction is obtained. Numerical results show that the proposed method can provide improved directional patterns of the scattered waves, and the range of applicability is significantly expanded.     

任意形状凸粗糙物体高斯光束相干散射研究

研究了任意形状凸粗糙物体对高斯光束的相干散射特性。由平面波谱展开法推导出粗糙面高斯波束散射场表达式．并根据物理光学近似和稳相法原理得到相干散射截面的理论公式。与平面波解不同的是,在公式中引入了波束因子这一表征波束作用的重要参量,该参量与束腰半径、束腰中心与物体中心距离和物体照射面积以及入射、散射方向有关。最后数值计算了1．06μm激光波束对粗糙球的散射,分析了波束因子．介电常量和极化状态对红外激光相干散射截面的影响,重点讨论了波束因子的变化规律。分析表明．当波束半径远大于物体尺寸时,波束入射的结果可退化到平面波情况。     

两个相邻目标对平面波、高斯波束的光散射

基于等效原理和互易性定理研究了两个靠近目标对平面波、高斯波束的光散射问题,给出了这一复合光散射模型的二阶散射结果。通常一阶散射结果容易求解,但由于耦合效应的复杂性,很难给出二阶散射结果的解析形式。为了解决这一问题,应用互易性定理给出了求解任意相邻介质目标二阶散射场的公式,同时借助等效原理将求解散射场公式中的体积分简化为面积分的形式,从而降低了求解难度。求解了两相邻球形粒子的复合散射场,并将求解结果与应用时域积分方程法求得的结果进行了比较。同时,还讨论了束腰半径、目标位置对散射截面及偏振度的影响。     

Scattering of evanescent electromagnetic waves by a cylinder near the flat boundary: the Green function and fast numerical method

The scattering of plane evanescent waves by a cylinder is studied. The Green function for the Helmholtz equation for two dielectrics with flat interface is found and applied for the numerical calculation of the scattered field by the boundary elements method. The Green function keeps close track of scattering, including multiple reflections. The result may be applicable for the data analysis in near-field optical microscopy.