Plane Wave and Gaussian Beam Scattering by Long Dielectric Cylinders: 2.5D Simulations versus Measurements

For the development of millimeter wave imaging systems, it is important to be able to simulate some representative scattering configurations. Typically, Gaussian beams are used in active imaging systems. Since these beams only illuminate a spatially limited region, many objects can be treated as infinitely long 2D (in)homogenous cylinders. However, the incident Gaussian beams have a 3D character. Therefore, a dedicated 2.5D scattering simulator was developed. In this paper, simulation results obtained with this simulator are compared to measurements obtained from a bi-static microwave set-up and from a W-band millimeter wave set-up. Comparison of simulations and measurements proves that the 2.5D algorithm is a good simulation tool to study scattering of long inhomogeneous cylinders, illuminated by 3D plane waves or 3D Gaussian beams under different elevation angles.     

Quadratic cross-sections in the multiple scattering by a pair of liquid cylinders insonified by arbitrary-shaped acoustical sheets

Stemming from the law of energy conservation applied to scattering, generalized exact partial-wave series expressions are derived for the extrinsic and intrinsic acoustic scattering, extinction and absorption cross-sections for a pair of fluid/liquid-like (viscous) cylinders of arbitrary radii. The incident insonifying field is of arbitrary shape such that any structured wavefront in two-dimensions is accomodated by this formalism, in contrast with the case of plane waves. The modal expansion method in combination with the translational addition theorem for cylindrical wave functions are used to derive the exact analytical expressions for the quadratic (nonlinear) cross-sections, and numerical computations for a non-paraxial focused Gaussian acoustical sheet chosen as an example illustrate the analysis. The results clearly show the difference between the behavior of the extrinsic and intrinsic cross-sections. The formalism presented here is generalized for any acoustical sheet such that Airy, Hermite-Gaussian and other wavefronts (in 2D) can be considered provided the appropriate beam-shape coefficients are used. The analogy with the optical counterpart is also noted.     

An investigation of transmission coefficients for finite and semi-infinite coupled plate structures

This paper introduces a method for determining the transmission coefficient for finite coupled plates using an analytical waveguide model combined with a scattering matrix. In the scattering matrix method, the amplitudes of the structural waves impinging on a junction are separated into incident, reflected, and transmitted components. The energy flow due to each of these waves is obtained using a wave impedance method, which is subsequently used to determine the transmission coefficient. Transmission coefficients for semi-infinite and finite L-shaped plates are investigated for single and multiple point force excitations, and for controlled incident wave sources. It is shown that the transmission coefficients can also be calculated from details of the modal transmission coefficients and the modal composition of the energy incident on the junction. Results show that the modal transmission coefficients are largely independent of whether the plates have finite or semi-infinite boundary conditions, and are only dependent on the details of the coupling. Finally, frequency averaged transmission coefficients are compared for semi-infinite and finite structures. In the cases considered, it is found that the semi-infinite system is a good approximation for finite systems after frequency averaging, especially if the system is excited with multiple point force excitation.     

A General Spectral-Domain Formulation of the Electromagnetic Scattering by a Perfectly Conducting Circular Cylinder

A full-wave method for the two-dimensional scattering problem by a perfectly conducting circular cylinder is presented, providing an exact solution for the Helmholtz equation in very general cases. The method is based on the Fourier series expression of the boundary conditions (Dirichlet and Neumann) generated by an arbitrary, finite-power, incident beam, and the analysis is performed in the complex plane of the analytic continuation of a space spectral variable. This approach allows us to define an analytic continuation for cylindrical wave expansions, working with lossy propagation media and with a full incident spectrum, including inhomogeneous waves, both in E and in H polarization. Convergence of the modal expansion is investigated, to verify that very weak hypotheses are needed, and no geometrical or paraxial approximation is required. Extact expressions for the expansion coefficients are given, in terms of complex intergrations involving the Fourier spectrum of the incident beam.     

Extremely asymmetrical scattering of slab modes in periodic Bragg arrays

The steady-state extremely asymmetrical scattering of electromagnetic modes in a slab with a periodically corrugated boundary is analyzed theoretically. A new approach, based on allowance for the diffractional divergence of a scattered wave, is used with the approximation of slowly varying amplitudes and a Fourier analysis. The structure of the incident and scattered waves inside and outside the array is determined. The amplitudes of the scattered waves are found to be much larger than the amplitude of the incident wave. The typical time of relaxation to steady-state scattering is found to depend on the distance from the array boundary through which the incident wave enters the array. Conditions of applicability of the results obtained are also presented.     

Truncating cylindrical wave modes in two-dimensional multiple scattering

When analyzing the two-dimensional multiple scattering of electromagnetic waves by cylinders, the incident, scattered, and transmitted fields need to be represented by infinite sums of cylindrical wave modes. These infinite sums need to be truncated to a finite limit in order to calculate the scattering matrix. The accuracy of the scattered field representation and the stability of the matrix inversion are both critically dependent on the truncation limit. The parameters involved in the scattering are analyzed to determine their effect on the upper and lower bounds of an appropriate modal truncation.     

The scattering of guided waves in partly embedded cylindrical structures

The scattering of ultrasonic guided waves at a point where a free cylindrical waveguide enters an embedding material is investigated. A modal solution that is valid when the guided waves are incident from the free section of the waveguide is developed. It is shown that in this case it is valid to consider only the modal fields over the cross section of the waveguide, neglecting the fields in the embedding material. As an application, the scattering of the lowest-order longitudinal mode in a cylindrical waveguide, L(0,1), is examined in detail. As well as considering epoxy resin as an embedding material, the case where the embedding material is replaced by a perfectly rigid boundary is discussed. The latter gives some insight into the role of nonpropagating and inhomogeneous waveguide modes in the scattering process. The results from the modal solution are validated using Finite Element modeling, very good agreement being obtained.     

Phase velocities of plane waves in a pipe with a flow whose velocity varies along the radius

The phase velocities of plane waves in a pipe filled with a moving acoustic medium are studied for different laws of flow velocity variation along the pipe radius. The wave equation is solved by the discretization method, which breaks the entire pipe volume into individual cylinders under the assumption that, within each of the cylinders, the flow velocity of the medium is constant. This approach makes it possible to reduce the solution to the wave problem to solving Helmholtz equations for individual cylinders. Based on boundary conditions satisfied at the boundaries between neighboring cylinders, a homogeneous system of linear algebraic equations is obtained. From this system, with the use of the scattering matrices, a simple dispersion equation is derived for determining the phase velocities of plane waves. The stability of the numerical solution to the dispersion equation with respect to the number of cylinders is investigated. The phase velocities of quasi-homogeneous and inhomogeneous waves in a pipe are numerically calculated and analyzed for different velocities of a moving medium and different laws of flow velocity variation along the radius. It is shown that the variation that occurs in the phase velocity of a homogeneous plane wave in a pipe due to the motion of the medium is identical to the mean flow velocity for different laws of flow velocity variation along the radius. For inhomogeneous plane waves, the phase velocity increment exceeds the mean flow velocity several times and depends on both the law of wave amplitude distribution along the radius and the law of the flow velocity variation along the radius.     

Scattering of bulk acoustic waves with different polarizations on a statistically rough free surface of a solid at oblique incidence

In the first Born approximation of the perturbation theory by a Green's function method developed by Maradudin, Mills [7] and Kosachev, Lokhov, Chukov [8,9] the problem of scattering bulk acoustic waves with different polarizations at oblique incidence on a statistically rough free boundary of an isotropic solid was solved. When the correlation function of the surface roughness is of a Gaussian form, the expressions for the transformation energy factor of the incident wave in the scattered volume and surface Rayleigh waves with respect to polarization, frequency and grazing angle of the incident wave as well as the roughness parameters and the Poisson coefficient of the medium were obtained. These results are helpful in accounting for the experiments on residual losses [15–17].     

A stationary phase argument for the modal wave beam deviation in the time-space domain for anisotropic multilayered media

The aim of the paper is to describe the physical phenomenon of the excitation of modal waves, such as Lamb waves, in anisotropic multilayered media by a monochromatic incident beam and then by a time depending signal. A modal beam is generated in the structure and, due to the anisotropy of the media constituting the structure, is deviated with respect to the sagittal plane of the incident bounded beam. Using a stationary phase approach, it is possible to determine the deviation direction of the modal beam in the far field at a given frequency. This direction is normal to the modal curve, at the point corresponding to the main modal wave vector. Using Lagrange multipliers, it is possible to obtain the equation of an oblique plane in which the modal beam reradiates in the external fluid. As the modal waves are dispersive, the group velocity and the direction of propagation of the principal modal wave vary with the frequency. So, in the far field, for a time depending signal, the different monochromatic components of the main modal wave are found in different directions. In general, the main crest line of this modal wave packet is not a straight line.     

平行柱体对平面波/高斯波束电磁散射

基于等效原理和互易性定理，研究了N个相互平行二维柱体对平面波/高斯波束的电磁散射特性，给出了求解N阶散射场公式.一阶散射可通过求解单个柱体的散射场得到，但对于高阶散射场而言，由于耦合散射的复杂性，很难给出精确的解析解.为了解决这一问题，借助等效原理和互易性定理给出了求解N阶散射场的面积分公式.只要给出柱体的i-1阶散射场及相关目标表面上的等效电流和(或)等效磁流，就可应用此公式求解i阶散射场.应用该近似方法计算了相互平行非均匀等离子体涂层导体圆柱的单/双站散射宽度，讨论了束腰半径、等离子体涂层厚度、电子密度、碰撞频率及雷达频率等对散射结果的影响.     

Debye series expansion of shaped beam scattering by GI-POF

We derive Debye series expansion (DSE) for infinitely long multilayered cylinders normally incident by shaped beam. Typically the interaction between multilayered cylinders and Gaussian beam is derived in detail, and localized approximation is introduced to calculate the beam shaped coefficients. Finally DSE is employed to the study of rainbow scattering by graded-index polymer optical fiber (GI-POF).     

Acoustic scattering by multiple elliptical cylinders using collocation multipole method

This paper presents the collocation multipole method for the acoustic scattering induced by multiple elliptical cylinders subjected to an incident plane sound wave. To satisfy the Helmholtz equation in the elliptical coordinate system, the scattered acoustic field is formulated in terms of angular and radial Mathieu functions which also satisfy the radiation condition at infinity. The sound-soft or sound-hard boundary condition is satisfied by uniformly collocating points on the boundaries. For the sound-hard or Neumann conditions, the normal derivative of the acoustic pressure is determined by using the appropriate directional derivative without requiring the addition theorem of Mathieu functions. By truncating the multipole expansion, a finite linear algebraic system is derived and the scattered field can then be determined according to the given incident acoustic wave. Once the total field is calculated as the sum of the incident field and the scattered field, the near field acoustic pressure along the scatterers and the far field scattering pattern can be determined. For the acoustic scattering of one elliptical cylinder, the proposed results match well with the analytical solutions. The proposed scattered fields induced by two and three elliptical–cylindrical scatterers are critically compared with those provided by the boundary element method to validate the present method. Finally, the effects of the convexity of an elliptical scatterer, the separation between scatterers and the incident wave number and angle on the acoustic scattering are investigated.     

水中密排圆柱体群的超声多重散射参数

以水中紧密排列的平行圆柱体群为对象,研究平面超声脉冲经多重散射后的透射波性质,通过分析其中头波和散射波的特征获得对应的多重散射参数.对直径随机分布、位置无序排列、数量密度约100个/cm2、面积占空比约0.53的非接触圆柱体群,采用中心频率2.5 MHz的宽带脉冲波入射。为解决透射信号在时域表现出随机性的问题,将散射体尺寸、分布都相同但位置分布不同的多个模型仿真的透射波叠加平均后用于分析.在频域对头波的宽带衰减系数进行分析,并在时域研究散射波声强的时间演化曲线,获得了系统的弹性平均自由程、传输平均自由程等多重散射参数。经多重散射后,透射波中的头波表现出相干性,由不相干近似理论可对其对应的散射参数进行定性描述;散射波是不相干的,其对应的多重散射参数可近似利用扩散近似理论获得。      

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.     

Correlation between helical surface waves and guided modes of an infinite immersed elastic cylinder

Scattering of obliquely incident plane acoustic waves from immersed infinite solid elastic cylinders is a complex phenomenon that involves generation of various types of surface waves on the body of the cylinder. Mitri [F.G. Mitri, Acoustic backscattering enhancement resulting from the interaction of an obliquely incident plane wave with an infinite cylinder, Ultrasonics 50 (2010) 675-682] recently showed that for a solid aluminum cylinder, there exist acoustic backscattering enhancements at a normalized frequency of ka?0.1. The incidence angle α_c at which these enhancements are observed lies between the first (longitudinal) and second (shear) coupling angles of the cylinder. He also confirmed the observations previously reported by the authors that there exist backscattering enhancements of the dipole mode at large angles of incidence where no wave penetration into the cylinder is expected. In this paper, physical explanations are provided for the aforementioned observations by establishing a correlation between helical surface waves generated by oblique insonification of an immersed infinite solid elastic cylinder and the longitudinal and flexural guided modes that can propagate along the cylinder. In particular, it is shown that the backscattering enhancement observed at ka?0.1 is due to the excitation of the first longitudinal guided mode travelling at the bar velocity along the cylinder. It is also demonstrated that the dipole resonance mode observed at incidence angles larger than the Rayleigh coupling angle is associated with the first flexural guided mode of the cylinder. The correlation established between the scattering and propagation problems can be used in both numerical and experimental studies of interaction of mechanical waves with cylinders.     

Gauss声束对离轴椭圆柱的声辐射力矩

利用部分波展开法求解得到了Gauss声束入射下刚性和非刚性椭圆柱的声散射系数,推导了一般情况下的声辐射力矩表达式.在此基础上,通过一系列数值仿真详细分析了离轴距离、入射角度和束腰半径对声辐射力矩的影响.结果表明:正向与负向声辐射力矩均可以在一定条件下存在;低频情况下刚性椭圆柱比非刚性椭圆柱更容易产生较强的声辐射力矩;特定频率的入射声场可以激发出非刚性椭圆柱不同阶的共振散射模式,因而非刚性椭圆柱的声辐射力矩峰值与频率的关系更密切;增加束腰半径有利于扩大散射截面,进而增加椭圆柱的声辐射力矩.该研究结果预期可以为利用声辐射力矩实现粒子的可控旋转和流体黏度的反演提供一定的理论指导.     

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.     

Spontaneous emission and elastic scattering of light from quantum-well excitons in a Fabry-Perot microcavity

A theory of spontaneous emission and elastic light scattering by quasi-two-dimensional excitons in a quantum well placed in a Fabry-Perot microcavity is developed. The problem is solved by means of electrodynamic Green’s functions with inclusion of fluctuations of the quantum-well width and cavity wall shape treated as a perturbation. General expressions are found in a zero approximation of perturbation theory (plane interfaces) for the radiative decay rates of quasi-two-dimensional excitons and for their energy shifts in the cavity. The boundary conditions for the electromagnetic field are taken into account through the coefficients of inward light reflection from the cavity walls. Resonance contributions to the scattering cross sections, which differ in the polarizations (p or s) of the incident and scattered waves, are derived in the lowest (Born) approximation in quantum-well width fluctuations. The spectral and angular dependences of elastic light scattering are studied numerically for Gaussian and exponential correlation functions. It is shown that the contribution from quantum-well width fluctuations to light scattering exceeds that due to single interfaces (surfaces) of a heterostructure by two orders of magnitude.     

A wavepacket approach to gas-surface scattering: Application to surfaces with imperfections

A time dependent wavepacket approach is applied to diffractive scattering from surfaces with imperfections. This semiclassical method is based on Gaussian wavefunctions whose average positions and momenta are those of classical trajectories. The approach can be applied to arbitrary potentials. Positions, shapes and magnitudes of the diffraction peaks are obtained in a single calculation. In a first example the wavepacket method is applied to a stepped surface. The diffraction pattern is calculated for different incident scattering angles and for various regular and random distributions of steps with two different sizes. Second, the approach is used to study the scattering for an interaction potential modeling a corrugated surface with adsorbed atoms. The diffraction intensities are examined for several final scattering directions and again for regular and random arrangements of the adsorbed atoms.