Specular propagation over rough surfaces: numerical assessment of Uscinski and Stanek's mean Green's function technique

The purpose of this paper is to numerically evaluate the effectiveness and accuracy of Uscinski and Stanek's mean Green's function technique for computing the mean field of a wave scattered by a rough surface. We present here a direct comparison of this technique with a rigorous numerical method, the forward scattering integral equation method, and another analytical method, the first-order smoothing approximation. Furthermore, we compare the roughness generated equivalent admittance using the three methods. Numerical computations reveal that the scattered field calculated by this technique is not accurate particularly for the equivalent admittance at low grazing angles, even though the mean surface current density is recovered when the wave has traversed several correlation lengths on the surface.     

Absorption of flexural waves by a pair of mechanical resonator chains mounted on a plate

The scattering of flexural waves by two chains of mechanical resonators characterized by effective admittances is considered. In the first (lower) chain, the effective admittance is represented by a susceptance, whereas, in the second (upper) chain, the resonators are characterized by a complex admittance. The spatial periods of the chains are identical. A plane harmonic flexural wave is obliquely incident on the upper chain, and the scattered field formed by the chains is expressed as a superposition of homogeneous and inhomogeneous Bragg spectra. Intense scattering of the incident wave only occurs in the case of mutual compensation of the resonator susceptance and the radiation admittance. A pair of chains with periods not exceeding the half-wavelength of the flexural wave represents an effective insulator for this wave. In the half-space behind the first chain, the zeroth spectral component of the scattered field completely cancels the resonance-frequency incident flexural wave. Let the second chain be positioned at one of the displacement antinodes of the total field formed by the incident field and the zeroth scattered spectrum. Then, if the active components of the effective admittance of resonators belonging to the second chain are identical to the radiation admittance, the incident flexural wave is completely absorbed by the resonators.     

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.     

采用球面波叠加法还原自由声场的方法

为解决非自由声场中近场声全息重建时,干扰声在目标声源表面产生的散射影响,提出一种基于球面波叠加法的自由场还原技术。该技术首先采用基于球面波叠加法的声场分离技术获得向内和向外传播的声场,然后以目标声源的表面导纳作为边界条件,实现目标声源辐射声和散射声的分离,从而获得等效于自由声场的测量条件。该技术为准确实现非自由声场中的噪声源识别创造了条件。文中首先详细描述了该技术的基本原理,并提出一种最优球面波展开项数选取方法,最后通过数值仿真说明了该技术的有效性。结果表明:在频率较低时,散射声影响较小,采用声场分离技术和自由场还原技术效果相当;但随着频率升高,散射声影响逐步增强,必须采用自由场还原技术才能准确获得目标声源辐射声。      

Recovery of the free field in noisy environment by using the spherical wave superposition method

To remove the scattering effect of the disturbing sound on the target source when implementing nearfield acoustic holography in a non-free field, a free field recovery technique based on the spherical wave superposition method is proposed. In the method, the sound field separation technique based on the spherical wave superposition method is first used to separate the incoming and outgoing fields, and a further step for separating the radiated and scattered fields is performed by utilizing the surface admittance of the target source as the boundary condition. The technique makes it possible to correctly identify noise sources in a non-free sound field. The basic principle of the technique is described firstly, a method for choosing the optimal number of spherical wave expansion terms is given, and two numerical simulations are used to demonstrate the validity of this technique. It is shown that, for the lower frequency, the scattering effect can be neglected, and the radiated field of the target source can be obtained by the sound field separation technique, however, as the increasing of the frequency, the scattering effect cannot be neglected, and the free field recovery technique has to be used to obtain the radiated field of the target source.     

Scattering of a Rayleigh surface acoustic wave by a small-size inhomogeneity in a solid half-space

We use the Born approximation of the perturbation method to solve the problem of scattering of a harmonic Rayleigh surface acoustic wave by a weak-contrast inhomogeneity that is small compared with the wavelength and is located in a solid half-space near its boundary. The material of the inhomogeneity differs from the material of the half-space only in its density. The Rayleigh wave incident on the inhomogeneity is excited by a monochromatic surface force source acting normally to the half-space boundary. We derive expressions for the displacement fields in the scattered spherical compressional and shear (SV- and SH-polarized) waves. Scattering of the Rayleigh wave into a Rayleigh wave is studied in detail. We find expressions for the vertical and horizontal components of the displacement vector in the scattered Rayleigh wave as well as its radiated power. It is shown that the field of the scattered surface wave is mainly formed by vertical oscillations of the inhomogeneity in the field of the incident wave. In this case, the radiated power for the scattered Rayleigh wave formed by vertical motion of the inhomogeneity in the incident-wave field depends on the depth of the inhomogeneity as the fourth power of the function describing the well-known depth dependence of the vertical displacements in the Rayleigh surface wave. Correspondingly, the dependence of the radiated power for the scattered Rayleigh wave formed by horizontal motion of the inhomogeneity depends on its location depth as the fourth power of the depth dependence of the horizontal displacements in the Rayleigh surface wave. We perform calculations of the ratio between the powers of the scattered and incident Rayleigh waves for different ratios between the velocities of the compressional and shear waves in a solid. It is shown that the radiated power for the scattered surface wave decreases sharply with increasing depth of the subsurface-inhomogeneity location. Thus, the scattering of a Rayleigh wave into a Rayleigh wave is fairly efficient only when the location depth of the inhomogeneity does not exceed about one-third of the wavelength of the shear wave in an elastic medium.     

Sound diffraction at Sierpinski carpet

The sound field scattered by a fractal surface in the form of a Sierpinski carpet is calculated in the framework of the perturbation method. The Sierpinski carpet has an alternating acoustic admittance preset at its squares, which sequentially scale down. It is demonstrated that such a Sierpinski carpet scatters sound almost uniformly in all directions.     

Acoustic scattering from a rough sea surface: the mean field by the integral equation method

The scattering of an acoustic signal incident from below at low angles on a rough sea surface is treated by the integral equation method in the parabolic approximation. Equations are obtained allowing the mean scattered field to be calculated even when the surface causes a large phase modulation in the incident wave. Solutions are found using the method of Laplace transforms and some results are presented for a specific type of rough surface.     

Average scattered field from a random PEC cylinder buried below a slightly rough surface

Scattering from a perfect electric conducting cylinder with random radius buried below a half space dielectric homogenous interface is studied. The cylindrical wave scattered by cylinder is expanded in terms of plane wave spectrum. Small perturbation method is used to study the interaction of each plane wave with the interface. The zeroth order term yields solution for a flat interface, whereas scattering from a rough surface is given by first-order term. Results are obtained for both TM and TE polarizations. Analytical expressions of the average scattered field are obtained and verified using numerical evaluation. Different scattering scenarios are simulated by varying the distribution of the radius. It is observed that average scattering cross section of an ensemble with normal/uniform distribution is almost equal to that of a cylinder with mean radius.     

一种半导体表面上微粒缺陷散射场的计算方法

本文通过分析半导体表面上微粒缺陷散射场的光波传播规律,建立了表面上微粒缺陷场的传输模型和数学模型,使定量计算表面上微粒缺陷的散射场成为可能。进一步将入射场和散射场都表达成球矢量波函数的形式,并考虑表面的二次散射作用,用T矩阵将入射场和散射场的展开项系数连系起来。从而得到散射场与入射场之间的一系列定量表达式,并给出计算结果。     

Acoustic scattering from a rough sea surface: the mean field by the integral equation method

Abstract

The scattering of an acoustic signal incident from below at low angles on a rough sea surface is treated by the integral equation method in the parabolic approximation. Equations are obtained allowing the mean scattered field to be calculated even when the surface causes a large phase modulation in the incident wave. Solutions are found using the method of Laplace transforms and some results are presented for a specific type of rough surface.     

Nonlinear least-squares analyses of complex impedance and admittance data for solid electrolytes

A nonlinear least-squares curve fitting technique, suitable for use with a laboratory minicomputer, is described for the analysis of a complex impedance (admittance) spectrum in which distortions of the various shapes constituting the complex plane plot occur because of overlapping time constants. With this technique, estimates of the parameter values occurring in an equivalent circuit are first obtained by a geometrical-fitting procedure and these are then used as the initial parametric values in a complex least-squares method which simultaneously fits the real and imaginary parts of the impedance (admittance) to a model (equivalent circuit), thereby yielding best-fit values of the circuit parameters as well as their confidence intervals. The method is illustrated by analyzing: (1) artificial, computer-generated impedance (admittance) data constructed for some simple RC circuits commonly used to model solid electrolyte behavior; and (2) measured admittance response of the fast sodium ion conductor NASICON at 486 K.     

Apparent and real roughness

Some works have studied the light scattering from a rough surface immersed in a liquid, where the light scattered from the immersed rough surface was assumed to be equivalent to that scattered from a fictitious rough surface with a different texture. This work deals with this kind of problems analyzing the light scattered by a reflecting strong scatterer and the light scattered by a rough surface immersed in a transparent liquid. The general Kirchhoff solution for scattering from a rough surface has been used.It is shown that under certain conditions, the mean scattered intensity (MSI) from a surface immersed in a liquid can be quasi-indistinguishable from that scattered from a non-immersed surface with an “equivalent texture”. An expression relating the equivalent texture and the immersed surface texture was obtained.The results of this work allow to evaluate the characteristics of any surface immersed in a liquid with a known refractive index.     

Scattering of a plane wave by one-dimensional dielectric random rough surfaces—study with the curvilinear coordinate method

We present a method giving the bi-static scattering coefficient of a one-dimensional dielectric random rough surface illuminated by a plane wave. The theory is based on Maxwell's equations written in a nonorthogonal coordinate system. For each medium, this method leads to an eigenvalue system. The scattered field is expanded as a linear combination of eigensolutions satisfying the outgoing wave condition. The boundary conditions allow the diffraction amplitudes to be determined. The Monte Carlo technique is applied and the bi-static scattering coefficient is estimated by averaging the scattering amplitudes over several realizations. The results of a Gaussian random process with a Gaussian roughness spectrum are compared to published experimental and numerical data. Comparisons are conclusive.     

基于AlN声表面波滤波传感器器件的有限元仿真

声表面波器件是一种利用压电材料的压电效应与逆压电效应工作电子器件, 文章首先详细描述了声表面波器件的设计与仿真过程,运用有限元分析的方法分别计算了利用声表面波的 SAW 器件与利用体波的 BAW 器件的性能与各项参数,对相关的器件进行了计算分析,分别用上述方法研究了基于 AlN 薄膜的声表面波器件和悬臂梁结构的体波器件,推导得出了器件的电学导纳与频率之间的关系, 通过分析器件的导纳-频率曲线,推导出器件内部声波的模式以及合适的工作频率,最终得出在 IDT 周期为 8 微米的情况下,SAW 器件的理想工作频率是 0.7-1.95GHz,BAW 器件的理想工作频率在 0.6-3.2GHz 的结果。     

Scattering of electromagnetic waves from two-dimensional perfectly conducting random rough surfaces – study with the curvilinear coordinate method

We present a method giving the bi-static scattering coefficient of two-dimensional (2-D) perfectly conducting random rough surface illuminated by a plane wave. The theory is based on Maxwell's equations written in a nonorthogonal coordinate system. This method leads to an eigenvalue system. The scattered field is expanded as a linear combination of eigensolutions satisfying the outgoing wave condition. The boundary conditions allow the scattering amplitudes to be determined. The Monte Carlo technique is applied and the bi-static scattering coefficient is estimated by averaging the scattering amplitudes over several realizations. The random surface is represented by a Gaussian stochastic process. Results are compared to published numerical and experimental data. Comparisons are conclusive.     

Scattering of electromagnetic waves from two-dimensional perfectly conducting random rough surfaces - study with the curvilinear coordinate method

We present a method giving the bi-static scattering coefficient of two-dimensional (2-D) perfectly conducting random rough surface illuminated by a plane wave. The theory is based on Maxwell's equations written in a nonorthogonal coordinate system. This method leads to an eigenvalue system. The scattered field is expanded as a linear combination of eigensolutions satisfying the outgoing wave condition. The boundary conditions allow the scattering amplitudes to be determined. The Monte Carlo technique is applied and the bi-static scattering coefficient is estimated by averaging the scattering amplitudes over several realizations. The random surface is represented by a Gaussian stochastic process. Results are compared to published numerical and experimental data. Comparisons are conclusive.     

有限波束作用下掩埋球体的散射声场计算

计算并分析了海底掩埋物体的三维散射声场。采用“等效垂直线列阵”方法来进行有限波束的建模,并将浅海波导中点声源散射声场的波数积分计算方法,推广到有限波束作用下海底掩埋物体的散射场计算,本文导出了物体位于沉积层中的散射声场计算公式。计算结果表明,在波导中垂直面内的散射声场,与沉积层中点源形成的声场非常相似;当距离较远时,散射声波呈柱面波衰减。文章还分析利用海面反射以提高散射能量的可能性,表明波束指向性及波束宽度对散射声场有较大影响。