Low frequency electromagnetic scattering by a perfectly conducting moving sphere

The paper investigates the propagation of a plane electromagnetic waves in the exterior of a moving obstacle. Under the assumption that the obstacle moves with uniform velocity and more slowly than the incident field, we apply the Lorentz transformation. In the object’s frame, where the scatterer is stationary, we introduce the low-frequency approximation technique. For the near electromagnetic field we obtain the Rayleigh low-frequency coefficients while in the far field we derive the leading non-vanishing terms for the scattering amplitude and scattering cross-section. Finally, using the inverse transformation we express the same quantities in the observer’s frame.     

Low-frequency acoustic reflection at a hard–soft lining transition in a cylindrical duct with uniform flow

The low-frequency limit of the reflection coefficient for downstream-propagating sound in a cylindrical duct with uniform mean flow at a sudden hard–soft wall impedance transition is considered. The scattering at such a transition for arbitrary frequency was analysed by Rienstra (2007, J Eng Maths 59:451–475), who, having derived an exact analytic solution, also considered the plane-wave reflection coefficient, R ₀₁₁, in the low-frequency limit, and it is this result that is reconsidered here. This reflection coefficient was shown to be significantly different with or without the application of a Kutta-like condition and the corresponding inclusion or exclusion of an instability wave over the impedance wall, assuming an impedance independent of frequency. This analysis is here rederived for a frequency-dependent locally-reacting impedance, and a dramatic difference is seen. In particular, the Kutta condition is shown to have no effect on R ₀₁₁ in the low-frequency limit for impedances with Z(ω) ~ ?ib/ω for some b > 0 as ω → 0, which includes the mass–spring–damper and Helmholtz resonator impedances, although, interestingly, not the enhanced Helmholtz resonator model. This casts doubt on the usefulness of the low-frequency plane-wave reflection coefficient as an experimental test for the presence of instability waves over the surface of impedance linings. The plane-wave reflection coefficient is also derived in the low-frequency limit for a thin shell boundary, based on the scattering analysis of Brambley and Peake (2008, J Fluid Mech 602:403–426), who suggested the model as a well-posed regularization of the mass–spring–damper impedance. The result might be interpretable as evidence for the nonexistence of an instability over an acoustic lining.     

Comparison of Cartesian grid configurations for application of the finite-difference time-domain method to electromagnetic scattering by dielectric particles

Two grid configurations can be employed to implement the finite-difference time-domain (FDTD) technique in a Cartesian system. One configuration defines the electric and magnetic field components at the cell edges and cell-face centers, respectively, whereas the other reverses these definitions. These two grid configurations differ in terms of implication on the electromagnetic boundary conditions if the scatterer in the FDTD computation is a dielectric particle. The permittivity has an abrupt transition at the cell interface if the dielectric properties of two adjacent cells are not identical. Similarly, the discontinuity of permittivity is also observed at the edges of neighboring cells that are different in terms of their dielectric constants. We present two FDTD schemes for light scattering by dielectric particles to overcome the above-mentioned discontinuity on the basis of the electromagnetic boundary conditions for the two Cartesian grid configurations. We also present an empirical approach to accelerate the convergence of the discrete Fourier transform to obtain the field values in the frequency domain. As a new application of the FDTD method, we investigate the scattering properties of multibranched bullet-rosette ice crystals at both visible and thermal infrared wavelengths.     

The coated thermoelastic body within a low-frequency elastodynamic field

A superposition of a longitudinal and a transverse plane elastic wave excites a small body which is embedded in an infinite elastic medium. The interior of the body exhibits thermoelastic behaviour of the Biot type and it contains a core which is also thermoelastic but with different thermal and elastic parameters. Integral representations for the near as well as the far-field are obtained which involve volume integrals over the shell and the core and surface integrals over the surface of the scatterer and the core–shell interface. Complete low-frequency expansions are provided and the scattering problem is reduced to a sequence of transmission problems for the determination of the coefficients of these expansions. It is shown that the thermal character of the interior media is observed in the low-frequency approximations of order higher or equal to three, when we are close to the scatterer and higher or equal to five, when we are far away from it. Furthermore, the thermoelastic behaviour of the scatterer affects only the radial scattering amplitude, which is of the longitudinal type, while the tangential scattering amplitudes, which are of the transverse type, coincide with the corresponding expressions for scattering by an elastic body with a penetrable elastic core.     

A Simple Model for a Microrough Diffraction Grating That Predicts Diffuse Light Bands

Abstract

A real diffraction grating is simulated by a plane boundary with a coordinate-dependent surface impedance. This surface impedance is constructed as the sum of two complex functions: a perfectly periodic function representing a grating without defects, plus a randomly varying, spatially localized function that represents the microroughness or defects of a real grating. This alternative scattering problem is solved in a rigorous electromagnetic manner for two polarizations of the incident field. Our results show that when the magnetic field is parallel to the grooves the scattered light pattern exhibits intensity maxima. The behaviour of these peaks reproduces that reported for the diffuse light bands observed in the spectrum of a real grating.     

Evaluation of Surface Impedance Models for Axisymmetric Eddy-Current Fields

We have investigated the range of validity of the perfect electric conductor and of the standard Rytov–Leontovich impedance boundary condition models for the analysis of axisymmetric eddy-current problems. Using these models, we derived approximate expressions for the magnetic vector potential, field quantities, Joule losses, and forces for conducting spheroids placed in external nonuniform magnetic fields produced by coaxial circular turns carrying currents varying sinusoidally with time. We compared our numerical results for the magnetic field intensity at the conductor surface, power losses, and forces (for both prolate and oblate spheroidally shaped conducting objects) with the results from analytical expressions obtained by applying the exact boundary conditions. While the simpler perfect conductor model can be employed only when the electromagnetic depth of penetration is much smaller than the smallest local radius of curvature, the results obtained by using the standard surface impedance model for conducting prolate and oblate spheroids of various axial ratios are in good agreement with the exact results for skin depths of about 1/5 of the semi-minor axis for electromagnetic forces and for skin depths less than 1/20 of the semi-minor axis for Joule losses.      

Alternative approaches to the numerical calculation of impedance

In many practical applications of numerical analysis applied to low-frequency electromagnetic problems, the desired output is often in terms of coil impedance. The mesh variable calculated by the more commonly used numerical formulations is the magnetic vector potential from which quantities like field intensities, eddy currents and others are calculated. In nondestructive testing applications, the quantity of interest is often the impedance of a coil or an array of coils. This paper discusses the calculation of impedance as a post-processing computation and introduces a new method of calculation of impedances and inductances based on computation of energy in the finite element mesh. The results presented clearly show the advantage of using direct integration methods for 2D and axisymmetric geometries. The energy approach, while valid regardless of dimensionality, should be restricted to 3D applications. Multiple-coil configurations in 3D applications present a special problem in analysis. The total impedance or inductance can be easily calculated but not independent coil or differential impedances. A method for calculation of these quantities in 3D computations is also presented.     

Exception for the zero-forward-scattering theory

Studies on single scattering of electromagnetic waves by magnetic particles were reported in the 1980s by Kerker et al. [J. Opt. Soc. Am.73, 765 (1983)]. They obtained that very small spherical particles with electric permittivity and magnetic permeability values such that epsilon=(4-mu)/(2mu+1) do not produce forward scattering. We show here that this condition contains an interesting exception at (epsilon=-2, mu=-2) when electric and magnetic resonances are present and around which the scattered field distribution is computed and described showing a polarization-insensitive behavior at the point (epsilon=-2, mu=-2).     

BaTiO_3@Cu核-壳复合粒子电/磁双响应性能

以平均粒径约为500nm的BaTiO_3微球为基核,通过"一步法"成功地制备了BaTiO_3@Cu核-壳复合粒子。利用SEM、TEM、XPS、介电测量分析仪和阻抗分析仪等对复合粒子的组成、结构、介电性能和磁性能进行测定。另外将纯BaTiO_3和BaTiO_3@Cu核-壳复合粒子分别分散到水凝胶中,通过测量和分析在有/无电场、磁场和电磁复合场作用下得到的水凝胶的储能模量,考察粒子在水凝胶中的电、磁和电磁响应性能。结果表明,BaTiO_3@Cu复合粒子具有完整清晰的核-壳结构,在整个表面壳层铜元素中,Cu(0)的原子分数达到了90at%,具有优良的介电性能和磁性能。BaTiO_3@Cu核-壳复合粒子是一种对外加电场和磁场作用都具有响应性能的多功能新型智能材料,且其电磁复合响应性能显著强于纯BaTiO_3粒子。     

Three-dimensional boundary element analysis of electromagnetic wave scattering by penetrable bodies

A frequency domain boundary element methodology of solving three dimensional electromagnetic wave scattering problems by dielectric particles is reported. The method utilizes a computationally attractive surface integral equation containing only weakly and strongly singular integrals in the contrast to most formulations involving not only strongly singular but hypersingular integrals as well. The main advantage of this integral equation is the fact that its strongly singular part is similar to the one appearing in the corresponding integral equation of dynamic elasticity. Thus, well known advanced integration techniques used successfully in elastic scattering problems can be directly applied to the present analysis. Both continuous and discontinuous quadratic elements are employed in order to accurately treat dielectric scatterers with smooth and piecewise smooth boundaries. Numerical examples dealing with three dimensional electromagnetic wave scattering problems demonstrate the accuracy and efficiency of the proposed boundary element formulation.     

Finite-difference time-domain solution of light scattering and absorption by particles in an absorbing medium

The three-dimensional (3-D) finite-difference time-domain (FDTD) technique has been extended to simulate light scattering and absorption by nonspherical particles embedded in an absorbing dielectric medium. A uniaxial perfectly matched layer (UPML) absorbing boundary condition is used to truncate the computational domain. When computing the single-scattering properties of a particle in an absorbing dielectric medium, we derive the single-scattering properties including scattering phase functions, extinction, and absorption efficiencies using a volume integration of the internal field. A Mie solution for light scattering and absorption by spherical particles in an absorbing medium is used to examine the accuracy of the 3-D UPML FDTD code. It is found that the errors in the extinction and absorption efficiencies from the 3-D UPML FDTD are less than approximately 2%. The errors in the scattering phase functions are typically less than approximately 5%. The errors in the asymmetry factors are less than approximately 0.1%. For light scattering by particles in free space, the accuracy of the 3-D UPML FDTD scheme is similar to a previous model [Appl. Opt. 38, 3141 (1999)].     

Estimate for the effect of forward scattering on the measurement of extinction for particles by cavity ringdown spectroscopy

An analytical model is formulated for the extinction of light by particles in a cavity ringdown spectroscopy measurement. The electromagnetic field inside the cavity is assumed to be the lowest-order Gaussian beam, and the scattering by the particles is incorporated using van de Hulst's approximation for the scattering by a sphere. This model includes both coherent scattering in the forward direction and strong scattering in the forward direction for electrically large particles. The model is used to estimate the amount of energy scattered by the particles that is coupled back into the incident beam. The consequences of this coupling for the measurement of the extinction cross section of spherical particles are examined.     

Light scattering simulation by oblate disc spheres using the null field method with discrete sources located in the complex plane

The T-matrix method, which is also known as the null field method (NFM) or extended boundary condition method (EBCM), has established itself as a well known and highly regarded method for calculating light scattering by non-spherical particles. Its biggest advantage is the possibility to obtain all information about the scattering characteristics of the particle and to store it into one matrix. This enables one to do additional investigations with low efforts. Unfortunately the standard NFM fails to converge for particles with extremely non-spherical particle shapes, like long cylinders or coin-like flat cylinders. In this paper we investigate light scattering by finite particles in the form of an oblate disc sphere, which can be described as flat cylinders with a rounded edge. We use an advanced form of the T-matrix method—the null field method with discrete sources (NFM-DS). By presenting light scattering results we would like to demonstrate the potential this advanced NFM-DS offers. It allows one to calculate particle shapes with aspect ratios (relation between radius and thickness of the particle) up to 100:1 and size parameters (relation between radius and wavelength) up to 30.     

Isogeometric FEM‐BEM coupled structural‐acoustic analysis of shells using subdivision surfaces

We introduce a coupled finite and boundary element formulation for acoustic scattering analysis over thin‐shell structures. A triangular Loop subdivision surface discretisation is used for both geometry and analysis fields. The Kirchhoff‐Love shell equation is discretised with the finite element method and the Helmholtz equation for the acoustic field with the boundary element method. The use of the boundary element formulation allows the elegant handling of infinite domains and precludes the need for volumetric meshing. In the present work, the subdivision control meshes for the shell displacements and the acoustic pressures have the same resolution. The corresponding smooth subdivision basis functions have the C¹ continuity property required for the Kirchhoff‐Love formulation and are highly efficient for the acoustic field computations. We verify the proposed isogeometric formulation through a closed‐form solution of acoustic scattering over a thin‐shell sphere. Furthermore, we demonstrate the ability of the proposed approach to handle complex geometries with arbitrary topology that provides an integrated isogeometric design and analysis workflow for coupled structural‐acoustic analysis of shells.     

Diffraction Grating EfficienciesConformal Mapping Method for a Good Real Conductor

The metallic diffraction grating problem has been solved for P-polarization using a conformal mapping and the surface impedance boundary condition. The method is used to calculate the electromagnetic fields diffracted by a grating having a cycloidal groove shape. The numerical results are compared with those obtained using the direct differential formalism. For low conductivities the coincidence between both results is only qualitative, whereas there exists a zone for greater conductivities where the differences are smaller than 0·;005. For even greater conductivities the approximated boundary condition employed holds more exactly, but the comparison is not possible because the direct differential method involves numerical problems.     

Finite element solution for electromagnetic scattering from two-dimensional bodies

The problem of scattering from bodies in free space is formulated using a differential equation approach. The finite element mesh extends outward into the far field region of the scattering body, where the outer boundary condition is evaluated using the asymptotic expression for the scattered field. Numerical results for two scattering bodies are presented and discussed. Non-physical, standing waves appear in the results due to the inadequacy of the outer boundary condition in fulfilling the radiation condition for the scattered field. The differential equation approach does not appear to be competitive with integral equation approaches for thin bodies, but seems promising for handling scattering from thick inhomogeneous bodies into which the field penetrates.     

Arbitrary order edge elements for electromagnetic scattering simulations using hybrid meshes and a PML

The use of arbitrary order edge elements for the simulation of two‐dimensional electromagnetic scattering problems on hybrid meshes of triangles and quadrilaterals is described. Single‐frequency incident waves, generated by a source in the far field, are considered and the solution is determined in the frequency domain. For numerical simulation, the solution domain is truncated at a finite distance from the perfectly conducting scatterer and the non‐reflecting boundary condition at the truncated boundary is imposed by the use of a perfectly matched layer (PML). Several examples are included to demonstrate the performance of the proposed procedure. Copyright © 2002 John Wiley & Sons, Ltd.     

Influence of a circular crack on the electromagnetic field in a conductor

The problem of scattering of low-frequency electromagnetic fields on circular cracks is reduced by the method of small parameter to a system of hypersingular integral equations of the Newton-potential type. For the solution of these equations, we propose to use the method of orthogonal polynomials of two variables. It is shown that the electric dipole whose moment is proportional to the normal component of the sounding field is an electrodynamic analog of the crack.     

Determination of Thickness of Silver Coatings on Brass by Measuring the Impedance of a Thin Elliptic Coil

To measure the impedance of a thin elliptically shaped coil, in presence of a flat plate with a coat of metal, can be an instrument for determination of the cladding thickness. An electromagnetic field from the coil is then forced to the object, producing eddy currents inside the object. These are influenced by the characteristics of the object and the coil and give rise to an impedance change, which can be detected and correlated to the thickness of the coating. An electromagnetic model accounting for the impedance of the elliptic coil with different values on the numerical eccentricity and the coating thickness is described. The model is based on a dyadic Green function formulation of the problem from which the electric field and hence the impedance is evaluated by utilizing the method of scattering super position. Numerical calculations based on the model and experimental measurements have been taken. An example shows how the model can be used to model a brass surface with a coat of silver to find expected impedance as function of the coating thickness     

基于单频数据重构散射障碍的新型线性采样方法

散射及反散射的数学理论与计算一直是应用数学领域中的重要课题，其成果在地质勘探、无损探测、医学成像等领域都具有广泛的应用．线性采样方法（LSM）是近年来反散射理论中一类非常流行的非迭代型重建算法，但是这种方式很难推广到如半空间中障碍反散射等更为复杂的问题中．本文基于单频数据研究Dirichlet障碍反散射问题的数值重建算法．通过构造带有阻尼边界条件的辅助边值问题，提出了一类新型的线性采样方法，并在理论上严格证明了该方法在任意给定的波数下重构障碍形状及位置的有效性．