Electromagnetic wave scattering by a system of two spheroids ofarbitrary orientation

An exact solution to the problem of the scattering of a plane electromagnetic wave by two perfectly conducting arbitrarily oriented prolate spheroids is obtained by expanding the incident and scattered electric fields in terms of an appropriate set of vector spheroidal eigenfunctions. The incident wave is considered to be a monochromatic, uniform plane electromagnetic wave of arbitrary polarization and angle of incidence. To impose the boundary conditions, the field scattered by one spheroid is expressed in terms of its spheroidal coordinates, using rotational-translational addition theorems for vector spheroidal wave functions. The column matrix of the scattered field expansion coefficients is equal to the product of a square matrix which is independent of the direction and polarization of the incident wave, and the column matrix of the known incident-field expansion coefficients. The unknown scattered-field expansion coefficients are obtained by solving the associated set of simultaneous linear equations. Numerical results for the bistatic and backscattering cross sections for prolate spheroids with various axial ratios and orientations are presented     

Low-frequency scattering from two-dimensional perfect conductors

Exact expressions are obtained for the leading terms in the low-frequency expansions of the far field scattered by an arbitrarily shaped cylinder with finite cross section, an arbitrarily shaped cylindrical bump on a ground plane, and an arbitrarily shaped cylindrical dent in a ground plane. By inserting the low-frequency expansions of the incident plane wave and Green's function into exact integral equations for the surface current, integral equations are obtained for the leading terms in the low-frequency expansions of the surface current. Simple integration of these leading terms of the current expansion yield the leading terms in the low-frequency expansions of the scattered fields. The general low-frequency expressions are confirmed by comparing them to low-frequency results obtained from exact time-harmonic eigenfunction solutions     

Scattering by an arbitrary cylinder at a plane interface: broadsideincidence

The problem of the determination of the fields scattered by an infinite dielectric cylinder of arbitrary cross section located at the interface between two semi-finite dielectric media is reduced to the solution of integral equations for unknown functions defined on the boundaries. These boundary functions are chosen so as to minimize their number. The incident field is that of a plane monochromatic wave. The derivation of the integral equations is given for the transverse electric (TE) mode for a dielectric cylinder and for a perfectly conducting cylinder. The exact electromagnetic fields are obtained from the solutions of the integral equations by integration, and the radar cross section can be computed from the far-field approximation. Sample outputs of the computer programs that implement this solution are shown     

TM scattering from a hollow slotted circular cylinder withthickness

TM scattering from a hollow, slotted, circular cylinder with thickness is investigated. The mode-matching technique (MMT) is used to express the scattered and guided fields in the angular spectral domain in terms of the radial waveguide mode. The boundary conditions are enforced on the conducting surface and the slot to obtain simultaneous equations. The simultaneous equations are solved to represent the fields in an analytic series form. The computed results are in very good agreement with other data. The numerical computations are performed to illustrate scattering behavior in terms of cylindrical geometry, incident angle, and frequency     

Scattering of Gaussian Beam by a Conducting Spheroidal Particle with Confocal Dielectric Coating

An analytic solution to the scattering by a coated spheroidal particle, for arbitrary incidence of a Gaussian beam, is constructed by expanding the incident and scattered electromagnetic fields in terms of spheroidal vector wave functions. The unknown expansion coefficients are determined by a system of linear equations derived from the appropriate boundary conditions. Numerical results of the normalized differential scattering cross section of the conducting and coated spheroidal particle are evaluated, and the scattering characteristics are discussed concisely.     

在轴零阶贝塞尔波束对手征介质球的散射特性分析

贝塞尔波束自产生以来,凭借其无衍射、自修复特性已经获得了越来越多学者的关注。基于广义洛伦兹米理论, 将在轴贝塞尔波束与手征介质球相互作用的入射场及散射场展开为球矢量波函数的表达式。结合球矢量波函数的正交完备性及电磁场的连续性边界条件,推导出了在轴零阶贝塞尔波束对手征介质球电磁散射的解析解。数值模拟了散射强度随散射角的分布,将在轴贝塞尔波束退化为平面波照射手征介质球的散射结果与文献比较,吻合得较好。分析了波束及介质球参数、介质球偏离波束中心位置对散射强度的影响。该理论为手征材料和手征涂覆目标在微波工程及目标隐身中的应用提供了很好的理论应用价值。     

Efficient solution for backscattered field of a dihedral cornerreflector

The problem of transverse magnetic (TM) plane wave scattering from a dihedral corner reflector is investigated. Using the mode matching technique (MMT), the transmitted and scattered fields are expressed in the angular spectral domain in terms of radial waveguide modes. The boundary conditions are enforced to obtain simultaneous equations for the transmitted and scattered fields. The simultaneous equations are then solved to represent the fields in a series form. Numerical results obtained by this method compare favourably with those obtained by other methods     

Electromagnetic scattering from a coaxial dielectric circularcylinder loading a semicircular gap in a ground plane

An exact dual series solution of a plane wave incident on a coaxial dielectric circular cylinder imbedded in a semicircular gap of a ground plane is presented. Both TM and TE cases are considered here. The scattered field is represented in terms of an infinite series of cylindrical waves with unknown coefficients. By applying the boundary conditions and employing the partial orthogonality of the trigonometric functions the scattering coefficients are obtained. The resulting infinite series is then truncated to a finite number of terms to produce numerical results. For the sake of comparison with the published data some special cases are introduced first. The comparisons showed excellent agreement in all cases     

Scattering of electromagnetic waves by a system of two dielectricspheroids of arbitrary orientation

By means of modal series expansion of the incident, scattered, and transmitted electric and magnetic fields in terms of appropriate vector spheroidal eigenfunctions an exact solution is obtained to the problem of electromagnetic scattering by two dielectric spheroids of arbitrary orientation is obtained. The incident wave is considered to be a monochromatic uniform plane electromagnetic wave of arbitrary polarization and angle of incidence. To impose the boundary conditions at the surface of one spheroid, the electromagnetic field scattered by the other spheroids is expressed as an incoming field to the first one, in terms of the spheroidal coordinates attached to it, using rotational-translational addition theorems for vector spheroidal wave functions. The solution of the associated set of algebraic equations gives the unknown expansion coefficients. Numerical results are presented in the form of plots for the bistatic and backscattering cross sections of two lossless prolate spheroids having various axial ratios, center-to-center separations, and orientations     

Scattering from a chirally coated DB elliptic cylinder

An exact analytic solution to the problem of scattering of a plane electromagnetic wave from a chirally coated elliptic cylinder defined by a DB boundary has been obtained, by expanding the different electromagnetic fields associated with the problem in terms of suitable elliptic vector wave functions and a set of expansion coefficients. The incident field expansion coefficients are known, but the expansion coefficients associated with the fields scattered outside the coated cylinder and the fields transmitted inside the coating are unknown. These unknown coefficients are obtained by imposing appropriate boundary conditions at the two boundaries. Results have been presented as normalized bistatic and backscattering widths for a variety of admittances, permeabilities, and permittivities of the chiral materials used for the coating, to show their effects on scattering from the chirally coated cylinder.     

Electromagnetic plane wave scattering by a system of two parallel conducting prolate spheroids

By means of modal series expansions of electromagnetic fields in terms of prolate spheroidal vector wave functions, as exact solution is obtained for the scattering by two perfectly conducting prolate spheroids in parallel configuration, the excitation being a monochromatic plane electromagnetic wave of arbitrary polarization and angle of incidence. Using the spheroidal translational addition theorems recently presented by the authors which are necessary for the two-body (or multibody) scattering solution, an efficient computational algorithm of the translational coefficients is given in terms of spherical translational coefficients. The field solution gives the column vector of the series coefficients of the scattered field in terms of the column vector of the series coefficients of the incident field by means of a matrix transformation in which the system matrix depends only on the scatterer ensemble. This eliminates the need for repeatedly solving a new set of simultaneous equations in order to obtain the scattered field for a new direction of incidence. Numerical results in the form of curves for the bistatic and monostatic radar cross sections are given for a variety of prolate spheroid pairs having resonant or near resonant lengths.     

Analysis of Electromagnetic Scattering from an Eccentric Multilayered Sphere

An exact analytic solution of a plane electromagnetic (EM) wave scattered by an eccentric multilayered sphere (EMS) is obtained. It is assumed that the layers are perfect dielectrics and that the innermost core is a perfectly conducting sphere. Each center of a layer is translated along the incident axis. All fields are expanded in terms of the spherical vector wave functions with unknown expansion coefficients. The addition theorem for spherical wave functions is used prior to applying the boundary conditions. The unknown coefficients are determined by solving a system of linear equations derived from the boundary conditions. Numerical results of the scattering cross sections are presented on the plane of φ=0 degrees and φ=90 degrees. The convergence of modal solutions and the characteristics of patterns are examined with various geometries and permittivity distributions     

Scattering and coupling properties of a slotted elliptic cylinder

Near-field analysis and coupling of a perfectly conducting slotted elliptic cylinder excited by an electric line source placed inside or outside the cylinder is considered. The solution can be easily extended to account for a z-polarized incident plane wave excitation. The separation of variables technique is used to express external and internal fields in terms of Mathieu and modified Mathieu functions with unknown expansion coefficients. The problem is then reduced to an integral equation in terms of the aperture field. The solution of the integral equation is carried out by expressing the aperture field in terms of a Fourier series expansion with unknown coefficients. Then Galerkin's technique is introduced to solve for the unknown aperture field coefficients. Results for the penetrated and near fields are given in terms of different parameters such as location and type of the excitation, aperture width, cylindrical axial ratio, and the loading of the cylinder     

Scattering from a coated perfect electromagnetic conducting elliptic cylinder

An exact analytic solution is presented to the problem of scattering from a coated perfect electromagnetic conducting (PEMC) elliptic cylinder, when it is illuminated by a plane wave as well as a line source. The problem is formulated by expanding the various fields in terms of appropriate angular and radial Mathieu functions and a set of expansion coefficients. The expansion coefficients associated with the incident fields are known, but those associated with the scattered fields and the fields within the coating are unknown. Imposing boundary conditions at the surface of the PEMC elliptic cylinder and the surface of the coating, enables the determination of the unknown expansion coefficients. Results are presented in the form of normalized scattering widths for elliptic cylinders of various sizes, PEMC admittances, and different coatings, to show the effects of these on scattering.     

手征涂覆球对高斯波束的散射

在广义米理论的基础上,通过把入射高斯波束、散射场和内部场用适当的球矢量波函数展开,给出了一种求解手征涂覆球对高斯波束散射的解析方法。待定的展开系数可由从边界条件得到的线性方程组求出。对于波束的区域近似模型,给出了微分散射截面的数值结果。结果表明：与介质涂覆的情况相比,手征涂覆对微分散射截面和散色场的极化特性都产生了较大的影响。     

Electromagnetic plane wave scattering by a system of two uniformlylossy dielectric prolate spheroids in arbitrary orientation

By means of modal series expansions of electromagnetic fields in terms of prolate spheroidal vector wave functions, an exact solution is obtained for the scattering by two uniformly lossy dielectric prolate spheroids in arbitrary orientation embedded in free space, the excitation being a monochromatic plane electromagnetic wave of arbitrary polarization and angle of incidence. Rotational-translational addition theorems for spheroidal vector wave functions are employed to transform the outgoing wave from one spheroid into the incoming wave at the other spheroid. The field solution gives the column vector of the unknown coefficients of the series expansions of the scattered and transmitted fields expressed in terms of the column vector of the known coefficients of the series expansions of the incident field and the system matrix which is independent of the direction and polarization of the incident wave. Numerical results in the form of curves for normalized bistatic and monostatic radar cross sections are given for a variety of two-body system of uniformly lossy dielectric prolate spheroids in arbitrary orientation having resonant or near resonant lengths and different distances of separation     

Scattering by a conducting spheroidal object with dielectriccoating at axial incidence

An analytic solution of a plane electromagnetic wave scattering by coated prolate spheroidal bodies is obtained, for axial incidence, by expanding the incident and scattered fields in terms of prolate spheroidal vector wave functions. The unknown expansion coefficients are determined by an infinite system of equations derived using appropriate boundary conditions. To solve for the unknown coefficients, the system of equations is truncated by retaining only the first N equations in N unknowns, where N depends on the size of the body and the desired accuracy. Numerical results for the scattering cross section are presented to show the effect of different coatings on the magnitude of the scattered field     

Coupling phenomena in concentric multi-applicator phased arrayhyperthermia systems

The coupling between the waveguide applicators of a four-element phased array hyperthermia system irradiating a three-layered cylindrical tissue model of circular cross section is analyzed theoretically. The fields inside the tissue layers are expressed in terms of cylindrical vector wave functions satisfying the corresponding wave equations, while the fields inside each waveguide are expanded in terms of guided and evanescent normal modes. Then, by implementing the appropriate boundary conditions, a system of four coupled integral equations is derived in terms of the unknown electric field distributions on the open waveguide apertures. This system is solved by expanding the unknown electric field on each aperture into waveguide normal modes and by applying a Galerkin's procedure. The self reflection coefficient and the mutual coupling coefficients are then determined and numerical results for a four-element phased array hyperthermia system are computed and presented for different waveguide applicator sizes and settings     

Dyadic Green's functions inside/outside a dielectric elliptical cylinder: theory and application

Dyadic Green's functions in two regions separated by an infinitely long elliptical dielectric cylinder are formulated in this paper. As an application, the plane electromagnetic wave scattering by an isotropic elliptical dielectric cylinder is revisited by applying these dyadic Green's functions and the scattering-to-radiation transform. First, the dyadic Green's functions are formulated and expanded in terms of elliptical vector wave functions. The general equations are derived from the boundary conditions and expressed in matrix form. Then the scattering and transmission coefficients coupled to each other are solved from the matrix equations. To verify the theory developed and its applicability, we revisit the plane electromagnetic wave scattering (of TE- and TM-polarizations) by an infinitely long elliptical cylinder, and consider it as a special case of electromagnetic radiation using the dyadic Green's function technique. The derived equations and computed numerical results are then compared with published results and a good agreement in each case is found. Special cases where the elliptical cylinder degenerates to a circular cylinder and where the material of the cylinder is isorefractive are also considered, and the same analytical solutions in both cases are obtained.     

Two-Dimensional Scattering by a Conducting Elliptic Cylinder Coated With a Homogeneous Anisotropic Shell

A solution to the two-dimensional scattering properties of a conducting elliptic cylinder coated with a confocal homogeneous anisotropic elliptical shell is obtained. The transmitted field of the anisotropic shell is expressed as an integral equation based on waves with different wave numbers and different directions of propagation. The waves in all directions are represented as the eigenfunction expansion in elliptic coordinates in terms of Mathieu functions. In order to solve the nonorthogonality properties of Mathieu functions, Galerkin's method is applied and a matrix is required for the computation of unknown expansion coefficients of the scattered and transmitted fields. Only the transverse magnetic (TM) polarization is presented, while the transverse electric (TE) polarization can be obtained in the same way. Some numerical results are presented in graphical forms. The result is in agreement with that available as expected when a coated elliptic cylinder degenerates to the coated circular one.