A new numerical approach to the calculation of electromagnetic scattering properties of two-dimensional bodies of arbitrary cross section

A new method is introduced for formulating the scattering problem in which the scattered fields (and the interior fields in the case of a dielectric scatterer) are represented in an expansion in terms of free-space modal wave functions in cylindrical coordinates, the coefficients of which are the unknowns. The boundary conditions are satisfied using either an analytic continuation procedure, in which the far-field pattern (in Fourier series form) is continued into the near field and the boundary conditions are applied at the surface of the scatterer; or the completeness of the modal wave functions, to approximately represent the fields in the interior and exterior regions of the scatterer directly. The methods were applied to the scattering of two-dimensional cylindrical scatterers of arbitrary cross section and only the TM polarization of the excitation is considered. The solution for the coefficients of the modal wave functions are obtained by inversion of a matrix which depends only on the shape and material of the scatterer. The methods are illustrated using perfectly conducting square and elliptic cylinders and elliptic dielectric cylinders. A solution to the problem of multiple scattering by two conducting scatterers is also obtained using only the matrices characterizing each of the single scatterers. As an example, the method is illustrated by application to a two-body configuration.     

On scattering of the fields of cylindrical and plane waves by compact lossy-metamaterial structuress

The article presents a rigorous solution to the problem of scattering of a cylindrical (or plane) wave by cylindrical metamaterial structures of various geometries. Negative refraction of a plane wave is shown, and total internal reflection for such structures is studied. Masking of a perfectly conducting cylinder placed in a metamaterial cylinder in the geometric-optics shadow is demonstrated.     

Diffraction of plane and cylindrical waves by a cylindrical metamaterial shell with a negative refractive index

The problems of scattering of plane and cylindrical waves by a cylindrical metamaterial shell are solved rigorously. The influence of the geometric dimension of the shell, the value of the negative refractive index of the metamaterial medium, and the location of the cylindrical wave source on the near (far) field structure is investigated. It is shown that, in the quasi-opticl region, a caustic with one cusp is formed inside an electrically thick shell and whispering-gallery waves or standing waves are formed in between the facets of an electrically thin shell. It is found that, in the resonance region, reactive (surface) fields with substantial amplitudes are observed near the boundaries of a thin shell.     

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     

Finite length cylindrical scatterer near perfectly conducting ground--A transmission line mode approximation

A Pocklington type integro-differential equation, possessing an exact kernel, is formulated in terms of a complex frequency for the current induced on a thin finite-length cylindrical scatterer which is above, near, and parallel to a perfectly conducting ground plane. The circumferential variation of the axial current is assumed to be described by a transmission line mode approximation when the scatterer is near the ground plane. The integro-differential equation is reduced to a system of algebraic matrix equations through application of the method of moments. The singularity expansion method is utilized to determine the transient current response of the cylindrical scatterer to a unit step incident plane wave. Complex natural frequencies, natural mode vectors, normalization coefficients, and induced currents are compared to those found through a similar procedure with an approximate kernel, which assumes uniform circumferential variation of the axial current. The exact kernel with an assumed circumferential variation of the axial current is shown to be necessary when the thin cylindrical scatterer is near the ground plane.     

The near field of a wire grid model

The extreme near-field behavior of the wire grid model of a conducting surface is examined. Using a wire grid model of an infinite transverse magnetic circular cylinder, it is verified that the best accuracy for the E-field is obtained when the wire satisfies the `same surface area' rule of thumb. Two excitations are considered: a uniform surface current and plane wave incidence. In the first case, although the boundary value match between the wires is poor the extreme near field is still quite accurate. In the second case, the near field is also accurate, however, the largest errors occur not between the wires, but in the interior of the scatterer. In both cases, the boundary match between the wires as a check on the accuracy of the solution is misleading     

Diffraction of plane and cylindrical waves by a metamaterial cylinder

Rigorous solution of the problem of plane- and cylindrical-wave scattering by a circular cylinder made from a metamaterial is presented. It is shown that, inside a metamaterial cylinder, a symmetric caustic of refracted geometrical-optics rays with one cuspidal point is formed. The influence of the position of a cylindrical-wave source and the absolute value of the refractive index of the metamaterial both on the scattering pattern and the near field structure is studied.     

Exterior moment method analysis of conducting scatterers by using the interior Green's function

A new method using a Green's function in the interior region of a conducting scatterer is proposed to obtain a mutual admittance matrix in an exterior moment method analysis. A numerical example of a two-dimensional magnetic strip source located on an exterior surface of a perfectly conducting rectangular cylinder shows the validity of the method.<>     

Extended integral equation formulation for scattering problems froma cylindrical scatterer

An extended integral equation is developed for electromagnetic scattering from a perfectly conducting cylinder and a dielectric cylinder. The conventional surface integral equations cannot yield unique solutions when the wavenumber of the electromagnetic wave is equal to an eigenwavenumber of the system. Several methods to overcome this difficulty have been presented, but each method includes some drawbacks. A numerical method is proposed in which the boundary element method is applied to the extended integral equations with the observation points lying on a closed surface inside the scatterer. It is shown that the extended integral equations have unique solutions for any given wavenumber. As examples, plane wave scattering from a perfectly conducting elliptic cylinder, a dielectric elliptic cylinder, and a dielectric rectangular cylinder is numerically analyzed     

Gaussian beam scattering from a conducting cylinder partially buried in a ground plane

The problem of scattering from an infinitely long conducting cylinder that is partially buried in a perfectly conducting ground plane due to an obliquely incident gaussian beam is solved by an exact procedure based on the method of images by first adopting a simplification originally proposed by Kozaki. The incident and the specularly reflected fields are expressed in terms of cylindrical vector wave functions multiplied by a weighting function which involves the beam parameters like the radial distance of the source and beam width. The scattered fields originating from the cylinder and its image in the ground plane are expressed in terms of cylindrical vector wave functions. The boundary conditions on the surface of the cylinder are then imposed and this procedure leads to a coupled infinite system of equations for the even and odd mode expansion coefficients of the scattered field. These equations are solved numerically for the case of cylinders having electrical radius in the Rayleigh and resonance regions. Both the transverse magnetic and transverse electric polarizations of the incident beam wave are considered and some representative numerical results for the scattered far-field are presented in graphical form. The magnitude of the induced current for the TM polarization is calculated and compared with the corresponding case of plane wave incidence.     

Surface currents and RCS of a spherical shell with a circular aperture

The electromagnetic scattering behavior of a perfectly conducting, infinitesimally thin, spherical shell with a circular aperture is studied. A time-harmonic plane wave is symmetrically incident upon the aperture. The problem is formulated in terms of theE-field integral equation. This produces two coupled integral equations for the tangential components of the currents on the scatterer surface. The equations are cast into matrix form by application of the method of moments, and expressions for the matrix elements are derived. Calculated values of the surface currents and radar cross sections, not previously available in the open literature, are presented and discussed for several cases of interest.     

On a generalization of the extended boundary condition method

The elementary problem of scattering of an E-polarized plane wave by a circular perfectly conducting cylinder is used for verifying the efficiency of the boundary deformation method (BDM) that has recently been proposed as a generalization of the extended boundary condition method (EBCM). It is shown that the BDM can ensure the highly accurate fulfillment of the null-field condition on an interior contour spaced from the boundary in accordance with this method. However, when the accuracy of the fulfillment of the aforementioned condition on the contour near the boundary or on the boundary itself corresponds to the solution found for the current, this accuracy is substantially worse than the accuracy achieved in the case when the standard EBCM with a contour located near the boundary is applied. In addition, it is shown that, when the singularities of the wave field are enclosed by the contour chosen according to the BDM, a correct solution to the problem is not guaranteed.     

FINITE DIFFERENCE METHOD FOR ELECTROMAGNETIC SCATTERING FROM PERFECTLY CONDUCTING CYLINDER

A numerical method of solving electromagnetic wave scattering problem is described.Radiation boundary condition(RBC)is applied to confine EM scattering problem in unboundedregion into problem in finite region.Combined with RBC and scatterer surface boundary condi-tion,Helmholtz equation in the finite region is solved numerically by the finite difference method.Thus the distribution of induced surface current on conducting cylinder and near field can beobtained.Computational results for both polarizations for circular,elliptic and square cylindersare presented.These results are in excellent agreement with those obtained by the eigenfunctionexpansion method or moment method and much better then the results of OSRC method.     

Scattering by a rotating circular cylinder with finite conductivity

The effect of motion on the signal scattered by a rotating circular cylinder with finite conductivity is investigated. The problem is solved by means of the "instantaneous rest-frame" hypothesis. The analysis shows that a surface current must be taken into account to calculate the jump in the tangential magnetic field at the cylindrical surface. This holds even in the case of finite conductivity. For a perfectly conducting cylinder, the influence of the motion on the fields is negligible. This is shown by considering the limit of high but finitesigma.     

改进的FD—TD法分析二维理想导体TM近区散射问题

本文针对一般ＦＤ－ＴＤ方法分析计算二维理想导体散射问题所遇到散射体边角处难以精确处理的缺点进行了改进。将边角处总场近似解析解直接引入ＦＤ－ＴＤ法差分公式，得到了有关修正系数，为了检验此方法的有效性，有无限长导体方柱为例分别用一般ＦＤ－ＴＤ法和本文的ＦＤ－ＴＤ方法进行了分析研究，并与ＭＯＭ法进行了比较，所得结果说明改进后的ＦＤ－ＴＤ方法对分析计算导体边角附近电流分布特性是较有效的。     

Electromagnetic diffraction from a dielectric-filled slit-cylinderenclosing a cylinder of arbitrary cross section: TM case

A simple moment solution to the problem of the diffraction of a TM plane wave from an infinite, perfectly conducting slotted cylinder of an arbitrary cross section is summarized. The slit cylinder encloses a smaller perfectly conducting cylinder of an arbitrary cross section, and the space between the cylinders is filled with a dielectric material. The equivalence principle is used to obtain a set of coupled integral equations for the induced/equivalent surface currents on the cylinders, and the method of moments is used to solve numerically the integral equations. The electric field integral equation formulation is used. The advantages and the limitations of the method are discussed. Sample results for the induced current, aperture field, internal field, and scattering cross sections are given. These are in good agreement with some of the available published data     

Electromagnetic imaging for an imperfectly conducting cylinder

A computational approach to the imaging or inverse scattering of an imperfectly conducting cylinder is presented. A conducting cylinder of unknown shape and conductivity scatters the incident wave in free space and the scattered field is recorded on a circle surrounding the scatterer. By properly processing the scattered data, the shape and conductivity of the scatterer can be reconstructed. The problem is formulated in the form of nonlinear integral equations, which can be solved numerically by the Newton-Kantorovitch algorithm. The pseudoinverse technique is used to overcome the ill-posedness, and the condition number of the matrix is also discussed. Numerical examples are given to illustrate the capability of the inversion algorithm using the simulated scattered fields in both near and far zones. Multiple incident directions permit good reconstruction of shape and, to a lesser extent, conductivity in the presence of noise in measured data     

Shadow boundary incremental length diffraction coefficients appliedto scattering from 3-D bodies

Shadow boundary incremental length diffraction coefficients (SBILDCs) are high-frequency fields designed to correct the physical optics (PO) field of a three-dimensional (3-D) perfectly electrically conducting scatterer. The SBILDCs are integrated along the shadow boundary of the 3-D object to approximate the field radiated by the nonuniform shadow boundary current (the difference between the exact and PO currents near the shadow boundary). This integral is added to the PO field to give an approximation to the exact scattered field that takes into account both PO and nonuniform shadow boundary currents on the scatterer. Like other incremental length diffraction coefficients, any SBILDC is based on the use of a 2-D canonical scatterer to locally approximate the surface of the 3-D scatterer to which it is applied. Circular cylinder SBILDCs are, to date, the only SBILDCs that have been obtained in closed form. In this paper, these closed-form expressions are validated by applying them for the first time to a 3-D scatterer with varying radius of curvature-the prolate spheroid. The results obtained clearly demonstrate that for bistatic scattering the combined PO-SBILDC approximation is considerably more accurate than the PO field approximation alone     

Low-Frequency Shielding Properties of Conducting Cylindrical Shells of Arbitrary Cross Section

The shielding properties of general, two dimensional, finitely conducting shells with vanishingly thin walls are analyzed by the integral-equation method. For the circular cylinder case, a field plot throughout the shield interior reveals that, at the 'no shielding' frequencies found by Schieber, fields are attenuated greatly, except near the center. The influence of slots in the shell walls is also assessed for both circular and rectangular cylinders. Due to focusing effects, the field at the shield center is even stronger than the incident field at certain resonant frequencies for the slotted cylindrical shells.     

FFT-based algorithm for scattering from a circular, cylindrical shell in the presence of an inhomogeneous cylinder

An FFT-based algorithm is proposed to solve the problem of scattering from a homogeneous, thin, circular, dielectric cylindrical shell in the presence of an inhomogenous, cylindrical scatterer. The incident wave is taken to be transverse magnetic (TM); the problem considered is one of two-dimensional, scalar type. Results of computer simulations are provided illustrating the method proposed.<>