Surface integral representations for electromagnetic scattering from dielectric cylinders

The surface integral representations are derived for electromagnetic wave scattering from dielectric bodies. Several kinds of integral equations are given for dielectric cylinders immersed in an obliquely incident wave. The interior resonant solutions, the cause of erroneous solutions, accompanied with the equations presented here and the removal of these solutions are briefly discussed.     

Application of the unimoment method to electromagnetic scattering of dielectric cylinders

The unimoment method is applied to calculate the scattered fields of dielectric cylinders of arbitrary cross section or of inhomogeneous material. The basic technique of the method is the use of the finite element methods inside a mathematical circle, which encloses the inhomogeneous body. The fields outside are expanded in the usual cylindrical harmonics. The interior and exterior problems are then coupled at the circle. The versatility is increased greatly by introducing the method of "inhomogeneous element." The advantage of the proposed method is the simplicity and efficiency in programming. The validity of the computer program has been verified by comparing results with calculations from other methods for i) an off-centered circular cylinder, ii) two circular cylinders, and iii) a circular cylindrical shell.     

Analysis of electromagnetic scattering from dielectric cylinders using a multifilament current model

A moment solution is presented for the problem of transverse magnetic (TM) scattering from homogeneous dielectric cylinders. The moment solution uses fictitious filamentary currents to simulate both the field scattered by the cylinder and the field inside the cylinder and in turn point-matches the continuity conditions for the tangential components of the electric and magnetic fields across the cylinder surface. The procedure is simple to execute and is general in that cylinders of arbitrary shape and complex permittivity can be handled effectively. Metallic cylinders are treated as reduced cases of the general procedure. Results are given and compared with available analytic solutions, which demonstrate the very good performance of the procedure.     

The use of the transfinite interpolation in the method of momentsapplied to electromagnetic scattering by dielectric cylinders

The method of moments (MoM) solution of electromagnetic scattering presents two major numerical difficulties: the number of unknowns and the computation time necessary to calculate the matrix elements. To circumvent these problems, a MoM using the transfinite interpolation and a reduced integration scheme is presented here. The so-called h and p versions of the new method are applied to the scattering of an electromagnetic wave by an infinite dielectric cylinder (TM case) in the Richmond formulation. The transfinite and classical methods are compared in terms of the convergence rates of the radar cross section and of the total electric field inside the dielectric. The results confirm the superiority of the new schemes as predicted by the theory     

Inverse scattering of dielectric cylinders by a cascaded TE-TMmethod

A novel approach for inverse scattering of dielectric objects Is proposed. This reconstruction algorithm aims to synthesize individual TE and TM inverse scattering in order to decrease the effect of ill-posedness. The proposed synthesizing method has a cascade structure composed of TE and TM inverse scattering algorithms. Appropriate approaches are adopted in these two algorithms to take advantage of the physical difference between them. A diversity scheme of multiple incident views and receiving points is also incorporated. Numerical simulations are conducted to compare the proposed synthesizing method with two other methods using individual TE or TM information. Some advantages of the synthesizing method are also observed     

A new sectioning procedure for calculating scattering andabsorption by elongated dielectric objects

The iterative extended boundary condition method (IEBCM) has recently been developed to calculate scattering and absorption by elongated dielectric objects. The authors present a new sectioning procedure to improve the computational efficiency of the IEBCM. In this technique, the total geometry of the object is divided into overlapping sections, each of which includes only 3-5 spherical expansions to describe the internal fields. The total number of expansions required to describe the internal fields in the overall object may be as large as 15. Results illustrating the improvement in the computational efficiency of the IEBCM, as well as the dependence of the minimum number of expansions that should be included in each section on the dielectric properties of the scatter and on the frequency, are presented. It is shown that the sectioning procedure is particularly useful at frequencies below (ka<3) and above the resonance frequency of the object (4<ka<7)     

Analysis of the electromagnetic scattering by perfectly conducting convex polygonal cylinders

An effective method for the analysis of the scattering by a perfectly conducting convex polygonal cross-section cylinder is presented. The effectiveness stems from the generalization of the Neumann series, factorising the right edge behavior of the electromagnetic field, thus leading to a quickly convergent method. The induced currents, the radar cross section (RCS) and the induced field ratio have been evaluated.     

Solution of the problem of electromagnetic scattering by a thin dielectric cylinder with the use of the auxiliary source method

The problem of electromagnetic scattering by a thin solid dielectric cylinder is solved in the resonance frequency range by means of the auxiliary source method. The developed computer code is briefly described. The domain of applicability of the method for calculating the scattering characteristics of thin dielectric objects is investigated. The scattering cross sections of cylinders having various lengths and various values of the relative permittivity are numerically calculated.     

Optical theorems for electromagnetic scattering by inhomogeneitiesin layered dielectric media

The optical theorem, which relates the forward scattering amplitude to the total cross section of a scatterer in free-space, is extended to problems of scattering of an incident transverse electric plane wave or guided mode by inhomogeneities in lossless, waveguiding, dielectric interfaces or layers. The cases of a compact irregularity on either the interface between two unbounded dielectric media or in the waveguiding layer of a dielectric-slab waveguide are considered. Simple formulas that connect the scattered amplitudes of the different types of waves excited by the incident energy are derived. They can be used as an independent check of numerical codes when benchmark solutions are not available or are hard to obtain. In addition, a relationship between the scattered amplitudes and the spectral power of each excited wave is derived using the method of stationary phase     

Scattering of electromagnetic waves by arrays of conducting and dielectric cylinders

A method is developed that enables the solution of scattering by a finite number of cylinders in a convenient and accurate form. It is based on an analytic formulation using the boundary value problem and an application of a point matching technique. The method is then applied to study the scattering properties of both conducting and dielectric cylinders. It is also used to determine the size and spacing of passive scatterers to improve the directivity of linear antennas. In the latter case, a combination of the present method and a space perturbation technique is utilized to optimize the antenna gain.     

A stable integral equation for electromagnetic scattering fromhomogeneous dielectric bodies

It is shown that a previously derived integral equation for electromagnetic scattering from a homogeneous dielectric body (see ibid., vol.AP-32, p.166-172, Feb. 1984) does not have a unique solution at resonant frequencies of the cavity formed by making the surface S of the body perfectly conducting and filling the region internal to S with the external medium. This integral equation was formulated so that an equivalent electric current radiates in the presence of the homogeneous external medium to produce the scattered field external to the body. A combination of equivalent electric and magnetic currents is used to formulate an integral equation whose solution is always unique     

A tetrahedral modeling method for electromagnetic scattering by arbitrarily shaped inhomogeneous dielectric bodies

A method for calculating the electromagnetic scattering from and internal field distribution of arbitrarily shaped, inhomogeneous, dielectric bodies is presented. A volume integral equation is formulated and solved by using the method of moments. Tetrahedral volume elements are used to model a scattering body in which the electrical parameters are assumed constant in each tetrahedron. Special basis functions are defined within the tetrahedral volume elements to insure that the normal electric field satisfies the correct jump condition at interfaces between different dielectric media. An approximate Galerkin testing procedure is used, with special care taken to correctly treat the derivatives in the scalar potential term. Calculated internal field distributions and scattering cross sections of dielectric spheres and rods are compared to and found in agreement with other calculations. The accuracy of the fields calculated by using the tetrahedral cell method is found to be comparable to that of cubical cell methods presently used for modeling arbitrarily shaped bodies, while the modeling flexibility is considerably greater.     

Another method of extending the boundary condition for the problem of scattering by dielectric cylinders

Another method of extending the boundary condition resembling the extended boundary condition first developed by Waterman for the problem of scattering by homogeneous isotropic dielectric obstacles is presented. Differences between both methods are discussed from theoretical and numerical viewpoints.     

Variational reaction formulation of scattering problem for anisotropic dielectric cylinders

The variational reaction theory is applied to obtain the (E_{Z}, H_{z})formulation for the scattering problem when a plane wave is obliquely incident upon an inhomogeneous and anisotropic dielectric cylinder. The variational equation is then solved by the finite element method together with the frontal solution technique. Numerical results for scattering cross sections of anisotropic LiNbO³cylinders are included to discuss the influence due to material anisotropy and oblique incidence. Also depicted is the guiding characteristics of the cylinder when the inhomogeneous wave is considered, in addition, the formulas of scattering cross sections at low frequencies are derived and compared with the numerical results.     

A method of moments solution for electromagnetic scattering by inhomogeneous dielectric bodies of revolution

A method of calculating the electromagnetic scattering from and internal field distribution of inhomogeneous dielectric bodies of revolution (BOR) is presented. The method uses a typical mode-by-mode solution scheme. The electric flux density is chosen as the unknown quantity, which, together with the special construction of basis and testing functions, enables considerable reduction of the number of unknowns. A key element in this technique is expressing of the azimuthal field components of basis functions in terms of transverse components. A Galerkin testing procedure is used, with special attention put on the efficiency of calculating scalar potential term. Results of calculation for a few classes of dielectric bodies are given and compared with calculations done by other authors.     

A scattering model for thin dielectric cylinders of arbitrary crosssection and electrical length

A scattering solution for long, thin, dielectric cylinders of arbitrary cross section and electrical length is presented. The infinite-cylinder scattering formulation is shown to be an asymptotic solution for the finite-cylinder case, regardless of cylinder electrical length or cross section. The generalized Rayleigh-Gans (GRG) approximation for circular cylinders is shown to be a specific case of this general formulation, and therefore, the assertions of GRG are explicitly proven. A moment-method (MM) solution for thin circular cylinders is likewise presented and is used to examine and quantify the asymptotic errors associated with this solution     

A new iterative procedure to solve for scattering and absorption by dielectric objects

We have devised a new iterative technique to improve the Extended Boundary Condition Method (EBCM) frequently used to solve for the scattering and absorption by lossy dielectric objects. This technique has two main features: 1) it requires an initial assumption of the external surface fields, and 2) it partitions the interior of the object into a number of overlapping subregions, thus assuring a more efficient numerical convergence. Preliminary results indicating the enhanced stability of the new iterative EBCM technique are presented.     

FEM analysis of unbounded electromagnetic scattering by the Robiniteration procedure

A new accurate procedure for the FEM solution of unbounded electromagnetic scattering problems is described. The scatterers are enclosed in a fictitious boundary on which a Robin condition is initially guessed, and then iteratively improved using the Green formula. The method does not present interior resonances and is easy to implement     

A partitioning technique for the finite element solution ofelectromagnetic scattering from electrically large dielectric cylinders

A finite element partitioning scheme has been developed to reduce the computational costs of modeling electrically large geometries. In the partitioning scheme, the cylinder is divided into many sections. The finite element method is applied to each section independent of the other sections, and then the solutions in each section are coupled through the use of the tangential field continuity conditions between adjacent sections. Since the coupling matrix is significantly smaller than the original finite element matrix, it is expected that both the CPU time and memory costs can be significantly reduced. The partitioning scheme is coupled to the bymoment method to account for the boundary truncation. Numerical results are presented to demonstrate the efficiency and accuracy of the method     

A new theory for scattering of electromagnetic waves fromconducting or dielectric rough surfaces

The problem of electromagnetic scattering from a conducting or dielectric rough surface with arbitrary shape is studied. An exact solution, using a differential method, is provided for a plane wave with one-dimensional irregularity of the interface. The problem is reduced to the resolution of a linear system of partial differential equations with constant coefficients, and to the computation of eigenvalues and eigenvectors of a truncated infinite matrix. Numerical application is made to show the angular distribution of energy density in the case of an arbitrary profile of the scattering surface and its evolution when the nonperiodic profile tends to become periodic. The near field is computed on the interface and its enhancement in the illuminated region is observed. It increases with the height of the irregularity and with the frequency