Scattering by superquadric dielectric-coated cylinders using higherorder impedance boundary conditions

A general method for deriving higher order impedance boundary conditions is described. It is based on solving an appropriate canonical problem exactly in the spectral domain. After approximating the spectral impedance terms as a ratio of polynomials in the transform variable, elementary properties of the Fourier transform are used to obtain the corresponding boundary condition in the spatial domain. The method is applicable to multilayer coatings with arbitrary constitutive relations. Higher-order boundary conditions which neglect the effects of curvature are derived for a dielectric coating using the method. The boundary condition equation and the magnetic field integral equation are solved simultaneously using the method of moments, yielding the bistatic and monostatic radar cross section for dielectric-coated superquadric cylinders. The method is also applicable to a combined field integral equation (CFIE) solution, which can be used to eliminate the internal resonance problem associated with either the electric field integral equation (EFIE) or magnetic field integral equation (MFIE)     

Numeric reconstruction of smooth dielectric profiles

The one-dimensional inverse scattering problem can be solved in principal by use of the Gel'fand-Levitan integral equation. However, explicit solutions of this equation are seldom easy to obtain. Here we develop an iterative numeric procedure to reconstruct arbitrary smooth dielectric profiles. Several cases exemplify the simplicity and economy of the technique.     

Electromagnetic scattering from composite objects using a mixtureof exact and impedance-boundary conditions

Different surface integral equations for characterizing the electromagnetic scattering from a surface impedance object partially coated with dielectric materials are presented. The impedance boundary condition (IBC) is applied on the impedance surface and the exact boundary condition is applied on the dielectric surface. The resulting integral equations are solved for bodies of revolution using the method of moments. The numerical results are compared with the exact solution for a sphere. Other geometries are considered, and their results are verified by comparing results of the numerical solutions which were obtained using different formulations. The internal resonance problem is examined. It is found that the combined field integral equation (CFIE) can be used at any frequency and with any surface impedance     

A Quasi-Dynamic Method of Solution of a Class of Waveguide Discontinuity Problems (Short Papers)

It is shown that, if expansion terms of all the modes appearing in the Green's function for the problem are retained, the singular integral equation method can be made to apply by generating a differential equation for this integral. The solution of the differential equation is straightforward, and the inversion of the resulting integral equation then follows standard methods. The process is applied in detail to the case of the capacitive diaphragm, and the results compared to the quasi-static method with correction terms. The results are close for small guide widths, but the present method should give superior results if the guide width permits some overmoding.     

Low-Frequency Electromagnetic Penetration of Loaded Apertures

Low-frequency (quasi-static) electromagnetic penetration of an aperture can be reduced by loading the aperture with a conductive film or a bonded-junction wire mesh. A quantitative analysis of this phenomenon is carried out in this paper for a loaded circular aperture in a perfectly conducting ground plane of infinite transverse extent. Contact resistance between the aperture loading and the rim is taken into account. The quasi-static magnetic-field problem and the electrostatic field problem from which the aperture polarizabilities and penetrant fluxes are determined are shown to reduce to the problem of solving a single Fredholm integral equation. Exact (numerical) and approximate (variational) solutions to this integral equation are obtained, and the latter are used to represent the polarizabilities and penetrant fluxes by simple analytical formulas and equivalent circuits. These representations are found to be quite accurate when the contact resistance is not too large     

Wavelength Converters Placement in All Optical Networks Using Particle Swarm Optimization

Placement of wavelength converters in an arbitrary mesh network is known to be a NP-complete problem. So far, this problem has been solved by heuristic strategies or by the application of optimization tools such as genetic algorithms. In this paper, we introduce a novel evolutionary algorithm: particle swarm optimization (PSO) to find the optimal solution to the converters placement problem. The major advantage of this algorithm is that does not need to build up a search tree or to create auxiliary graphs in find the optimal solutions. In addition, the computed results show that only a few particles are needed to search the optimal solutions of the placement of wavelength converters problem in an arbitrary network. Experiments have been conducted to demonstrate the effectiveness and efficiency of the proposed evolutionary algorithm. It was found that the efficiency of PSO can even exceed 90% under certain circumstances. In order to further improve the efficiency in obtaining the optimal solutions, four strategic initialization schemes are investigated and compared with the random initializations of PSO particles.     

Electromagnetic radiation of antennas in the presence of anarbitrarily shaped dielectric object: Green dyadics and theirapplications

Although numerical solutions to the electromagnetic scattering by an arbitrarily shaped object have been obtained using Waterman's (1971) T-matrix method (TMM), the general electromagnetic radiation due to an antenna of a three-dimensional (3-D) current distribution in the presence of an arbitrarily shaped object has not been well considered. In this paper, the technique of surface integral equations has been employed; and as a result, a terse and analytical representation of the dyadic Green's functions (DGFs) in the presence of an arbitrarily shaped dielectric object is obtained for the antenna radiation. In a form similar to that associated with the electromagnetic radiation in the presence of a dielectric sphere, the DGFs inside and outside of the object of arbitrary shape are expanded in terms of spherical vector wave functions. However, their coefficients are no longer decoupled due to the arbitrary surface of a 3-D object. The coupled coefficients are then determined using the surface integral equation approach, in a fashion similar to that in the T-matrix method. To confirm the applicability and correctness of the approach in this paper a dielectric sphere, as a special case, is utilized as an illustration. It is found that exactly the same expressions as in the rigorous analysis for the inner and outer spherical regions of the object are obtained using the different approaches. As applications of the approach in this paper, radiation problems of an electric dipole in the presence of superspheroids and rotational parabolic bodies are solved     

Quasi-static image theory for the bi-isotropic sphere

Image theory for the static point charge and the conducting sphere, produced by Kelvin's inversion theory, is extended to the bi-isotropic sphere, including the chiral sphere as a special case. Image expressions for the bi-isotropic sphere can be derived in a manner similar to that of the dielectric sphere except that the quasi-static problem now involves both electric and magnetic scalar potentials, coupled through the interface conditions at the spherical surface. The image is a combination of electric and magnetic line charges along the axis connecting the point charge and the center of the sphere, and their expressions are obtained through what can be labeled as finite Mellin transformation. The expressions derived can find application in more complete quasi-static analyses of interactions of bi-isotropic spherical particles in artificial bi-isotropic media     

Quick quasi-TEM analysis of multiconductor transmission lines withrectangular cross section

This paper presents an efficient and accurate procedure for computing the quasi-static matrix parameters ([C], [L], [G], and [R]) of rectangular-shaped conductors embedded in a multilayered dielectric medium over an infinite ground plane. An additional top ground plane can also be considered., The problem is formulated in terms of the space-domain integral equation for the free-charge distribution on the slab conductor surfaces. The spatial Green's function is computed from its spectral counterpart using system identification techniques [Prony's method or matrix pencil method (MPM)]. The integral equation is solved by means of a Galerkin scheme employing entire domain basis functions. This results in a small matrix size. In addition, the quasi-analytical evaluation of the entries of the Galerkin matrix leads to a very efficient and accurate computer code. A detailed study on the convergence and accuracy of the method has been included     

Calcul des réponses impulsionnelles de cibles acoustiquement réfléchissantes

From the wave equation and the use of boundary conditions of the problem we have developped an integral equation which is time dependant. The particular form of this integral equation is well suited to a numerical approximation method which gives the solution as a single boundary layer. If one knows this boundary layer for all space and for all time, one can calculate the spacetime response of the target under investigation. The method is a very general one and can be applied to targets of arbitrary shape. To check the efficiency of the algorithm a computation has been done in the particular case of a perfectly reflecting sphere. Results are in good agreement with classical ones reported in the littérature.     

A numerical investigation of interior resonances in the hybrid FEM/MoM method

The interior resonance problem that can occur when using a hybrid finite-element method/method of moments (FEM/MoM) method to model electromagnetic scattering problems is investigated. Calculations of the bistatic radar cross section of a coated dielectric sphere are presented using different formulations, solution approaches, and solvers. The solutions using the electric-field integral equation have significant errors near an interior resonance frequency. When the combined-field integral equation is employed, satisfactory solutions can be obtained that do not depend on the particular solution approach or solver.     

Electromagnetic induction in thin sheet conductivity anomalies at the surface of the earth

Lateral variations in the Earth's conductivity complicate considerably the calculation of the electromagnetic response of the Earth to an external inducing field which is uniform and horizontal. Although analytic solutions have been found for a few simple two-dimensional models in which the conductivity varies in one horizontal direction only, it is necessary, in general, to resort to numerical methods. If the conductivity variations of interest are confined to a surface layer it is often possible to represent the Earth mathematically as a uniform conducting half-space covered by an infinitely thin sheet of variable surface conductance. This simplification effectively reduces by one the number of dimensions over which the field equations need to be integrated numerically. It is shown that for a two-dimensional model the horizontal component of the electric field satisfies an integral equation on the surface of the thin sheet, which can be solved numerically for arbitrary sheet conductance. The accuracy of the numerical procedure is confined by applying it to E- and B-polarization induction in two adjacent half-sheets and then comparing the solution obtained with known analytic solutions of the same problem. In three-dimensions the two horizontal components of the surface electric field satisfy a coupled pair of double integral equations which can also be solved numerically for an arbitrarily varying conductance of the surface sheet.     

Scattering from cylinders with arbitrary surface impedance

This paper presents an integral equation method for the solution of the field scattered by a set of cylinders with arbitrary cross-sectional shape, and arbitrarily varying anisotropic surface impedance. The integral equations are given for an arbitrary source with arbitrary harmonic variation along the cylinder axis. The scattering problem can be solved for arbitrary three-dimensional sources by expansion of the source in a Fourier integral over the axial propagation constant. The integral equations have been programmed for a CDC 1604A computer. The program developed has been used to solve a great variety of scattering, antenna, and propagation problems, and, depending upon accuracy desired, will handle cylinders up to about 150-wavelengths total perimeter. Numerical results on scattering from cylinders with specific cross sections are presented to illustrate the utility of the program developed.     

Scattering by a chiral cylinder of arbitrary cross section

An integral equation and method-of-moments (MM) solution to the problem of scattering by an inhomogeneous chiral cylinder of arbitrary cross section is presented. The volume equivalence theorem for chiral media is developed and used to formulate a set of coupled integral equations for the electric and magnetic volume polarization currents representing the chiral cylinder. These coupled integral equations are solved using a standard pulse basis and point-matching MM solution. Numerical results, including echo width and internal fields, are presented for the scattering by chiral slabs and circular cylinders. These results are compared to exact solutions when available     

A three-dimensional iterative scheme for an electromagneticcapacitive applicator

An efficient iterative method for solving quasi-static electromagnetic field problems is presented. A relaxation function is introduced in the quasi-static field equations. Then, the resulting equations can be solved by iteration. The method is similar to the one of solving a Laplace equation by computing the stationary state of a diffusion equation. Next, for a radially layered configuration the numerical results are compared with the results from an existing integral equation method. Subsequently, for a realistic three-dimensional model of a human knee numerical results are arrived at.     

Comprehensive analysis of strip- and slot-line guided forward,backward, and complex magnetostatic waves

This paper presents a comprehensive and accurate analysis of the guidance of volume and surface magnetostatic waves by strips or slots in the presence of a ferrite slab magnetized to saturation by an external uniform magnetic field. The strip/slot can be directly printed on the ferrite surface or separated from it by means of a dielectric layer of arbitrary thickness. The problem is posed in terms of a suitable integral equation accounting for the magnetostatic limit. This equation is solved by using a spectral-domain formulation. The proposed method allows for the consideration of arbitrary magnetization angles and the presence of upper and/or lower ground planes. Strip-guided forward, backward, and complex surface magnetostatic waves have been obtained and analyzed in terms of the appropriate waveguide parameters. Slot-guided backward volume magnetostatic waves have been also computed and studied. Theoretical results have been checked against theoretical (magnetostatic and full wave) and experimental data available in the literature with reasonable agreement     

The Electromagnetic Problems of a Cylinder or Elliptic Cylinder with Infinite Axial Slits and Others

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Near-zone gain of open-ended rectangular waveguides

Full-wave solutions to the problem of radiation by open-ended rectangular waveguides (OEG) are presented. The radiation problem is formulated in terms of an electric field integral equation (EFIE). The EFIE is solved using the method of moments for three OEG antennas covering the frequency range from 200 to 750 MHz. Results for the near-zone gains as a function of both frequency and distance from the OEG aperture are presented. Estimates for uncertainties in the calculated gain are also given     

Electromagnetic resonances and Q factors of a chiral sphere

A study of electromagnetic resonances of an isotropic chiral sphere is presented. The characteristic equation of a chiral sphere, which is complex and transcendental, is obtained by forming solutions of the electromagnetic field for a chiral sphere in terms of the spherical vector wave functions. The characteristic equation is solved by using a computer. Resonant frequencies and Q factors of the first few modes for relative permittivities of two and ten are reported and discussed. These modes are hybrid modes. They are classed as either hybrid electric (HE) modes or hybrid magnetic (HM) modes. Chirality is observed to have a significant effect on the resonances of a sphere.     

Electromagnetic scattering from and transmission through arbitraryapertures in conducting bodies

The general 3-D aperture coupling problem is formulated in terms of an integral equation for the equivalent magnetic current in the aperture, which is numerically solved by the method of moments. The aperture is characterized by two aperture admittance matrices, one for the exterior region and the other for the interior region. These two admittance matrices are determined separately but in a similar manner if the pseudo-image method is used. Numerically workable expressions are developed for the two aperture admittance matrices by decomposing each of them into a half-space admittance matrix and a supplementary admittance matrix. The half-space admittance is relatively easy to compute and has been investigated in the literature. The supplementary admittance matrix is expressed in terms of the generalized impedance combining the existing numerical codes for an arbitrarily shaped scatterer and for an arbitrary aperture in a conducting plane, one can obtain a code which is especially designed for an arbitrary aperture in a conducting surface of arbitrary shape