Electromagnetic scattering from a chiral cylinder of arbitrarycross section

A simple moment solution is presented to the problem of electromagnetic scattering from a homogeneous chiral cylinder of arbitrary cross-section. The cylinder is assumed to be illuminated by either a TE or a TM wave. The surface equivalence principle is used to replace the cylinder by equivalent and magnetic-surface currents. These currents radiating in unbounded external medium produce the correct scattered field outside. When radiating in an unbounded chiral medium, they produce the correct total internal field. By enforcing the continuity of the tangential components of the total electric field on the surface of the cylinder, a set of coupled integral equations is obtained for the equivalent surface currents. Unlike a regular dielectric, the chiral scatterer produces both copolarized and cross-polarized scattered fields. Hence, both the electric and magnetic current each have a longitudinal and a circumferential component. These four components of the currents are obtained by using the method of moments (MoM) to solve the coupled set of integral equations. Pulses are used as expansion functions and point matching is used. The Green's dyads are used to develop explicit expressions for the electric field produced by two-dimensional surface currents radiating in an unbounded chiral medium. Some of the advantages and limitations of the method are discussed. The computed results include the internal field and the bistatic and monostatic echo widths. The results for a circular cylinder are in very good agreement with the exact eigenfunction solution     

Scattering from multiple conducting and dielectric bodies ofarbitrary shape

A simple moment-method solution is presented for the problem of electromagnetic scattering from structures consisting of multiple perfectly conducting and dielectric bodies of arbitrary shape. The system is excited by a plane wave. The surface equivalence principle is used to replace the bodies by equivalent electric and magnetic surface currents, radiating into an unbounded medium. A set of coupled integral equations, involving the surface currents, is obtained by enforcing the boundary conditions on the tangential components of the total electric and magnetic fields. The method of moments is used to solve the integral equations. The surfaces of the bodies are approximated by planar triangular patches, and linearly varying vector functions are used for both expansion and testing functions. Some of the limitations of the method are briefly discussed. Results for the scattering cross sections are presented. The computed results are in very good agreement with the exact solutions and with published data     

Transmission through dielectric-filled slots in a conductingcylindrical shell of arbitrary cross section: TE case

A simple moment solution is summarized for the problem of electromagnetic transmission through dielectric-filled slots in a conducting cylindrical shell of arbitrary cross section. The system is excited by a plane-wave polarized transverse electric (TE) to the axis of the shell. The equivalence principle is used to replace the shell and the dielectric by equivalent electric and magnetic surface currents radiating into an unbounded medium. Two different sets of coupled integral equations involving the surface currents are obtained by enforcing the boundary conditions on the tangential components of the total electric and magnetic fields. The method of moments is used to solve the integral equations. Pulses are used for both expansion and testing functions. Special attention is paid to circular and rectangular shells. Results for shell surface current, the internal field, and the aperture field are presented. For the case of air dielectric filling, the results computed using the electric field and/or the magnetic field formulation are in very good agreement with published data. In general, it is observed that the effect of filling a slot with a dielectric is not predictable from a simple theory     

RCS of two-dimensional structures consisting of both dielectricsand conductors of arbitrary cross section

The problem of determining the electromagnetic field scattered by two-dimensional structures consisting of both dielectric and conducting cylinders of arbitrary cross section is considered. The conductors may be in the form of strips and the dielectrics may be in the form of shells. The conductors may be partially or fully covered by dielectric layers, while the dielectrics may be partially covered by conductors. Only homogeneous dielectrics are studied. Both the transverse electric (TE) and the transverse magnetic (TM) cases are considered. The problem is formulated in terms of a set of coupled integral equations involving equivalent electric and magnetic surface currents radiating in unbounded media. The method of moments is used to solve the integral equations. Simple expansion and testing procedures are used. Numerical results for scattering cross sections are given for various structures     

Electromagnetic radiation and scattering from finite conducting anddielectric structures: surface/surface formulation

An efficient and accurate numerical procedure for the analysis of the electromagnetic scattering and radiation from arbitrarily shaped, composite finite conducting and dielectric bodies is proposed. A set of coupled electric field integral equations involving surface equivalent electric and magnetic currents is used. The coupled integral equations are solved through planar triangular patch modeling and the method of moments. Two separate, mutually orthogonal vector functions for each edge connecting a pair of triangular patches have been developed. Numerical results for disk/cone and cylinder/cone structures are compared with other available data. Limited comparison with experimental data has also been made     

A Nonmodal Formulation for Electromagnetic Transmission through a Filled Slot of Arbitrary Cross Section in a Thick Conducting Screen

This paper considers the two-dimensional problem of electromagnetic transmission through a filled slot of arbitrary cross section in a thick perfectly conducting screen. The equivalence principle is used to divide the original problem into three isolated parts where postulated equivalent sources radiate into unbounded, homogeneous media. These equivalent electric and magnetic currents are chosen to ensure continuity of the tangential components of electric and magnetic fields at each aperture. An integral equation is written for each of the three parts with the equivalent currents as unknowns. The resulting set of coupled integral equations is solved by the method of moments. It is shown in the Appendix that this set of equations has a unique solution. The primary quantities computed are the equivalent magnetic and electric currents on each aperture and the electric current on the remaining portions of the slot cross section. These results are compared with those obtained from a modal solution, where the fields in the slot cross section are expressed in terms of parallel-plate waveguide modes.     

Electromagnetic scattering from arbitrary shaped conducting bodiescoated with lossy materials of arbitrary thickness

A simple and efficient numerical technique is presented to solve the electromagnetic scattering problem of coated conducting bodies of arbitrary shape. The surface equivalence principle is used to formulate the problem in terms of a set of coupled integral equations involving equivalent electric and magnetic surface currents which represent boundary fields. The conducting structures and the dielectric materials are modeled by planar triangular patches, and the method of moments is used to solve the integral equations. Numerical results for scattering cross sections are given for various structures and compared with other available data. These results are proved accurate by a number of representative examples     

Planar near-field to far-field transformation using an equivalentmagnetic current approach

An alternative method is presented for computing far-field antenna patterns from near-field measurements. The method utilizes the near-field data to determine equivalent magnetic current sources over a fictitious planar surface that encompasses the antenna, and these currents are used to ascertain the far fields. Under certain approximations, the currents should produce the correct far fields in all regions in front of the antenna regardless of the geometry over which the near-field measurements are made. An electric field integral equation (EFIE) is developed to relate the near fields to the equivalent magnetic currents. The method of moments is used to transform the integral equation into a matrix one. The matrix equation is solved with the conjugate gradient method, and in the case of a rectangular matrix, a least-squares solution for the currents is found without explicitly computing the normal form of the equation. Near-field to far-field transformation for planar scanning may be efficiently performed under certain conditions. Numerical results are presented for several antenna configurations     

Single integral equation for electromagnetic scattering bythree-dimensional homogeneous dielectric objects

A single integral equation formulation for electromagnetic scattering by three-dimensional (3-D) homogeneous dielectric objects is developed. In this formulation, a single effective electric current on the surface S of a dielectric object is used to generate the scattered fields in the interior region. The equivalent electric and magnetic currents for the exterior region are obtained by enforcing the continuity of the tangential fields across S. A single integral equation for the effective electric current is obtained by enforcing the vanishing of the total field due to the exterior equivalent currents inside S. The single integral equation is solved by the method of moments. Numerical results for a dielectric sphere obtained with this method are in good agreement with the exact results. Furthermore, the convergence speed of the iterative solution of the matrix equation in this formulation is significantly greater than that of the coupled integral equations formulation     

Electromagnetic Simulation of Missile Exhaust

A simple moment solution is given for the problem of electromagnetic transmission through dielectric-filled slots in a conducting cylindrical shell of arbitrary cross section. The exciting source is assumed to be either a TM plane wave (receive mode) or an electric line current placed inside the shell (transmit mode). The surface-equivalence principle is used to replace the surfaces of the shell and the dielectrics by equivalent surface currents radiating in an unbounded medium. The application of the appropriate boundary conditions yields a set of coupled integral equations for the surface currents. The moment method with pulse expansion and point-matching testing procedures is used to solve the integral equations. Shells of different cross-sectional shapes are considered. Special attention is paid to circular and rectangular shells. In the transmit mode, the total far field transmitted through the slot is computed. In the receive mode, the aperture field and the field at the center of the shell are computed. For the case of air dielectric filling the slots, the computed results are in very good agreement with available published data.     

Reconstruction of Equivalent Currents Distribution Over Arbitrary Three-Dimensional Surfaces Based on Integral Equation Algorithms

A technique for the determination of the equivalent currents distribution from a known radiated field is described. This Inverse Radiation Problem is solved through an Integral Equation algorithm that allows the characterization of antennas of complex geometry both for near field to far field (NF-FF) transformation purposes as well as for diagnostic tasks. The algorithm is based on the representation of the radiating structure by means of a set of equivalent currents over a three-dimensional (3D) surface that can be fitted to the arbitrary geometry of the antenna. The innovative formulation uses an integral equation involving the electric field due to the currents tangential components to the represented antenna 3D surface. For that purpose, both the magnetic and electric equivalent currents are considered in the integral equations. Regularization techniques are also introduced to improve the convergence of the proposed iterative solution. The paper concludes with several results related to the practical verification of the Equivalence Principle and the characterization of a horn antenna.     

Green's function for arbitrarily shaped dielectric bodies of revolution

In this paper, a solution is developed to calculate the electric field at one point in space due to an electric dipole exciting an arbitrarily shaped dielectric body of revolution (BOR). Specifically, the electric field is determined from the solution of coupled surface integral equations (SIE) for the induced surface electric and magnetic currents on the dielectric body excited by an elementary electric current dipole source. Both the interior and exterior fields to the dielectric BOR may be accurately evaluated via this approach. For a highly lossy dielectric body, the numerical Green's function is also obtainable from an approximate integral equation (AIE) based on a surface boundary condition. If this equation is solved by the method of moments, significant numerical efficiency over SIE is realized. Numerical results obtained by both SIE and AIE approaches agree with the exact solution for the special case of a dielectric sphere. With this numerical Green's function, the complicated radiation and scattering problems in the presence of an arbitrarily shaped dielectric BOR are readily solvable by the method of moments.     

Surface integral formulation for calculating conductor anddielectric losses of various transmission structures

The power-loss method, along with a surface integral formulation, has been used to compute the attenuation constant in microstrip and coplanar structures. This method can be used for the analysis of both open and closed structures. Using the surface equivalence principle, the waveguide walls are replaced by equivalent electric surface currents and dielectric surfaces are replaced by equivalent electric and magnetic surface currents. Enforcing the appropriate boundary condition, and E-field integral equation (EFIE) is developed for these currents. Method of moments with pulse expansion and point matching testing procedure is used to transform the integral equation into a matrix one. The relationship between the propagation constant and frequency is found from the minimum eigenvalue of the moment matrix. The eigenvector pertaining to the minimum eigenvalue gives the unknown electric and magnetic surface currents     

Electromagnetic Scattering From Arbitrarily Shaped Dielectric Bodies Using Paired Pulse Vector Basis Functions and Method of Moments

A pair of orthogonal pulse vector basis functions is demonstrated for the calculation of electromagnetic scattering from arbitrarily-shaped material bodies. The basis functions are intended for use with triangular surface patch modeling applied to a method of moments (MoM) solution. For modeling the behavior of dielectric materials, several authors have used the same set of basis functions to represent equivalent electric and magnetic surface currents. This practice can result in zero-valued or very small diagonal terms in the moment matrix and an unstable numerical solution. To provide a more stable solution, we have developed orthogonally placed, pulse basis vectors: one for the electric surface current and one for the magnetic surface current. This combination ensures strongly diagonal moment matrices. The basis functions are suitable for electric field integral equation (EFIE), magnetic field integral equation (HFIE), and combined field formulations. In this work, we describe the implementations for EFIE and HFIE formulations and show example results for canonical figures.      

Moment method analysis of the magnetic shielding factor of aconducting TM shield at ELF

This paper presents an integral equation and method of moments (MoM) solution to the problem of TM transmission by a metallic conducting shield at extremely low frequencies (ELF). In order to accurately compute the total fields interior to the shield, equivalent problems are formulated which avoid the numerically difficult problem of computing the total fields as the sum of the incident plus scattered fields. In particular, the total electric field on the interior surface of the shield is obtained by a volume current equivalent problem, and then the total magnetic field interior to the shield is formulated in terms of equivalent magnetic surface currents flowing on the interior surface of the shield replaced by a perfect conductor     

Characteristic modes for slots in a conducting plane, TE case

Consider an infinitely long slot in a perfectly conducting plane in an unbounded medium illuminated by a uniform transverse electric (TE) (to the slot axis) plane wave. The theory of characteristic modes for apertures is applied to solve the problem. For a narrow slot, analytic expressions for the first two characteristic currents and the equivalent magnetic current are given. As computed by the method of moments, numerical results for the characteristic currents and fields, the equivalent magnetic current, and the transmitted field pattern are presented for the slot whose width is one wavelength.     

Electromagnetic Transmission through a Filled Slit in a Conducting Plane of Finite Thickness, TE Case

A solution is developed for computing the transmission characteristics of a slit in a conducting screen of finite thickness placed between two different media. The slit may be filled with Iossy material while the two regions on either side of the screen are assumed Iossless. A magnetic line source excitation is used (TE case) which is parallel to the axis of the slit. The equivalence principle is invoked to replace the two slit faces by equivalent magnetic current sheets on perfect electric conductors. Two coupled integral equations containing the magnetic currents as unknowns are then obtained and solved for by the method of moments. Pulses are used for the expansion and testing functions. Quantities computed are equivalent magnetic currents, the transmission coefficient, the gain pattern, and the normalized far field pattern.     

Generalized formulations for electromagnetic scattering fromperfectly conducting and homogeneous material bodies-theory andnumerical solution

A generalized E-field formulation for three-dimensional scattering from perfectly conducting bodies and generalized coupled operator equations for three-dimensional scattering from material bodies are introduced. A fictitious electric current flowing on a mathematical surface enclosed inside the body is used to simulate the scattered field, and, in the material case, a fictitious electric current flowing on a mathematical surface enclosing the body is used to simulate the diffracted field inside the body. Application of the respective boundary conditions lead to operator equations to be solved for the unknown fictitious currents, which facilitates calculation of the fields in the various regions, using the magnetic vector potential integral. The existence and uniqueness of the solution are discussed. These alternative operator equations are solvable using the method of moments. The numerical solution is simple to execute, rapidly converging, and general in that bodies of smooth but otherwise arbitrary surface, both lossless and lossy, can be handled effectively. Comparison of the results with available analytic solutions demonstrates the accuracy of the moment procedure     

A hybrid FEM/MOM technique for electromagnetic scattering andradiation from dielectric objects with attached wires

A hybrid formulation is presented, which combines the method of moments (MOM) with the edge-based vector finite element method (FEM) to solve electromagnetic radiation problems from structures consisting of an inhomogeneous dielectric body of arbitrary shape attached to one or more perfectly conducting bodies. While either method alone fails to model these structures efficiently, a combination of both finite element and moment methods provides an excellent way to solve these problems. The FEM is employed to handle the interior domain of inhomogeneous dielectric bodies and the method of moments is used to develop surface integrals that relate the field quantities on boundary surfaces with the equivalent surface currents. These integral equations are then coupled to the finite element equations through the continuity of the tangential magnetic fields across the hybrid boundaries     

TM and TE scattering by a dielectric/ferrite cylinder in the presence of a half-plane

An integral equation solution to the problem of transverse magnetic (TM) or transverse electric (TE) scattering by an isotropic dielectric/ferrite material cylinder in the presence of a perfectly conducting half-plane is presented. The technique is termed a method of moments (MM)/Green's function solution since the method of moments is used to determine the electric and magnetic polarization currents representing the material cylinder, while the presence of the half-plane is accounted for by including the half-plane Green's function in the kernel of the integral equations. Numerical results are presented for the echo width, material cylinder interior fields, and the surface impedance of a material slab on the surface of a half-plane.