TM scattering by an impedance sheet extension of a paraboliccylinder

An integral equation and method of moments (MM) solution are presented for the two-dimensional (2-D) problem of transverse magnetic (TM) scattering by an impedance-sheet extension of a perfectly conducting parabolic cylinder. An integral equation is formulated for a dielectric cylinder of general cross section in the presence of a perfectly conducting parabolic cylinder. It is then shown that the solution for a general dielectric cylinder considerably simplifies for the special case of TM scattering by a thin multilayered dielectric strip that can be represented as an impedance sheet. The solution is termed an MM/Green's function solution, where the unknowns in the integral equation are the electric surface currents flowing in the impedance sheet; the presence of the parabolic cylinder is accounted for by including its Green's function in the kernel of the integral equation. The MM solution is briefly reviewed, and expressions for the elements in the matrix equation and the scattered fields are given. Sample numerical results are provided     

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.     

Electromagnetic scattering from electrically large coated flat and curved strips: Entire domain Galerkin formulation

Efficient numerical solutions are presented for electromagnetic scattering for classes of electrically large, coated, perfectly conducting strips which are flat or curved. The formulation is based on the solution of a coupled system of electric- and magnetic-field integral equations using the method of moments (MM). Entire domain Galerkin representations for the currents are used on the surface of the coating and at the coating-conductor interface. The resulting symmetric matrix equation is well conditioned and admits rapid, accurate solutions. Numerical results are presented for various coating thicknesses, strip widths, and curvatures for the transverse electric (TE) and transverse magnetic (TM) cases. The convergence of the Galerkin solution is examined as a function of these parameters. The effect of the edge approximation on the choice of expansion functions is discussed. The numerical results are compared with experimental measurements.     

Current induced by TE excitation on a conducting cylinder located near the planar interface between two semi-infinite half-spaces

An analysis is presented for determining the current induced by a known transverse electric excitation on a perfectly conducting cylinder located near the planar interface separating two semi-infinite, homogeneous half-spaces of different electromagnetic properties. The conducting cylinder of general cross section is of infinite extent and the excitation is transverse electric to the cylinder axis. Two types of integral equations, the magnetic field integral equation and the electric field integral equation, are formulated, and the Green's functions for the integral equations are derived in an appendix. Numerical solution methods for solving the integral and integrodifferential equations are presented. For a strip parallel or perpendicular to the interface, a circular cylinder, and a rectangular cylinder, data are presented and discussed for selected parameters, including the case of a cylinder resting on the interface.     

An asymptotic high-frequency analysis of the radiation by a sourceon a perfectly conducting convex cylinder with an impedance surfacepatch [antennas]

A high-frequency approximation is presented for the fields radiated by a magnetic line or line dipole source which is located on an impedance surface patch that partly covers an electrically large, perfectly conducting convex cylinder. Relatively simple asymptotic approximations are developed for the currents induced on the impedance surface by the line sources, and the radiation patterns are calculated by incorporating these surface currents into the radiation integral. The latter integral exists only over the patch region as it uses a perfectly conducting cylinder Green's function which is expressed in terms of a uniform geometrical diffraction (UTD) solution. Numerical results are presented and shown to compare very well with other independent calculations and measurements     

TM scattering by a dielectric cylinder in the presence of a half-plane

The problem considered is the transverse magnetic (TM) scattering by a dielectric cylinder in the presence of a perfectly conducting half-plane. An integral equation, involving the half-plane Green's function in its Kernel, is obtained for the equivalent volume currents representing the dielectric cylinder. This integral equation is solved by the method of moments. Numerical results are compared with measurements for the echo width of a dielectric slab on a half-plane. The dielectric slab surface impedance and the fields inside the dielectric are also shown.     

The Analysis of Monopole Antennas Located on a Spherical Vehicle: Part 2, Numerical and Experimental Results

Presented are various numerical results illustrating the behavior of thin monopole antennas located on a perfectly conducting sphere. The method of analysis, described in a previous paper, uses an integral equation solution for the unknown wire currents, and a modified Green's function to limit the range of integration to over the wires only. Studies are made of the input quantities, radiated currents and induced sphere currents for various antenna geometries. A comparison of the computed input impedance of monopole on the sphere is made with experimental data and good agreement is noted.     

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.     

Anomalous behavior of near fields calculated by the method of moments

The method of moments can be used to find solutionsJof the equationX(J) = lambda R(J), whereRandXare the real and imaginary parts (respectively) of theZ(impedance) operator of a perfectly conducting body. These solutions, called the characteristic currents, are characterized by an important near-field feature-the resulting free-space electric fields tangential to the body are constant in phase over the entire body. Although the method of moments is often used to solve electromagnetic problems where the far radiation fields of the solution currents are of interest, general moment-method theory indicates that the technique should also yield current solutions exhibiting accurate near-field behavior as the dimension of the solution space is increased. The near-field phase characteristics of resonant thin-wire characteristic current distribution, as calculated by several familiar moment-methods schemes, are presented. The ensuing discussion reveals several anomalies concerning the near-field behavior of the fields resulting from these currents. These anomalies are then discussed in light of the basic rudiments of the method of moments.     

Scattering from perfectly conducting and resistive strips on agrounded dielectric slab

The scattering properties of perfectly conducting and resistive strips are predicted for strips which are located on a dielectric slab backed by a perfectly conducting ground plane. The spectral domain Green's function is used to relate the currents and fields on the strip, and the resulting integral equation is solved using the method of moments. Both TE and TM strips are examined using piecewise linear and pulse subdomain basis functions, respectively, to model the current on the strip. Calculated results are compared with results measured at the NASA Langley Research Center     

Hybrid solutions for large-impedance coated bodies of revolution

Electromagnetic scattering solutions are developed for coated perfectly conducting bodies of revolution (BOR) that satisfy the impedance boundary condition. The integral equation arising from the impedance (Leontovich) boundary condition is solved by use of the method of moments (MM) technique along with an Ansatz for the surface currents that is derived from physical optics (PO) and the Fock theory that is modified for imperfectly conducting surfaces. The MM solution is expressed in terms of two integral (Galerkin) operators. The form of the Galerkin expansion used results in a symmetric MM system matrix. The hybrid solution is specialized for BOR's although the approach is applicable to a broader class of scatterers as well. The results are compared with the Mie solution for penetrable spherical scatterers, which satisfy the impedance boundary condition, and with recently published MM solutions for nonspherical scatterers.     

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     

Analytical simplification of the 2-D method of moments impedance integral

The elements of the two-dimensional (2-D), method of moments (MoM) impedance matrix are analytically reduced by way of an integral transform. The resulting impedance expression is a single integral with an analytic integrand for nearly arbitary shape and weight function sets. The reduced expression requires fewer computations, thereby reducing the matrix fill time. This moments via integral transform method (MITM) is based on an integral representation of the Green's function (Hankel function) and utilizes a special integral transform. The method is developed for 2-D perfectly electrically conducting bodies subjected to a transverse magnetic field. A comparison between brute force and MITM is presented for polynomial shape and weight functions.     

Combined field solution for TM scattering from multiple conducting and dielectric cylinders of arbitrary cross section

A simple moment solution is given for the problem of electromagnetic scattering from multiple conducting and dielectric cylinders of arbitrary cross section. The system of conducting and dielectric cylinders is excited by a plane-wave polarized transverse magnetic to the axis of the cylinders. The equivalence principle is used to obtain three coupled integral equations for the induced electric current on the conducting cylinders and the equivalent electric and magnetic currents on the surface of dielectric cylinders. The combined field integral equation (CFIE) formulation is used. Sample numerical results are presented. The agreement with available published data is excellent.     

Nonuniform currents on a wedge illuminated by a TE plane wave

Closed-form expressions for nonuniform currents on a perfectly conducting, infinite wedge illuminated by transverse electric (TE) plane wave are presented. These expressions are derived by requiring that they coincide with the current predicted by the asymptotic diffraction method far from the edge and, further, that they agree with the current predicted by the eigenfunction solution at the edge. The angle of incidence is arbitrary and our expressions remain valid even for glancing angles of incidence when either one or both faces of the wedge are in the vicinity of a geometric optic (GO) boundary. Formulas presented here are simple involving the well-known modified Fresnel functions but are not uniform. Exact expressions for nonuniform currents are available for the two special cases of half-plane and infinite plane. For these special cases, our solution reduces to the exact solution. Currents computed using the expressions developed here are compared with currents computed from the eigenfunction solution of the wedge. Good agreement is obtained throughout.     

Scattering from three-dimensional cracks

Scattering from three-dimensional cracks is analyzed and measured. The crack geometry is modeled as a rectangular groove in a perfectly conducting surface. The groove forming the crack may be terminated with an open aperture creating a slit in the conducting surface or with an impedance boundary creating a trough. The scattered fields from a crack are analyzed with two types of scattering mechanisms: a component directly related to the scattered fields from a two-dimensional crack, and a traveling-wave component     

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     

Diffraction of electromagnetic plane wave by a rectangular plateand a rectangular hole in the conducting plate

The problems of diffraction of an electromagnetic plane wave by a perfectly conducting rectangular plate and its complementary problem-diffraction by a rectangular hole in an infinite conducting plate-are rigorously solved using the method of the Kobayashi (1931) potential. The mathematical formulation involves dual integral equations derived from the potential integrals and the boundary condition on the plane where a plate or hole is located. The weighting functions in the potential integrals are determined by applying the properties of the Weber-Schafheitlin's integrals and the solution is obtained in the form of a matrix equation. Illustrative computations are given for the far diffracted field pattern and the current densities induced on the plate. The results of the patterns are compared with the results obtained from physical optics (PO) and the physical theory of diffraction (PTD). The agreement is fairly good, particularly with the PTD solutions     

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     

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.