Scattering by an indentation satisfying a dyadic impedance boundarycondition

We derive a pair of boundary integral equations for the problem of scattering of an electromagnetic wave by an indentation in a perfectly conducting screen. The wall of the indentation obeys a dyadic impedance boundary condition. The unknowns are the electric current density on the wall of the indentation and the total tangential magnetic field in the opening of the indentation. We also derive integral representations for the fields everywhere in free space, including the far-field region. In all cases, the integrals involved extend over finite surfaces only     

On the electromagnetic field in a cavity fed by a tangentialelectric field in an aperture in its wall

Heretofore, the electromagnetic field produced by a specified tangential electric field in an aperture in the wall of an arbitrarily shaped cavity has most often been expanded in terms of cavity modes. An alternative approach, that of the electric field integral equation is presented. In this approach, the cavity field is expressed as the field of a surface density of tangential electric current, or a surface density of tangential magnetic current, or a combination of surface densities of tangential electric and magnetic currents on the boundary of the cavity. Each surface density is characterized by a single tangential vector function which is determined by the integral equation requiring that the part of the electric field tangent to the boundary of the cavity must reduce to the specified tangential electric field in the aperture and zero elsewhere on the boundary of the cavity. The electric field integral equation method is specialized to more easily determine the field inside an arbitrary cylindrical cavity excited by a tangential electric field in an aperture in its lateral wall. The method is further specialized to a circular cavity     

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.     

On volume integral equations

The focus of this paper is on the volume integral representations to be used in constructing integral equations for composite volume media. The major thrust of the paper is to identify where derivatives of a discontinuous function arise in the derivation of the volume representation. Three different derivation methods are presented, resulting in identical representation independent of the derivation method. These representations agree with some in the existing literature and disagree with others. When an electric field formulation is considered, the source of disagreement manifests itself only when magnetic materials are present. Likewise, for the dual situation, the inconsistency appears for a magnetic field formulation of dielectric materials. This paper identifies the sources of error in the incorrect representations and its major contribution is the rigorously correct derivation of the representations to be used in volume integral equations. We also present numerical results for an integral equation derived from our representation. The numerical results employ only the E-field as the unknown and the singularity is handled in a manner analogous to a standard numerical treatment of the electric field integral equation.     

Scattering of E-polarized waves from conducting strips inthe presence of a magnetically uniaxial half-space-a singular integralequation approach

A method based on the theory of singular integral equations (SIE) is presented for treating analytically scattering by perfectly conducting infinitely long strips in the presence of a magnetically uniaxial half-space. A uniform plane wave, polarized parallel to the strip axis, is incident from the isotropic region. As a prerequisite to this approach, the E-mode scalar Green's function of the structure is developed. Use of the reciprocity theorem then leads to a SIE for the current density induced on the scatterer's surface. The solution of the SIE is carried out in the case of a strip parallel or perpendicular to the interface, either located above or embedded in the anisotropic space. Numerical results for the induced current density and for the scattered far field in a variety of cases are presented in graphical form     

Efficient Methods for Determining the Coupling to Wires in Circular Cavities

The electromagnetic field coupling to a loaded thin wire in a cylindrical/coaxial cavity is investigated. Computationally efficient methods are presented for determining the coupling to a thin wire located near a cavity wall in a system of cascaded and/or overlapping coaxial and circular cylindrical cavity sections, and the accuracy and limitations of these methods are established. The sections are coupled through apertures and conducting elements common to more than one section, which may have different axial and radial dimensions and which may be filled with material having different magnetic and electric properties. The loaded thin wire is close to the outer wall of a cavity section and may represent a cable or, perhaps, a conducting tube. The coupling of the cavity field to the wire is determined from an analysis of a distributed voltage and current source model based on transmission line theory as well as via coupled integral equations techniques. The accuracy of the results obtained from these analyses is supported by experimental data measured on a laboratory model of the cavity-wire structure.     

Current and Charge Integral Equation Formulations and Picard's Extended Maxwell System

Important connection between computational and mathematical electromagnetics is presented. The newly developed well-conditioned electromagnetic frequency domain surface integral equation formulations, the current and charge integral equations, are shown to be related to Picard's extended Maxwell system, an extended partial differential equation system that has the correct static behavior. Electromagnetic surface integral representations are derived in this paper for traditional surface integral equation formulations and for the Picard system using the fundamental solution approach, i.e., from the definition of Dirac's delta function. The surface integral representations are constructed with proper solid angle coefficients starting from the scalar Helmholtz equation. The traditional surface integral equation formulations are shown to be derived from Maxwell's curl equations and are thus lacking the contribution of the divergence equations at zero frequency. It is shown that the new current and charge formulations can be derived from the surface integral representation of the Picard system.     

Une approche rigoureuse pour l’étude de sources primaires. Applications aux antennes de satellites

A rigorous approach for radiating structures of revolution is presented, with applications to paraboloidal reflector antennas. Considering Maxwell’s equations in the sense of distributions, an equivalent problem appears for the exterior domain in a natural and exact way, leading to the formulation of the integral equations. The current density on the conducting surfaces and the reflection coefficient are determined. The computed radiating field shows an excellent agreement with experiment. The radiation characteristics of an offset paraboloidal antenna are then obtained from the physical optics integral and the extension to multibeam antennas with some examples of earth coverage is presented.     

Current induced by TE excitation on coupled and partially buriedcylinders at the interface between two media

An analysis is described for determining the current induced by transverse electric (TE) excitation on coupled conducting cylinders near the planar interface separating two semi-infinite homogeneous half-spaces of different electromagnetic properties and on partially buried conducting cylinders. The conducting cylinders, of general cross section, are of infinite extent and the excitation is transverse electric to the cylinder axes. Coupled integral equations for the currents induced on the cylinders are formulated and numerical methods for solving them are presented. Data showing the induced current distribution for various cylinders and media parameters of interest are presented and discussed. Relative to the homogeneous space case, the presence of the two media significantly alters the current distribution, especially near the interface     

Determination of electrostatic fields and equipotentials using Fredholm's method

The electrostatic field and potential induced by an electrical charge inside a conductive cavity are calculated. First, the density of charge induced on the internal surfaces of the cavity has to be determined. This density is related to the original charge by an integral equation. Then, by the use of Fredholm's method this integral equation is reduced to a conventional system of algebraic linear equations, yielding density values at definite points of the internal surfaces, and hence electrostatic field and potential values at any internal point of the cavity. Fredholm's method is well suited to cavities with internally intricated structure and avoids numerical convergence difficulties.     

Matching of equivalent field regions

In aperture problems, integral equations for equivalent currents are often found by enforcing matching of equivalent fields. The enforcement is made in the aperture surface region adjoining the two volumes on each side of the aperture. In the case of an aperture in a planar perfectly conducting screen, having the same homogeneous medium on both sides and an impressed current on one side, an alternative procedure is relevant. We make use of the fact that in the aperture the tangential component of the magnetic field due to the induced currents in the screen is zero. The use of such a procedure shows that equivalent currents can be found by a consideration of only one of the two volumes into which the aperture plane divides the space. Furthermore, from a consideration of an automatic matching at the aperture, additional information about tangential as well as normal field components is obtained. We compare the two procedures in this tutorial article.     

Coupling Between an Abruptly Terminated Optical Fiber and a Dielectric Planar Waveguide

The coupling between an optical fiber and a dielectric planar waveguide is analyzed when both guides are terminated abruptly and are facing each other. Mixed spectrum eigenwave representations of fields are employed inside the waveguides while Fourier integrals are utilized to describe the field in the space between the two guides. A coupled system of integral equations is derived by satisfying the boundary conditions on the terminal planes of both waveguides. A weak guidance approximation is assumed to facilitate the analysis. Numerical results are presented for several coupling geometries. Misalignment losses and coupling optimization phenomena are investigated.     

Multimode network description of a planar periodic metal-stripgrating at a dielectric interface. III. Rigorous solution

For pt.II see (ibid., vol.37, no.3, p.542-52, 1989). In pt.I the solution to the scattering problem posed by a plane-wave incident at an angle on a plane, periodic, metal-strip grating at a dielectric interface was formulated in terms of novel multimode equivalent network representations. The analytical phrasing followed in pt.I led to two Fredholm integral equations of the first kind with singular kernels. Here, the authors derive a rigorous analytical solution for one of the two integral equations derived in pt.I (see ibid., vol.37, no.3, p.534-41, 1989). Closed-form, rigorous, analytical expressions for the elements involved in the equivalent network representations derived are obtained. Numerical results obtained by using these rigorous equivalent network representations are presented for TE-mode and TM-mode incidence for the case in which the same dielectric is present on both sides of the grating as well as for the case in which the two dielectric media are different     

Improved temporal basis function for time domain electric field integral equation method

An improved stable procedure is presented for time domain electric field integral equations. The procedure employs a new temporal basis function, which makes the time derivative of the unknown current density continuous. Numerical examples that demonstrate the efficacy of the proposed procedure are presented.     

Scattering of TM excitation by coupled and partially buried cylinders at the interface between two media

An analysis of scattering from coupled conducting cylinders near the planar interface between two semi-infinite, homogeneous halfspaces of different electromagnetic properties and from partially buried conducting cylinders is presented. The perfectly conducting cylinders of general cross sections are of infinite extent and the excitation is transverse magnetic to the cylinder axes. Coupled integral equations for the unknown current induced on the cylinders are derived and a numerical method for solving them is described. In addition, a simple technique is employed to determine the far-zone scattered field from knowledge of the cylinder current. Data displaying the distribution of the induced current and the scattered field patterns for cylinders of interest are presented and discussed.     

Scattering of H-polarized waves from conducting strips inthe presence of an electrically uniaxial half-space-a singularintegrodifferential equation approach

Electromagnetic scattering from perfectly conducting infinitely long strips in the presence of an electrically uniaxial half-space is treated analytically. A uniform H-polarized plane wave is incident from the isotropic region. As a prerequisite to this approach, the H-mode scalar Green's function of the structure is developed. Its use in connection with the reciprocity theorem leads to a singular integrodifferential equation for the current density induced on the scatterer surface. The equation is solved for strips parallel or perpendicular to the interface, located above or embedded in the anisotropic region, following a special technique based on the theory of singular integral equations that has been developed in connection with strips and slots and E- or H-polarized incident waves. Numerical results for the induced current density and for the scattered far field in a variety of cases are presented in graphical form. Whenever possible they are compared with existing results based on purely numerical procedures     

Simplifications in the stochastic Fourier transform approach to random surface scattering

Further developments in the application of the stochastic Fourier transform approach (SFTA) to random surface scattering are presented. It is first shown that the infinite dimensional integral equation for the stochastic Fourier transform of the surface current can be reduced to the three dimensions associated with the random surface height and slopes. A three-dimensional integral equation of the second kind is developed for the average scattered field in stochastic Fourier transform space using conditional probability density functions. Various techniques for determining the transformed current (and, subsequently, the incoherent scattered power) from the average scattered field in stochastic Fourier transform space are developed and studied from the point of view of computational suitability. The case of vanishingly small surface correlation length is reexamined and the SFTA is found to provide erroneous results for the average scattered field due to the basic failure of the magnetic field integral equation (MFIE) in this limit.     

Regularization of space-time integral equations in the problem of diffraction of electromagnetic pulses by N slots

Space-time integral equations describing diffraction of ultrashort electromagnetic pulses by slots in a screen located on a media interface are solved. The solution is based on separation of the static components of the kernels of the integral equations and the subsequent application of the collocation method.     

Electromagnetic fields in a spherical cavity embedded in a dissipative medium

Time-harmonic and transient electromagnetic fields in spherical cavities whose walls are made of any material characterized by (sigma, mu, epsilon) are investigated. For time-harmonic fields the wave equation is solved exactly in both the cavity and wall regions when the excitation is an electric dipole located at the cavity center. Numerical information based on these exact solutions shows the influence of the wall parameters upon the fields and provides a basis for studying the applicability and validity of several often used approximations. From the time-harmonic solutions, the Laplace transforms of the field equations are determined. These transforms are very complex and therefore are inverted numerically. Numerical results describing the magnetic field due to a particular dipole current,i_{d}(t)=(J - e^{-dt}), are presented for several cases of interest.     

Subsurface electromagnetic fields of a circular loop of current located above ground

The electromagnetic fields produced by a circular loop of current is considered for a homogeneous half-space model of the earth. The integral representations for the subsurface field are evaluated numerically and presented in graphical form.