The Maxwell's equations in the sense of distributions

It is well known that there is no direct one-to-one correspondence between the electromagnetic theory based on the physical laws and that based on the Maxwell's differential equations. For example, in order to derive the boundary conditions from the Maxwell's differential equations, one assumes that some integral identities derived from them are valid even when the field components (or material parameters) are discontinuous. This assumption violates, in a sense, the completeness of the theory of electromagnetism based on the Maxwell's differential equations. We will prove that if one postulates that the Maxwell's equations are valid in the sense of distributions, then this incompleteness will be removed and the boundary conditions will appear implicitly in the basic differential equations.     

On the edge reflections of high-frequency surface currents inducedon a cylindrical strip

High-frequency surface currents induced on a surface with edges can be interpreted as being composed of components attributable to the reflections and edge or surface diffractions of the incident field as well as to the edge reflections of these components themselves. The explicit expressions of the former components can be obtained from a set of properly formulated canonical problems if the surface consists of a cylindrically or spherically curved sheet. These types of canonical problems are not suitable for the derivation of the edge-reflected components, a fact that should be considered in dealing with currents induced on sheets of finite extent. A conjecture is made about the edge-reflected currents induced on a cylindrically curved sheet, and some of its consequences are shown. The normal and oblique incidence cases are considered separately     

Inverse electromagnetic scattering by cylindrical bodies buried in a slab or a half-space

An exact theory of the inverse scattering problems related to cylindrical bodies buried in a slab is established in two-dimensional scalar case. The theory dwells on two functional equations interrelating the outgoing wave solutions of the wave equation, which can be observed physically, with incoming wave solutions that are physically meaningless and irrealizable. One of these functional equations involves the measured radiation pattern in its kernel (material relation) while the other is independent of the measured data (universal relation). To establish the material relation one has to make far-field measurements with various incidence angles at various observation points and frequencies. The universal relation which guarantees some analytical properties of the field function results in a Stieltjes type integral equation. By solving these equations one gets the location, shape and permittivity of the inaccessible body. When the material of the half-space below the slab is made identical to that of the slab, then the results are reduced to that of the bodies buried in a half-space.     

One-dimensional profile inversion of a half-space over a two-partimpedance ground

A method which permits one to reveal the one-dimensional (1-D) electromagnetic profile of a half-space bounded by a two-part impedance ground is established. The method reduces the problem to the solution of two functional equations. One of these equations is solved exactly by reducing it to a Riemann-Hilbert problem while the other is reduced under the Born approximation to a Fredholm equation of the first kind whose kernel involves the solution to the first equation. Since this latter constitutes an ill-posed problem, its regularized solution, in the sense of Tikhonov, is given. An illustrative application shows the applicability and the accuracy of the theory. The functional equations are valid also when the impedance of the ground varies in an arbitrary manner. The theory can be applied to a quick determination of the constitutive electromagnetic parameters of the atmosphere over a nonhomogeneous impedance ground     

High-frequency surface currents induced on a perfectly conducting cylindrical reflector

An explicit expression for the surface current induced by sources on a perfectly conducting cylindrical reflector is obtained by taking into account the locality of the high-frequency diffraction phenomenon. The results show that the component previously conjectured by Ufimtsev involves several components having different propagation behaviors that can be separated into three main groups. When the reflector becomes infinitely large, the currents excited by edge diffraction are shown to reduce to those for the classical half-plane problem. The results are independent of the actual source configuration and may thus be useful in more complicated situations.     

Straightforward derivation of boundary conditions on sheetsimulating an anisotropic thin layer

Approximate boundary conditions on a sheet simulating an anisotropic thin layer are derived using previously derived general boundary relations. The method depends on the concept of distribution and does not require complicated mathematical representations or unproved equivalence principles     

Die Berechnung des Wellenwiderstandes einer Bandleitung mit elliptischem Außenleiterquerschnitt

Übersicht In einer früheren Arbeit wurde der Wellenwiderstand einer Bandleitung mit kreisförmigem bzw. rechteckigem Außenleiterquerschnitt berechnet [1]. Hier wird nun die Formel für den Wellenwiderstand einer Bandleitung, bestehend aus einem sehr langen geraden Zylinder mit elliptischem Querschnitt als Außenleiter und bandförmigem Leiter als Innenleiter, mittels der Methode der konformen Abbildung berechnet.

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Contents In an earlier paper (see [1]) the characteristic impedance of strip lines with outer conductors of circular and rectangular contour were calculated. Here the formula is derived for the characteristic impedance of a transmission line with a strip and an elliptic cylinder as inner and outer conductors respectively.

     

Generalised boundary conditions for a material sheet with both sides coated by a dielectric layer

Many structures which play important roles in practical applications involve planar sheets coated with dielectric layers. In order to avoid the mathematical difficulties arising from this type of multilayered structures in antennas and propagation problems one tries to replace the coated sheet by an equivalent hypothetical plane having appropriate boundary conditions. A new and general method capable of obtaining these generalised boundary conditions is presented and applied to three important particular cases where the structure consists of a resistive or conductive or impedance plane with both faces coated with dielectric layers.<>