The Exact Analytical Solution for Large Circular Loops Radiating Around a Dielectric Coated Conducting Sphere

In this paper, the electromagnetic field of electrically large circular loop antennas, with different radii and different nonuniform current values, around a dielectric coated conducting sphere is considered. One or more loop antennas are located on the outer surface of a spherical dielectric shell covering a conducting sphere. Eigenfunction series solutions for the field are assumed in two regions. The current distribution on the wire loop, driven by a voltage source, is determined by Fourier series expansion and all necessary harmonics are taken into account. Exact analytical field expressions in closed forms are derived and field patterns are plotted. The antenna model and formulation presented in this paper offer exact analytical solutions to several loop antenna problems.      

On the reflection of light from an inhomogeneous shell

The main contribution to the reflected field from a radially inhomogeneous spherical shell is determined. It is shown that it is much smaller in amplitude than the field reflected by a perfectly conducting sphere coated with the same type of radially inhomogeneous dielectric.     

Diffraction by a wide double wedge with cylindrically capped edges

The diffraction by two conducting sharp wedges with cylindrically capped edges is investigated using a recent asymptotic solution proposed by the authors for the diffraction by a wide double wedge. AnE-polarized plane wave incident at any angle is considered and the cap is assumed to be either a conducting or dielectric cylinder whose axis coincides with the wedge edge and its radius is much less than the separation between the two virtual sharp edges. The effects of the cap radius, permittivity, and wedge angle on the diffraction pattern, transmission coefficient, and edge-edge interaction term are presented. The transmission coefficient of the aperture is increased over the uncapped wedge case for dielectric caps and decreased for conducting caps. Other effects of the caps on the diffraction pattern such as beamwidth, level, and position of the first sidelobe are also investigated.     

Deformation of the horizontal radiation pattern of TV transmittingantennas due to a thin dielectric radome

Two methods are presented to study the effect of a thin dielectric radome on the horizontal radiation pattern of TV transmitting antennas. Examples are given for two antenna systems, each consisting of four columns of horizontal dipoles supported by a perfectly conducting carrier post of either circular or square cross section. The radome is a thin circular cylindrical dielectric shell enclosing the antenna system. The problem is modeled by a two-dimensional system and two different surface formulations are used to determine the effect of the radome on the radiation pattern. The procedure developed is general; the post and the radome may be of arbitrary cross sections. The noncircularity of the radiation pattern is computed for transmitting antennas in TV bands IV and V (f=470-790 MHz). It is observed that the presence of a radome does not always imply degradation in the circularity of its pattern; it may even enhance the pattern circularity at some frequencies     

Insulated loop antenna in a conducting spherical shell

Wait has calculated the impedance seen by a small circular loop of wire placed in an insulating spherical cavity in an infinite homogeneous conducting dielectric. The same technique may be used to compute the impedance of a loop inside a spherical shell. Attention is focused on the change in impedance of an electrically small wire loop when it is placed inside a spherical shell of lossy dielectric material whose radius is small compared to the free-space wavelength. The self-impedance in the absence of the shell can be calculated separately. Simple formulas are developed for the case where the conduction currents in the shell dominate over displacement currents and the shell is thin compared to the skin depth.     

Radiation of an elementary cylinder antenna through a slotted enclosure

The shrouding of an elementary cylinder antenna by a concentric perfectly conducting axially slotted shell is considered. The problem is reduced to a Fredholm integral equation of the first kind, which is solved for the case of a narrow shell slot. The solution indicates that the slotted shell inhibits the antenna radiation only for certain parameter combinations; for most others, the radiation remains the same, and for some it is enhanced.     

The computation of electromagnetic scattering from concentric spherical structures

The computation of electromagnetic scattering from concentric spherical structures by means of the rigorously exact Mie series solution is discussed. Significant extension of existing numerical results is shown possible with a conventional program capable of handling problems involving 25 layers. Some aspects of the computation are briefly discussed indicating areas and techniques for improvement of accuracy. The results of three different problems are presented: a dielectric sphere, a dielectric shell spaced away from a central perfectly conducting sphere and both 5 and 10 discrete layer approximations to the Luneberg and Eaton-Lippmann radially-inhomogeneous spherical structures. The consideration of this computation technique is used to determine the efficacy of novel methods and approximations, and to indicate areas needing improved numerical analysis.     

Extended boundary condition integral equations for perfectly conducting and dielectric bodies: Formulation and uniqueness

The equivalence theorem is used to derive novel generalized boundary condition (GBC) integral equations for the tangential components of the electric and magnetic fields on the interfaces of a finite number of dielectric or conducting scatterers. Closed surface, plane, and line extended boundary conditions (EBC) equivalent to the GBC are introduced. The GBC integral equations can now be replaced by any of these EBC integral equations whose solutions are unique and easy to obtain numerically using the moment method. A perfectly conducting sphere and a dielectric sphere in the electrostatic field of two equal and opposite point charges are presented as simple examples of the general procedure.     

Eigenvalues of a dielectric-coated conducting cone

The general problem of radiation/scattering from a dielectric coated semi-infinite conical structure excited by an arbitrary surface current distribution on the dielectric layer is formulated. Since the angular eigenfunction expansion is not suitable for this problem, the radial eigenfunction expansion is employed. The boundary value method is applied to obtain the fields in the form of infinite double series over the appropriate eigenfunctions in terms of spherical Hankel and associated Legendre functions. The conical dielectric shell may be lossy or lossless and the series solution generally involves complex eigenvalues which are calculated numerically. Using a small conducting sphere at the tip of the cone, the singularity of the Hankel functions at the origin is overcome, thus permitting the use of the orthogonality relations of Sommerfeld's complex-order wave functions to solve the problem and construct sets of infinite simultaneous linear equations which are presented in matrix form.     

Scattering of electromagnetic waves from dielectric coated conducting spheres

Several series of rigorous numerical calculations of the backscatter cross section of a conducting sphere with a thin lossless dielectric coating were carried out. The ratio of the radius to wavelength was varied from about 0.02 to 10.0; the dielectric constant of the coating was taken to be 2.56, 4.0, or 6.0; and the thickness of the coating was 0.1 or 0.05 times the outer radius of the coated sphere. Curves of the results are presented which indicate that the backscatter cross section of a coated sphere may be increased by as much as a factor of ten over that of an uncoated sphere of the same size, and, due to interference effects, an even greater decrease may be obtained. Further, small changes (less than one per cent) in the thickness or dielectric constant of the coating, or in the wavelength, may bring about large changes in the cross section. The numerical results are also compared with some experimental measurements, and with predictions of a "creeping-wave" type of analysis carried out by Helstrom.     

Scattering of electromagnetic pulses by simple-shaped targets withradar cross section modified by a dielectric coating

We study the scattering interaction of electromagnetic pulses with a spherical target. The target is a perfectly conducting sphere coated with a thin dielectric layer. Two different hypothetical materials are specified: a lossy dielectric and a dielectric that also has magnetic losses. The monostatic radar cross section (RCS) is computed in each case and we examine the influence of the coating on the RCS. In particular, we compare the RCS of the coated sphere with the (normalized) backscattered power when a large perfectly conducting flat plate coated with the same dielectric layer is illuminated at normal incidence by the same waveform. In particular, we find that except for frequencies below those within the efficiency band of the absorbent material, the normalized RCS of the coated sphere agrees well with the power reflection coefficient of the plate covered with the same kind of coating. For low-frequency incidences, the peaks and dips in the RCS are more prominent for the coated target than they are for the bare one. Analyzing the response of the spherical targets in the combined time-frequency domain we demonstrate that the coating itself, although reducing the RCS could introduce additional resonance features in the target's signature at low frequencies that could be used for target recognition purposes. This observation is also confirmed by a study of the bistatic RCS of these coated objects, which we have displayed in various color graphs     

Scattering from a sphere of small radius embedded into a dielectricone

In this paper, the scattering of a plane electromagnetic wave from a metallic or dielectric sphere of electrically small radius, embedded into a dielectric one, is considered. The classical method of separation of variables is used, combined with translational addition theorems for spherical vector wave functions. Analytical expressions are obtained for the scattered field and the various scattering cross-sections, in the case of an inner sphere with electrically small radius. Numerical results are given for various values of the parameters and for metallic and dielectric inner sphere. Some remarks are made about the possibility of detection or identification of inhomogeneities or nonsymmetries     

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.     

Radar cross sections of dielectric or plasma coated conducting spheres and circular cylinders

Radar cross sections for a variety of spherical and cylindrical scatterers having homogeneous dielectric or plasma shells are obtained by using both the exact boundary value solutions and approximate, semi-empirical methods based on physical principles. The plasma is assumed to have the macroscopic properties of a lossless dielectric with a permittivity less than that of free space. A superposition approximation for the radar cross section of a dielectric coated conducting body is obtained by considering the scattered field to be the phasor sum of two principal components, the field scattered by the air-dielectric interface and the field scattered by an equivalent conducting body which differs from the actual body because of the lens action of the shell. This approximation yields very good agreement with the exact solutions for both spherical and cylindrical dielectric clad scatterers with radii in the Rayleigh region and in the resonant region, and for bistatic scattering as well as for backscatter. The echo area of a conducting sphere with nonconcentric spherical dielectric shell calculated by means of the superposition approximation is in excellent agreement with experimental measurements, thus demonstrating the validity of this method in a case for which the exact solution cannot be obtained.     

Scattering by a ferrite-coated conducting sphere

The theory for scattering by a perfectly conducting sphere with a coating of lossy, homogeneous, isotropic ferrite material is presented. In addition to the rigorous eigenfunction formulation, the physical optics (PO) and geometrical optics (GO) approximations are also included. Numerical results are shown in graphical form to illustrate the backscatter echo area versus the radius of the sphere, as well as the bistatic scattering patterns.     

Extension of on-surface radiation condition theory to scattering bytwo-dimensional homogeneous dielectric objects

A recent analytical formulation by G.A. Kriegsmann et al. (see ibid., vol.AP-35, p.153-61, Feb. 1987) of electromagnetic wave scattering by perfectly conducting two-dimensional objects using the on-surface radiation boundary condition approach is extended to the case of two-dimensional homogeneous convex dielectric objects. It is shown that a substantial simplification in the analysis can be obtained by applying the outgoing radiation boundary condition on the surface of the object. The analysis procedure decouples the fields in the two regions to yield explicitly a differential equation relationship between the external incident field excitation and the corresponding field distribution in the interior of the dielectric object. The interior fields can be obtained by solving the differential equation using either an analytical approach or a suitable numerical method. Two-dimensional scattering examples along with validations are reported, showing the near-surface field distributions for a homogeneous circular dielectric cylinder and an elliptic dielectric cylinder, with with transverse magnetic plane-wave excitation     

Multiple microstrip lines on a multilayered cylindrical dielectricsubstrate on perfectly conducting wedge

The quasi-TEM characteristics of a class of cylindrical microstrip lines are rigorously determined. The class of microstrip lines considered consists of multiple infinitesimally thin strips on a multilayered dielectric substrate on a perfectly conducting wedge. Expressions for the potential distribution inside and outside the dielectric substrate, charge distribution on the strips, and capacitance matrix of the microstrip lines are derived. The problems of a microstrip line on a cylindrically capped wedge and on a cylindrical dielectric substrate on perfectly conducting core are also considered as special cases. Sample numerical results based on the derived expressions are given and discussed     

Impedance and radiation pattern of antennas above flat discs

Antenna imaging by a perfectly conducting finite flat disc is investigated analytically and numerically as a function of the radius of the disc. A conical monopole of variable length is considered above the screen and the normalized terminal admittance of the antenna is plotted versus the disc radius. The radiation pattern is also plotted and the current distribution above and below the screen is evaluated. The results provide a quantitative measure of the effectiveness of finite screens in imaging antennas and bring to light the persistent distortion of the pattern caused by the finite size of the screen in contrast to the behavior of the impedance.     

Receiving and scattering characteristics of an imaged monopolebeneath a lossy sheet

An analytical treatment of the radiation, scattering, and receiving properties of an imaged monopole in trilayered media with a perfectly conducting ground plane, a dielectric substrate, an electrically or magnetically lossy sheet as superstrate, and a homogeneous cover region is carried out. It is shown that while the power received by the monopole antenna is reduced by the presence of the lossy sheet, the scattered field is more greatly reduced, in agreement with observed behavior. Comparison with experimental and previously published numerical results validates the analysis     

Scattering by imperfectly conducting spheres

The theory of scattering by an imperfectly conducting, dielectric, or plasma sphere is reviewed briefly. Numerical values of the backscattering and forward scattering cross sections of spheres are given over wide ranges of radius, conductivity, and permittivity including both positive and negative values. The angle of the electric field in the forward and backward directions is also represented.