Electromagnetic scattering from a wire grid parallel to a planar stratified medium

The theory for electromagnetic scattering from a special periodic structure adjacent to a stratified medium is given. The configuration consists of a parallel grid of thin wires that are located in a plane parallel to a planar stratified region. The case where the grid is outside the stratified half-space is considered first. Subject to the restriction on the thinness of the grid wires, an exact solution for the scattered fields is obtained. The final result, for the far-field scattering and transmission, can be interpreted clearly in terms of an equivalent transmission line circuit. In this case, the grid is represented as a shunt element. Finally, the theory is generalized to allow for the situation where the grid is within the stratified region.     

Electrostatic fields inside two planar distributions of potential

The potentials and fields inside two parallel planar distributions of potential can be written as Green's function integrals. Each Green's function can be evaluated numerically by decomposing it into two series of terms (one for large and one for small distances) which converge rapidly within their intervals of use. The accuracy of truncation after a few terms is evaluated.     

Electromagnetic fields due to dipole antennas embedded in stratified anisotropic media

A method is presented for calculating the electric and magnetic fields from dipoles embedded in anisotropic stratified media. By decomposing the fields into transverse electric (TE) and transverse magnetic (TM) modes, the results are obtained more directly and are more computationally efficient than methods using the Hertz potential. The electromagnetic fields are obtained for four types of dipole sources: horizontal electric, horizontal magnetic, vertical electric, and vertical magnetic. The source is embedded within one of several anistropic layers, which are further sandwiched between two semi-infinite media.     

ULF/ELF electromagnetic fields produced in a conducting medium of infinite extent by a linear current source of finite length

A linear current source of finite length embedded in a conducting medium of infinite extent is considered. Assuming a sea-water medium, the components of the electric and magnetic fields are numerically evaluated for two frequencies in the ULF/ELF range (frequencies less than 3 kHz). Comparison is made between the electric field vectors produced at the two different frequencies, and curves are plotted for one of the frequencies showing the variation with distance of the amplitudes of the electric and magnetic field components. A parametric approach is outlined that generalizes the field data presented in the figures and which enables the data to be extended to conducting media other than sea water and to other frequencies in the ULF/ELF range. Some practical applications of the data are discussed.     

New asymptotic solution for the electromagnetic fields of a dipole over a stratified medium

A straightforward method is described for obtaining an asymptotic solution of the fields of a dipole over a stratified halfspace. The results are valid for surface impedances which are not necessarily small compared with the intrinsic impedance of free space. The form of the expansions illustrates the differences from the more conventional theory which is based on the assumption of a small surface impedance.     

Faraday rotation in a stratified medium

The effect on Faraday rotation caused by stratification in an ionized medium and in semiconductor samples is examined. Expressions for rotation are derived in closed form for linear, exponential, and parabolic electron density profiles, including the effects of reflection at the boundaries. An expression in the form of a series is also derived for a general polynomial type of electron concentration variation. The change in rotation due to the deviation from the equivalent homogeneous carrier distribution is then examined for some experimental conditions in semiconductors and in the ionosphere.     

Electromagnetic fields due to a horizontal electric dipole antenna laid on the surface of a two-layer medium

With applications to geophysical subsurface probings, electromagnetic fields due to a horizontal electric dipole laid on the surface of a two-layer medium are solved by a combination of analytical and numerical methods. Interference patterns are calculated for various layer thickness. The results are interpreted in terms of normal modes and the accuracies of the methods are discussed.     

Ray path in a stratified absorbing medium

The ray tracing technique in absorbing, isotropic or anisotropic stratified media, and particularly in plane-stratified media is discussed. There are two approaches. One is to construct the complex refractive index vector and use the principle of stationary phase. The other is to impose a spatial beam signal on the medium having, e.g., a Gaussian profile and to find the peak of a component of the field intensity at each stratified layer. In this paper, we deal with the second approach. The resulting analytical expression for ray tracing is found to be identical with that obtained via the first method.     

Accurate approximation of Green's functions in planar stratified media in terms of a finite sum of spherical and cylindrical waves

A robust and computationally-expedient methodology is presented for accurate, closed-form approximation of the Green's functions used in the mixed-potential integral equation statement of the electromagnetic boundary value problem in planar stratified media. The proposed methodology is based on the fitting of the spectrum of the Green's function, after the extraction of the quasistatic part, making use of rational functions. The effectiveness and robustness of the proposed methodology rely upon the proper sampling of the spectrum in order to improve the accuracy of the rational function fit. The resulting closed-form approximation is in terms of both spherical and cylindrical waves. Thus, high accuracy is obtained in the approximation of the Green's function irrespective of the distance of the observation point from the source. The methodology is validated through its application to the approximation of the Green's function for a multi-layered, planar dielectric stack.     

Transient reflection of an electromagnetic signal from a stratified conducting medium†

The reflection characteristics of an electromagnetic pulse from a stratified conducting medium is analysed. For the case of a plane-wave signal with a Gaussian envelope, n simple expression for the reflected signal is obtained. The results show that the envelope of the reflected signal is not Gaussian any more. If there is a large number of carrier cycles in the envelope, it is found that the amplitude of the reflected signal is negligibly small as compared to that of incident signal.     

Electrostatic potential due to a potential drop across a slit

The electrostatic potential and charge density due to a potential drop across a slit in a thick conducting plane are obtained in analytic closed form. The Fourier transform, mode matching, and superposition are used to represent the potential in the spectral domain. The residue calculus is applied to represent the potential distribution in converging series form. Numerical computations are performed to illustrate the charge-density distribution through a slit     

The biconical antenna in a radially stratified medium

The theory of a transmitting biconical antenna in a radially and continuously stratified medium is developed; its input impedance is computed and plotted vs. its length for various media and cone angles. The medium extends to infinity and is characterized by a complex dielectric factorxi=epsilon-isigma/omega=epsilon_{0}f(r), whereris the radial distance from the center of the antenna. For the "stratification function" the formf(r)= (kr+a)/(kr+b)is considered, whereaandbare constant parameters, in general complex. The plots clearly exhibit all effects of dissipation and stratification expected on physical grounds and observed experimentally for dipole antennas.     

Electromagnetic fields of a small loop buried in a stratified Earth

The field structure of a buried vertical oscillating magnetic dipole is examined. The earth is represented as a two-layer half-space, and the source is located in the bottom semi-infinite region. Using numerical integration, the magnitude of the ratio of the horizontal to the vertical magnetic field is examined for an observer on the earth's surface. It is shown that at sufficiently low frequencies, the field ratio is not appreciably modified by the finite conductivity and the geometry of the layers.     

Electromagnetic fields of dipoles in stratified media

A general theory for the electromagnetic fields of dipoles in stratified isotropic media is outlined. The stratified model consists of a stack of layers sandwiched between two semi-infinite media. Either an electric or a magnetic dipole can be placed at any position in the stack, or in the upper or lower half-space. Dipoles can be electric or magnetic and can be oriented horizontally or vertically. The fields in the layer containing the source are given in terms of reflection coefficients, impedance and admittance terms, and wavenumber ratios. Recursion relations are developed to propagate the Hankel-domain field coefficients to other layers or to the half spaces. This allows the observation point to be placed anywhere except at the source. Numerical checks show that the derived algebra is at least self-consistent.     

Two-dimensional scattering from an inhomogeneous dielectriccylinder embedded in a stratified medium: case of TM polarization

Two-dimensional scattering of a TM-polarized electromagnetic wave from a transversely inhomogeneous isotropic body buried in a homogeneous layer of an arbitrarily stratified isotropic medium has been considered using the integral equation formulation over the cross section of the body and the moment method. The arising system of linear algebraic equations is solved with the aid of the conjugate gradient method and the one-dimensional fast Fourier transform. Illustrative numerical results are presented for both an inclusion in a half space and in a layer on a homogeneous substrate     

Mutual coupling in a finite planar array of circular apertures

Equations are presented for the calculation of the interelement mutual coupling in a finite size planar array of waveguide-fed apertures in an infinite flat conductor. The general mutual admittance expression is evaluated for circular apertures and the mutual coupling calculations are verified experimentally for twoTE_{11}mode excited apertures. Qualitative agreement between calculations for a 183 element array and an infinite array establishes the validity of the finite array theoretical model.     

Green's functions analysis of planar circuits in a two-layergrounded medium

A moment method analysis of planar circuits in a layered medium is developed. The Green's functions of a two-layer grounded medium are used in order to take into account the effect of the surface wave, coupling, and radiation. Interpolation techniques are used to increase computational efficiency. The embedded conductors are modeled with triangular patches. Results for several configurations, including direct and proximity coupled radiators, are in good agreement with measurements and other calculations     

The fields due to a small loaded loop in free space

A theoretical analysis of a resistively loaded, electrically small loop is presented which shows the variations of the transverse-wave impedance close to the loop as the resistive loading is altered. The theoretical results are compared with those obtained from a numerical simulation using Numerical Electromagnetics Code (NEC). Depending upon the loading, the loop exhibits electric (high wave impedance) or magnetic (low wave impedance) dipole properties, or intermediate wave impedances. These changes in wave impedance are closely related to variations in the far-field radiation pattern, and simulations are used to demonstrate this. Measured results are used to demonstrate that the variations predicted in wave impedance actually occur in practice. These results have bearing on the interpretation of emission measurements and on the design of circuits to minimize interference to other neighboring circuits