A heuristic UTD slope diffraction coefficient for rough lossywedges

Heuristic wedge diffraction coefficients for computing propagation path loss over finitely conducting earth are extended to include slope diffraction, with the assumption that propagation of energy through the wedge is negligible. The slope diffraction terms for the lossy wedge are obtained in an analogous manner as for the perfectly conducting case, except that special care must be taken with the factor multiplying the incident field for grazing incidence. Results given show that the slope diffraction term produces continuous results that behave reasonably when compared with results for perfectly conducting wedges     

Simple expressions for the electric and magnetic field strengths between the elements of an infinite array

Suitable engineering expressions for the electric- and magnetic-field strengths between the elements of an infinite array are derived by employing finitely conducting earth image-theory techniques.     

Scattering from cavity-backed apertures: The generalized dual series solution of the concentrically loadedE-pol slit cylinder problem

The generalized dual series solution to the scattering of anE-polarized (E-pol) plane wave from an infinite circular cylinder having an infinite axial slot and enclosing an infinite concentric impedance cylinder is presented. This solution explicitly exhibits the correct edge behavior, and it can handle cylinders that are either electrically small or large without special considerations. The angle of incidence is arbitrary. A variety of current, field, and cross-section results are presented. These are compared with the correspondingH-pol problem results to establish the polarization dependencies of the aperture coupling. It is also shown that effects corresponding to the presence of the interior cavity dominate all of the scattering data. In particular, the bistatic cross sections in either case and the current induced along an interior wire in theE-pol case exhibit new resonance features that are due to the cavity-backed nature of the aperture.     

Currents Induced by a Plane Wave on an Infinite Wire above a Flat Earth

A general formula for the currents induced in an infinitely long perfectly conducting wire above a finitely conducting ground plane is derived. The effects produced by multiple scattering from e the ground are discussed and are shown to be significant.     

Shapes and amplitudes of the initial peaks of lightning-induced voltage in power lines over finitely conducting earth: Theory and comparison with experiment

It is conclusively shown that lightning-induced voltages in power lines over finitely conducting earth can only be explained by considering the interaction of the horizontal field produced by the finitely conducting ground, with the conductors. The theory predicts narrow peaks of few microseconds width in the induced voltages, for particular positions of lightning with respect to the line. Wave propagation effects are found to be of considerable importance. To the extent allowed by the bandwidth of the measuring instruments used in this study, the prediction of the theory is confirmed.     

Modal approach to scattering of electromagnetic waves by a conducting tape helix

Electromagnetic wave scattering by a tape helix of infinite extent is studied by using Floquet wave expansions for the guided modes and scattered fields. The solution reduces to earlier results as a special limiting case for normal incidence on a sheath helix. The current induced on an infinite helix computed by the presented technique bears close resemblance to the current induced on a long but finite helix as computed by Galerkin's method. The spatial frequency spectrum of the induced current is plotted to show the dominance of the spatial harmonics that are phase matched with the guided modes of the helix. Azimuthal patterns of the scattered field are included to illustrate that interference increases as the diameter of the helix is increased.     

Mutual coupling between parallel columns of periodic slots in aground plane surrounded by dielectric slabs

Arrays of slots with arbitrary orientation in an infinite conducting plane that are infinitely periodic in one dimension and finitely periodic in another dimension are considered. The plane is bounded on each side of dielectric slabs of finite thickness and infinite extent. Single columns of slots are represented by equivalent magnetic scattering currents, which are solved for by the moment method. The mutual coupling (admittance) between slot columns in the presence of the stratified media is found by the array scanning method, which expresses the admittance as the average of the scan admittance of an artificially constructed doubly infinite array of slots over all real scan angles. The technique avoids the use of Sommerfeld integrals, but still gives rise to singularities at scan angles corresponding to the resonant excitation of surface waves. An analytical approximation removes these surface wave singularities, making numerical implementation of the method practical     

Gaussian beam scattering from a conducting cylinder partially buried in a ground plane

The problem of scattering from an infinitely long conducting cylinder that is partially buried in a perfectly conducting ground plane due to an obliquely incident gaussian beam is solved by an exact procedure based on the method of images by first adopting a simplification originally proposed by Kozaki. The incident and the specularly reflected fields are expressed in terms of cylindrical vector wave functions multiplied by a weighting function which involves the beam parameters like the radial distance of the source and beam width. The scattered fields originating from the cylinder and its image in the ground plane are expressed in terms of cylindrical vector wave functions. The boundary conditions on the surface of the cylinder are then imposed and this procedure leads to a coupled infinite system of equations for the even and odd mode expansion coefficients of the scattered field. These equations are solved numerically for the case of cylinders having electrical radius in the Rayleigh and resonance regions. Both the transverse magnetic and transverse electric polarizations of the incident beam wave are considered and some representative numerical results for the scattered far-field are presented in graphical form. The magnitude of the induced current for the TM polarization is calculated and compared with the corresponding case of plane wave incidence.     

Summary of image theory expressions for the quasi-static fields of antennas at or above the earth's surface

Expressions for the quasi-static range (the measurement distance is much less than a free-space wavelength) field components produced by infinitesimal dipole antennas located at or above that of the earth have been derived by employing finitely conducting earth theory techniques. Formulas for the field components produced by an elevated, finite-length, horizontal electric antenna are also presented. Image theory is employed because most of the resulting integrals encountered cannot be evaluated analytically. The image theory and previously derived analytical (or in some cases, numerical integration) results are in agreement throughout the quasi-static range.     

Radiation and scattering from electrically small conducting bodies of arbitrary shape above an infinite ground plane

A simple moment solution is given for the low-frequency electromagnetic scattering or radiation problem involving a small perfectly conducting body of arbitrary shape placed close to an infinite ground plane. The method of images is used to account for the presence of the ground plane. The dynamic problem is approximated by two uncoupled problems, an electrostatic one and a magnetostatic one. Each static problem is then solved using the method of moments. The surface of the perfectly conducting scatterer is modeled by a set of planar triangular patches. Pulse expansion and point-matching testing are used in the electrostatic problem. For the magnetostatic problem, a set of solenoidal vector expansion functions is used. The induced dipole moments are computed from the induced electrostatic charge and the magnetostatic current densities. The scattered field is the field of these induced dipoles oscillating with the frequency of the incident field. Scatterers of various shapes are studied. Special attention is given to a conducting box on the ground plane.     

Electromagnetic scattering from an infinite circular metalliccylinder coated by an elliptic dielectric one

The scattering from an infinite, circular, perfectly conducting cylinder coated by an elliptic dielectric cylinder is considered. The electromagnetic field is expressed in terms of both circular and elliptical cylindrical wave functions, which are connected with one another by well-known expansion formulas. In the special case of small h=ka/2 (a is the interfocal distance of the elliptic dielectric and k its wavenumber), exact, closed-form expressions of the form S(h)=S(0)[1+gh ²+O(h⁴)] are obtained for the scattered field and the various scattering cross sections. Both polarizations are considered for normal incidence. Graphical results for various values of the parameters are given     

A stochastic Fourier transform approach to scattering from perfectly conducting randomly rough surfaces

An exact alternative approach to the diagrammatic technique for treating scattering from rough surfaces is developed. The magnetic field integral equation for the current induced on the rough perfectly conducting surface is multiplied by a Fourier kernel involving all orders of surface height derivatives and their associated transform variables. Averages of this weighted equation are converted to convolations in the transform domain. The result of this operation is a singular integral equation of the first kind of infinite dimensions (because of the infinite number of height derivatives) for the stochastic Fourier transform of the current. A procedure is developed for estimating the effects of ignoring one or more surface height derivatives in terms of the range of validity of the resulting approximate solution. Special limiting cases of very gently undulating surfaces and uniformly rough surfaces are examined. New and illuminating results are obtained for the latter case.     

Scattering by a Conducting Infinite Cylinder Illuminated with a Shaped Beam

An analytic solution to the shaped beam scattering by a conducting infinite cylindrical particle is constructed within the framework of the generalized Lorenz-Mie theory (GLMT). The expansion coefficients of the scattered electromagnetic fields are derived by using the boundary conditions. As an example, for a tightly focused Gaussian beam propagating perpendicular to the cylinder axis, the scattering characteristics that obviously demonstrate the three-dimensional nature, as with the case of a dielectric infinite cylinder, are described in detail, and numerical results of the normalized differential scattering cross section are evaluated.     

Electromagnetic scattering by indented screens

The problem of three dimensional electromagnetic scattering from a perfectly conducting screen with a bounded indentation is formulated as a system of boundary integral equations for the electric current density on the cavity wall and the interface between the cavity and free space. It is shown how the fictitious current density on the interface may be eliminated resulting in an integral equation of the second kind for the current density on the cavity wall only, with no integration over the infinite screen. In addition, integral representations are derived that represent the field everywhere in space in terms of the current density on the cavity wall only. Furthermore, asymptotic expressions for the far field are also presented. The equations and representations simplify considerably in the two-dimensional scalar case and results are presented for both TE and TM polarization     

Electromagnetic scattering by a perfectly conducting patch array ona dielectric slab

The scattering characterization of an infinite and truncated periodic array of perfectly conducting patches on a dielectric slab is discussed. In particular, an approximate solution for the truncated array scattering that is based on the exact solution for the corresponding infinite array is presented. The latter is obtained numerically by solving for the patch currents using a conjugate-gradient fast Fourier transform (FFT) technique, eliminating the need to generate and store the usual square impedance matrix. The scattering pattern of the finite array is then computed approximately by integrating the infinite-period-array currents over the given finite array. Numerical results are presented for the infinite and finite arrays, and the accuracy of the approximate solution for the finite array is examined and discussed in relation to some available exact data. It is found that the approximate solution is of reasonable accuracy in predicting the scattering by the truncated array     

Image Theory Results for the Mutual Impedance of Crossing Earth Return Circuits

Suitable engineering expressions for the mutual impedance of crossing earth return circuits are derived by employing finitely conducting earth image theory techniques. It is shown that the image theory and previously derived analytical results, which are rather complicated, are in excellent agreement.     

Electromagnetic Coupling to an Infinite Cable Placed Behind a Slot-Perforated Screen

We present an analysis of the electromagnetic coupling from an external illuminating field to an infinitely long thin cable placed behind the conducting screen that is perforated by a narrow slot. By using a Fourier transform representation for the unknown electric current on the cable, we obtain an integro-differential equation for the distribution of the electric field in the slot that accounts completely for the coupling. The transfer admittance function so obtained, is in a form very convenient to estimate the electric current on the infinite cable. Results of the slot electric-field distribution and the current induced on the infinite cable are given for a few typical cases. Not surprisingly, the axial distribution of induced voltage on the slot is markedly affected by the presence of the cable.     

Spectral domain analysis of electromagnetic wave scattering by an infinite plane metallic grating

A new method, based on the spectral domain analysis, is presented for solving the electromagnetic wave scattering by an infinite plane metallic grating. The key point of the present method is discretization of spectral formulation in terms of the sampling theorem. Two different polarizations, transverse magnetic (TM) and transverse electric (TE) excitations, are considered here. Accuracy of the present method is examined numerically by comparison with the rigorous Wiener-Hopf solutions which are applicable only to a special case. Since the end effect of a conducting strip is taken into account analytically, final results show enough convergence to evaluate the near fields as well as the far fields with small matrix calculations. Some numerical examples are shown mainly for surface current distributions to make clear the differences between the two different polarizations.     

Current evaluation on the faces of an impedance wedge illuminatedby an electromagnetic pulse

The scattering of an electromagnetic time-dependent plane wave by the edge of an impedance wedge is analyzed. Suitable expressions are presented for the surface currents which are induced on the two faces of the wedge. Numerical results are shown for different electrical and geometrical configurations and compared with data available in the literature for the case of a perfectly conducting wedge     

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.