Moment-method modeling of short-pulse scattering from and theresonances of a wire buried inside a lossy, dispersive half-space

A frequency-domain method-of-moments (MoM) algorithm is used to model short-pulse plane-wave scattering from a wire buried inside a lossy, dispersive half-space with the time-domain scattered fields computed via the Fourier transform. Further, the complex resonant frequencies of such targets are also calculated via the MoM. The phenomenology associated with scattering from a buried wire is investigated in detail, and it is demonstrated that the time-domain scattered fields and the target resonances depend on the buried-wire orientation as well as the electrical properties of the half-space     

Three-dimensional inverse scattering of a dielectric target embedded in a lossy half-space

A modified iterative Born method is applied for three-dimensional inversion of a lossless dielectric target embedded in a lossy half-space. The forward solver employs a modified form of the extended Born method, and the half-space Green's function is computed efficiently via the complex-image technique. Example results are shown, with all scattering data based on a computational model, utilizing a rigorous forward solver distinct from that employed in the inversion. In addition, distinct gridding schemes are used in the forward and inverse solvers. Simple Tikhonov regularization is found to yield adequate results for inversion of noisy data.     

Diffraction tomographic algorithm for the detection ofthree-dimensional objects buried in a lossy half-space

A diffraction tomographic (DT) algorithm has been proposed for detecting three-dimensional (3-D) dielectric objects buried in a lossy ground, using electric dipoles or magnetic dipoles as transmitter and receiver, where the air-earth interface has been taken into account and the background is lossy. To derive closed-form reconstruction formulas, an approximate generalized Fourier transform is introduced. Using this algorithm, the locations, shapes, and dielectric properties of buried objects can be well reconstructed under the low-contrast condition, and the objects can be well detected even when the contrast is high. Due to the use of fast Fourier transforms to implement the problem, the proposed algorithm is fast and quite tolerant to the error of measurement data, making it possible to solve realistic problems. Reconstruction examples are given to show the validity of the algorithm     

High-frequency scattering by objects buried in lossy media

The uniform geometrical theory of diffraction (UTD) is extended so that it can be used to calculate the scattering from an object buried in a lossy medium. First, the accuracy of this high frequency method is examined by comparing numerical results for the scattering by a polygonal cylinder in a lossy medium of infinite extent with calculations based on a method of moments (MoM) solution. Next, the more difficult scattering problem of a polygonal cylinder in a lossy half space is treated. The UTD solution for the unbounded region is employed together with the fields of rays introduced by the interface between air and the lossy medium to obtain expressions for the scattered field in air and in the lossy medium     

Fast multipole method for scattering from an arbitrary PEC targetabove or buried in a lossy half space

The fast multipole method (FMM) was originally developed for perfect electric conductors (PECs) in free space, through exploitation of the spectral properties of the free-space Green's function. In the work reported here, the FMM is modified, for scattering from an arbitrary three-dimensional (3-D) PEC target above or buried in a lossy half space. The “near” terms in the FMM are handled via the original method-of-moments (MoM) analysis, wherein the half-space Green's function is evaluated efficiently and rigorously through application of the method of complex images. The “far” FMM interactions, which employ a clustering of expansion and testing functions, utilize an approximation to the Green's function dyadic via real image sources and far-field reflection dyadics. The half-space FMM algorithm is validated through comparison with results computed via a rigorous MoM analysis. Further, a detailed comparison is performed on the memory and computational requirements of the MoM and FMM algorithms for a target in the vicinity of a half-space interface     

Properties of a cylindrical antenna in an infinite planar or collinear array

A solution is given for the active impedance and current distribution on a cylindrical antenna in a uniform, infinite, planar, or collinear array. The analysis is applicable to the case in which the distance in the collinear direction between the ends of adjacent elements is small. The current distribution on the collinear array is found by relating the antenna current and electric-field variation on the cylindrical surface of infinite length which contains the array. This analysis is then extended to consider a planar array. Results obtained are applicable to any combination of element length and array phasing, for arrays with or without a ground plane. Comparisons with other investigations based upon sinusoidally distributed currents reveal substantial discrepancies for some configurations.     

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.     

Asymptotic theory for dipole radiation in the presence of a lossy slab lying on a conducting half-space

The basic theory for dipole radiation in the presence of a two-layer half-space is outlined with special reference to its use as a model for studying radio propagation through and over heavily vegetated terrain. The source dipole may be located above or below the top surface of the slab. The dipole orientation is either vertical or horizontal. The asymptotic derivations for the field expressions are carried out without making the usual assumption that the refractive index of the uppermost layer is large compared with unity. The final results exhibit the expected inverse square dependence of the field on horizontal range.     

Complex natural resonances of conducting planar objects buried in adielectric half-space

A scheme is presented to incorporate a mixed potential integral equation (MPIE) using Michalski's “formulation C” with the method of moments (MoM) for analyzing the scattering of a plane wave from conducting planar objects buried in a dielectric half-space. The robust complex image method with a two-level approximation is used for the calculation of the Green's functions for the half-space. To further speed up the computation, an interpolation technique for filling the matrix is employed. While the induced current distributions on the object's surface are obtained in the frequency domain, the corresponding time domain responses are calculated via the inverse fast Fourier transform (FFT). The complex natural resonances of targets are then extracted from the late time response using the generalized pencil-of-function (GPOF) method. The authors investigate the pole trajectories as they vary the distance between strips and the depth and orientation of single, buried strips. The variation from the pole position of a single strip in a homogeneous dielectric medium was only a few percent for most of these parameter variations     

Transient plane wave coupling to bare and insulated cables buriedin a lossy half-space

The current induced on an infinite bare or insulated cable buried in a lossy earth medium due to a transient plane wave is presented. An exact solution is formulated in the frequency domain using a spatial transform under the thin-wire approximation. The widely used equivalent circuit transmission line model is derived from the exact solution. Results are presented for typical transmission structures under high frequency transient excitation and the exact solution is compared with the transmission line approximation. The transmission line approach provides good results for a wide range of cases. For accurate results in the high frequency situation it is necessary that the correct incident field expressions be used and that a complete representation of the earth's electrical properties (σ and ϵ) be retained     

Multidomain pseudospectral time-domain simulations of scattering by objects buried in lossy media

A multidomain pseudospectral time-domain (PSTD) method with a newly developed well-posed PML is introduced as an accurate and flexible tool for the modeling of electromagnetic scattering by 2-D objects buried in an inhomogeneous lossy medium. Compared with the previous single-domain Fourier PSTD method, this approach allows for an accurate treatment of curved geometries with subdomains, curvilinear mapping, and high-order Chebyshev polynomials. The effectiveness of the algorithm is confirmed by an excellent agreement between the numerical results and analytical solutions for perfectly conducting as well as permeable dielectric cylinders. The algorithm has been applied to model various ground-penetrating radar (GPR) applications involving curved objects in a lossy half space with an undulating surface. This multidomain PSTD algorithm is potentially a very useful tool for simulating antennas near complex objects and inhomogeneous media.     

Plane wave scattering from 2-D perfectly conducting superquadriccylinders

The plane-wave scattering from perfectly conducting two-dimensional cylinders of arbitrary squareness parameter is investigated. A uniform geometrical optics (UGO) solution valid across the smooth caustics generated by the surface poles or zero curvature (inflection) points is developed based on physical optics (PO). The classical geometrical optics solution is modified using a multiplicative transition function that compensates for the caustic singularities and accounts for the complex ray contributions emanating from nonspecular scattering centers located near the surface poles. The transition function is heuristically derived on the basis of the PO radiation integral and involves a generalized (higher-order) form of Airy functions. The resulting UGO solution for the scattered field is simple, easy to apply, and computationally efficient for electrically large cylinders. It compares well with physical optics (numerical integration) and moment-method solutions for both backscatter and limited bistatic configurations     

Multiple scattering among vias in lossy planar waveguides using SMCG method

Large-scale full-wave multiple scattering among cylindrical vias in planar waveguides is modeled using the Foldy-Lax equation. The formulation includes the skin effects of the conducting power/ground plane. Numerical solution of the Foldy-Lax equation with large number of unknowns is computed efficiently using the sparse-matrix canonical-grid method. In this method, interactions among vias are decomposed into the strong interactions part and the weak interactions part. The calculation of the weak part is carried out using two-dimensional (2-D)-fast Fourier transform (FFT) by translating the locations of the vias onto the uniform grids. The final solution of the Foldy-Lax equations is calculated by an iterative method. The results show O (N log N) CPU efficiency and O (N) memory efficiency. This makes large scale via problems possible for computer simulation.     

Plane wave scattering from a cylinder loaded periodically withgroups of metallic rings

The scattering of an electromagnetic plane wave from a cylinder with circular cross-section loaded periodically with groups of metallic annular rings along the longitudinal axes is analysed. The incident plane wave is arbitrarily polarised and impinges on the cylinder at an oblique incidence     

Plane wave scattering by a material coated parabolic cylinder

An eigenfunction solution to the problem of transverse magnetic (TM) or transverse electric (TE) scattering by a coated parabolic cylinder is presented. Paralleling the well-known solution for the coated circular cylinder, eigenfunction expansions involving parabolic cylinder functions are obtained for the fields in the exterior and coating regions. Next, boundary conditions are enforced to obtain a pair of coupled equations for the unknown coefficients in the eigenfunction expansions for the fields. Unlike the corresponding solution for the coated circular cylinder, the eigenfunctions in the exterior and coating regions are not orthogonal, and an exact term-by-term solutions of these equations is not possible. Instead, the equations are solved by the method of moments. For thin coatings both an uncoupled-mode approximation and a surface-impedance model are described. In particular, for the TM polarization it is shown that a thin coating can be modeled by a specific nonuniform surface impedance for which an exact term-by-term solution is possible. Numerical data are presented, showing the convergence of the solution and comparing the solutions for the uncoupled-mode and surface-impedance models     

Coherent wave reflection from a random half-space

An exact solution to the scalar Dyson equation in the bilocal approximation is given for a scalar wave obliquely incident on a random half-space whose mean dielectric constant is the same as that for the uniform nonrandom medium in the conjugate halfspace. It is shown that in addition to the dominant coherent wave, a second highly damped wave is weakly excited at the interface.     

Radiation impedance of a dipole printed on periodic dielectric slabs protruding over a ground plane in an infinite phased array

The radiation impedance of a dipole printed on periodic dielectric slabs standing over a ground plane in an infinite phased array is calculated. The calculation is made by means of modal expansions in terms of longitudinal section electric (LSE) and longitudinal section magnetic (LSM) modes. Derivations of these hybrid space modes and development of the modal expansions are presented first. The impedance of the dipole element is then calculated by a method based on the complex power relations with the aid of Poynting's theorem. The results calculated by the present theory in the limiting case of no dielectric slab loading have been compared with the results calculated by the method of ordinary plane wave expansions. A comparison is also made between results calculated by the theory and the experimental data obtained from waveguide simulators or test array. These results are shown to be in good agreement. An outline of steps to formulate the solution of the current distribution on dipole is also given.     

On the scattering of electromagnetic waves by bodies buried in a half-space with locally rough interface

A method for the scattering of electromagnetic waves from cylindrical bodies of arbitrary materials and cross sections buried beneath a rough interface is presented. The problem is first reduced to the solution of a Fredholm integral equation of the second kind through the Green's function of the background medium. The integral equation is treated here by an application of the method of moments (MoM). The Green's function of the two-part space with rough interface is obtained by a novel approach which is based on the assumption that the perturbations of the rough surface from a planar one are objects located at both sides of the planar boundary. Such an approach allows one to formulate the problem as a scattering of cylindrical waves from buried cylindrical bodies which is solved by means of MoM. The method is effective for surfaces having a localized and arbitrary roughness. Numerical simulations are carried out to validate the results and to show the effects of some parameters on the total field. The present formulation permits one to get the near and far field expression of the scattered wave.