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.     

Electromagnetic boundary value problem in the presence of a partlylossy dielectric: considerations about the uniqueness of the solution

This paper deals with the uniqueness of the solution of a boundary value problem defined by specifying the tangential components of the electric field over the closed regular boundary (or the tangential components of the magnetic field over the boundary, or the former components over part of the boundary and the latter components over the rest of the boundary) of a limited region containing a linear dielectric material not lossy everywhere. In particular, the uniqueness of the solution is proved in the case where the dielectric is everywhere linear, homogeneous, and lossless, except for a subregion where the dielectric is lossy, linear but not necessarily homogeneous     

Reconstruction of multilayered lossy dielectrics from one-sidedplane wave impulse reflection responses: the bistatic case

Motivated by numerous scattering problems where the media is lossy and yet can only be investigated from a single side, the authors discuss algorithms for reconstructing a lossy, stratified dielectric from one-sided plane wave impulse reflection responses. Novel features of these algorithms include: 1) solving the lossy media problem using only one-sided reflection response data; 2) exploiting oblique probing angles; 3) having origins in digital signal processing (DSP) theory; 4) employing fast algorithms that have been modified to solve the forward scattering problem; and 5) solving the scattering problems exactly, including accounting for multiple reflections. A new algorithm is introduced that reconstructs such a media from one-sided transverse electric (TE) and transverse magnetic (TM) impulsive plane wave reflection responses from a single oblique angle. The oblique-probing angle necessitates a bistatic measurement configuration. New probing constraints are developed for a previously presented algorithm based on probing at two angles of incidence. Algorithm stability and data correction are addressed. Numerical examples illustrate the new algorithm in synthesizing the media transient response and reconstructing the media     

A modified geometrical optics method for scattering by dielectric bodies

A method based on ray optics is developed for calculating the scattering from dielectric bodies. The fields of geometrical optics are used except for two types of rays where the fields must be corrected from physical optics solutions. The customary advantages of ray techniques are realized, namely, a simplicity in the resulting formulas, a ready interpretation of the scattering mechanism and the possibility of extension to a wider class of problems through the inclusion of additional rays. The method has been applied to several lossless dielectric shapes: the circular cylinder, the sphere, the prolate spheroid and to a lossy dielectric shell. The relative dielectric constants considered range from 0.25 to 1.80, except in the case of the shell. The calculated results are compared with those obtained from boundary value solutions, with the exception of the spheroid where measured values are used. Good results are obtained for all sizes considered except those which are very small and behave as Rayleigh scatterers. The failure in the region of Rayleigh scattering is to be expected. Thus, for the class of dielectric scatterers treated here there is no region of scattering resonance corresponding to that of similar metallic shapes where the geometrical optics solution is no longer valid.     

A doubly periodic moment method solution for the analysis anddesign of an absorber covered wall

A periodic moment-method solution for scattering from a doubly periodic array of lossy dielectric bodies is developed. The purpose is to design electromagnetic wedge and pyramidal absorbers for low reflectivity so that one can improve the performance of anechoic chamber measurements. The spectral-domain formulation and the moment-method volume polarization current approach are used to obtain the expressions for determining the scattering from a doubly periodic array of lossy dielectric bodies. Some wedge and pyramidal absorber configurations that have been designed, fabricated, and tested in the OSU/ESL compact range measurement facility are presented. By taking into account the complexity of real-world material structures, good agreement between calculations and measurements has been obtained     

A comparison of formulations for the vector finite element analysisof waveguides

The principal formulations that have been proposed for finding the modes of waveguides by the finite element method are reviewed and compared. In each case, it is shown how Maxwell's equations may be reduced to matrix form using the method of weighted residuals. The formulations are compared from several points of view: their ability to handle spurious modes, lossy materials, and reentrant corners; the number of field components; and the properties of the matrices. Three benchmark problems are described and used to compare the formulations: a rectangular waveguide partially loaded with lossless dielectric; an air-filled, double-ridged waveguide; and a shielded image guide with either lossless or lossy dielectric     

An efficient algorithm for electromagnetic scattering from rough surfaces using a single integral equation and multilevel sparse-matrix canonical-grid method

An efficient algorithm for wave scattering from two-dimensional lossy rough surfaces is proposed. It entails the use of a single magnetic field integral equation (SMFIE) in conjunction with a multilevel sparse-matrix canonical-grid (MSMCG) method. The Rao-Wilton-Glisson (RWG) triangular discretization is adopted to better model the rough surface than the pulse basis functions used in the well-established SMCG method. Using the SMFIE formulation, only one unknown per interior edge of the triangular mesh approximating the rough surface is required, and the iterative solution to the moment equation converges more rapidly than that of the conventional coupled equations for dielectric rough surfaces. The MSMCG method extends the applicability of the SMCG method to rougher surfaces. Parallel implementation of the proposed method enables us to model dielectric surfaces up to a few thousand square wavelengths. Simulation results are presented as bistatic scattering coefficients for Gaussian randomly rough surfaces.     

A moment method solution for TMz and TEzwaves illuminating two-dimensional objects above a lossy half space

A moment method (MM) solution for analyzing the electromagnetic shielding and scattering properties of two-dimensional (2-D) objects over a lossy half space is presented. The materials of the objects can be metal, dielectric, or magnetic. Also, the lossy half space is included to simulate the effects of the earth ground or any flat homogeneous lossy surface. An MM based on a volume formulation and a special Green's function in the spectral domain is developed. Both TM _z and TE_z waves incident upon 2-D metal or lossy material structures are demonstrated for the shielding effects of those bodies in the presence of the lossy ground. Besides, the echo widths of a composite object either in free space or above the lossy half space are determined by using the MM. Some of the results are compared with those by other methods, and good agreements are obtained. The MM solution can be used to study the shielding and scattering problems for cylindrical structures located over a lossy ground     

Scattering of electromagnetic waves by a perfectly conductingcylinder with a thin lossy magnetic coating

We study the scattering interaction of electromagnetic (EM) waves with an infinite cylinder coated with a lossy dielectric material with frequency-dependent material properties. These properties are hypothetical, yet representative of a wide class of available materials. The monostatic and bistatic scattered widths (SW) are evaluated for the TM or TE polarization cases. These calculations require the use of algorithms to evaluate Bessel-Hankel functions of complex arguments. These algorithms are based on a continued fraction approach, which ensures stability of the recursion relations. The bistatic plots of the TM and TE scattering widths for the coated body are displayed in a convenient color-graded scale. The reductions in the scattering widths produced by this type of coating are determined in selected frequency bands and angular sectors, in both polarization cases. It is quantitatively shown how curvature and polarization shift the effectiveness band of the coating. The determined regions in which the SW are minimally affected are the most suitable for target identification purposes     

Complex resonances of conducting spheres with lossy coatings

The electromagnetic scattering amplitude for metal objects coated with a lossless dielectric exhibits a large number of resonances versus real frequency. These resonances are a function of the object shape and size, coating thickness, and coating electrical properties. Previously, it was shown that for coated spheres and nonspherical bare objects, these resonances can be understood in terms of phase matched circumnavigating surface waves and the objects' complex eigenfrequencies. The effect of dielectric loss in the coating on the complex eigenfrequencies and phase velocities of these surface waves is presented for a metal sphere coated with a uniform homogeneous dielectric coating. It is seen that the positions of the complex resonance frequencies move away from the real frequency axis under the influence of dielectric loss in the coating. The effect of this is shown to correspond to the changes in the backscatter spectrum versus real frequency as computed using a Mie series expansion. The significant difference between the lossless and lossy dielectric-coated sphere cases is seen to be due to a modification of the phase velocities of surface waves, particularly the whispering gallery types, and the increased attenuation of the surface wave modes     

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.     

Electromagnetic scattering by arbitrary shaped three-dimensional homogeneous lossy dielectric objects

The recent development and extension of the method of moments technique for analyzing electromagnetic scattering by arbitrary shaped three-dimensional homogeneous lossy dielectric objects is presented based on the combined field integral equations. The surfaces of the homogeneous three-dimensional arbitrary geometrical shapes are modeled using surface triangular patches, similar to the case of arbitrary shaped conducting objects. Further, the development and extensions required to treat efficiently three-dimensional lossy dielectric objects are reported. Numerical results and their comparisons are also presented for two canonical dielectric scatterers-a sphere and a finite circular cylinder.     

THE ELECTROMAGNETIC SCATTERING OF A RADIALLY INHOMOGENEOUS DIELECTRIC CYLINDER

A new method is demonstrated for solving the electromagnetic scattering problemof a radially inhomogeneous lossless or lossy dielectric cylinder by Fourier series expansion.Com-pared with other methods,the method is simpler in numerical calculation and can be used forsolving scattering problems of a cylinder due to an arbitrary incident electromagnetic beam.     

Scattering by thin dielectric strips

A plane wave incident on a thin dielectric strip with infinite length is considered, letting the incident electric field vector be parallel with the edges of the strip. The field is expanded in the dielectric region as the sum of three plane waves (the forced wave and two surface waves). Thex-axis andy-axis propagation constants are known for each wave, and Galerkin's method is employed to determine the amplitudes of these waves. Finally, the far-zone scattered field is determined by considering the polarization currents radiating in free space. Numerical data are presented to illustrate the scattering properties of lossless and lossy dielectric strips as a function of the angle of incidence and the width of the strip. The calculations show excellent agreement with an earlier moment method using pulse bases and point matching.     

Angularly propagating waves in a radially inhomogeneous, lossy dielectric cylinder and their connection with the natural modes

A physical interpretation is proposed for the natural modes of a radially inhomogeneous, lossy dielectric circular cylinder embedded in a homogeneous, lossless dielectric. These modes are either of the creeping-wave or of the whispering-gallery type. With the aid of a generalized Wentzel-Kramer-Brillouin (WKB) asymptotics, an asymptotic characteristic equation is derived for each type, which can be explained physically. Numerical results obtained from the exact characteristic equation and both approximate equations are presented and discussed.     

Prediction-correction method for electromagnetic imaging withcurrent reconstruction

A prediction-correction methodology is presented for improving the numerical stability of the iterative process involved in the solution of nonlinear inverse scattering problems related to the electromagnetic imaging of dielectric objects. In various methods developed so far, each iteration is performed by only using the results obtained in the preceding iteration. The results computed in the preceding iteration along with those acquired in previous iterations are employed selectively to make a prediction of the object function to be used in the next iteration. As a consequence, the numerical stability and the convergence of the iterative process are improved. This is illustrated by numerical computation results obtained for lossless and for lossy dielectric bodies     

Calibration of bistatic polarimetric radar systems

A calibration technique for laboratory type polarimetric, bistatic instrumentation radars is presented. It describes the errors induced by the standard radiation transfer approach (I-SRT) in a way similar to that for the monostatic case. A 12-term error correction and absolute polarimetric calibration is performed with two external reference targets. Only the polarimetric bistatic reference of the first target must be theoretically determined. The scattering reference of the second target is determined by a measurement during the calibration process (single reference calibration). The simulation of a third cross-polarization measurement is performed by an antenna rotation and a remeasurement of the second target. Thus all data are gained for the determination of the error terms and measurements of unknown objects can be full polarimetrically calibrated. The procedures are shown for an adapted dihedral corner reflector. Misalignment errors are discussed     

Field Solution for Radial Waveguides with Annular Discontinuities

A method is established which gives the internal field of a radial waveguide in the presence of annular-type slots on the conducting walls or metallic scatterers inside the guide. The exciting field can have a general form, and the dielectric constant of the region could be lossy or lossless. To obtain a solution, the induced currents (magnetic current in case of slot-type discontinuity) over the scattering bodies are expanded into a finite series of suitable basis functions with unknown coefficients. The total number of these functions is directly related to the electrical dimensions of the scatterers. The complex coefficients are then obtained by employing the appropriate Green's functions and an application of the boundary conditions over the scattering bodies. The method is then applied to the probIem of coupling between two radials waveguides by annular slots on the common boundary. It is shown that in general, higher order modes have significant effect on the solution, and for a precise evaluation of the field their contribution must also be included.     

Electromagnetic plane wave scattering by a system of two uniformlylossy dielectric prolate spheroids in arbitrary orientation

By means of modal series expansions of electromagnetic fields in terms of prolate spheroidal vector wave functions, an exact solution is obtained for the scattering by two uniformly lossy dielectric prolate spheroids in arbitrary orientation embedded in free space, the excitation being a monochromatic plane electromagnetic wave of arbitrary polarization and angle of incidence. Rotational-translational addition theorems for spheroidal vector wave functions are employed to transform the outgoing wave from one spheroid into the incoming wave at the other spheroid. The field solution gives the column vector of the unknown coefficients of the series expansions of the scattered and transmitted fields expressed in terms of the column vector of the known coefficients of the series expansions of the incident field and the system matrix which is independent of the direction and polarization of the incident wave. Numerical results in the form of curves for normalized bistatic and monostatic radar cross sections are given for a variety of two-body system of uniformly lossy dielectric prolate spheroids in arbitrary orientation having resonant or near resonant lengths and different distances of separation     

Input Admittance of a Circular Waveguide Aperture Covered by a Dielectric Slab

The input admittance of a circular waveguide opening onto an infinite flange with a homogeneous lossy dielectric coating is derived using integral transforms and assuming the dominant TE11mode as the trial field at the aperture. Admittance calculations for low-loss dielectric sheets of various thicknesses are given and compared with measurements obtained using ground planes of varying sizes. Excellent agreement with theory is obtained for the circular waveguide terminated into a square ground plane only1lambdato2lambda. on a side. A quantitative comparison of the surface wave contribution to the total admittance is also given.