Showing papers in "Journal of Electromagnetic Waves and Applications in 1989"

Boundary integral formulations for homogeneous material bodies

Abstract: There are many boundary integral formulations for the problem of electromagnetic scattering from and transmission into a homogeneous material body. The only formulations which give a unique solution at all frequencies are those which involve both electric and magnetic equivalent currents, and satisfy boundary conditions on both tangential E and tangential H. Formulations which involve only electric (or magnetic) equivalent currents, and those which involve boundary conditions on only tangential E (or tangential H) are singular at frequencies corresponding to the resonant frequencies of a resonator formed by a perfect conductor covering the surface of the body and filled with the material exterior to the body in the original problem.

K-distribution and polarimetric terrain radar clutter

Abstract: A multivariate K-distribution is proposed to model the statistics of fully polarimetric radar data from earth terrain with polarizations HH, HV, VH, and VV. In this approach, correlated polarizations of radar signals, as characterized by a covariance matrix, are treated as the sum of N n-dimensional random vectors; N obeys the negative binomial distribution with a parameter alpha and mean N-bar. Subsequently, an n-dimensional K-distribution, with either zero or nonzero mean, is developed in the limit of infinite N-bar or illuminated area. The probability density function (PDF) of the K-distributed vector normalized by its Euclidean norm is independent of the parameter alpha and is the same as that derived from a zero-mean Gaussian-distributed random vector.

Polarizability and Effective Permittivity of Layered and Continuously Inhomogeneous Dielectric Ellipsoids

Abstract: In this paper, the polarizabilities of partially and continuously inhomogeneous dielectric ellipsoids are analyzed. Multilayer inclusions where the boundaries between the layers are confocal ellipsoids, are solved in a static field. Transmission line analogy is applied, resulting in matrices with which the field components and the polarizability can be solved. In case of the continuous permittivity profile, a differential equation is derived for the scattered potential, and from the amplitude of this function, the polarizability results. The limitation in the continuous case is that the permittivity function of the ellipsoid depend only on one coordinate (ξ) in the ellipsoidal coordinate system. The theory is applied to calculating the microwave attenuation of melting hail at the frequency of 1 GHz, where the hydrometeors are modeled as two-layer ellipsoids.

The Phase Perturbation Technique vs. an Exact Numerical Method for Random Rough Surface Scattering

Abstract: There is a need for a solution to the problem of wave scattering from rough surfaces that is accurate when both the classical field perturbation and Kirchhoff approximations are not. In previous work it was shown numerically that the phase perturbation reflection and backscattering coefficients reduce to those of field perturbation theory and the Kirchhoff approximation in the appropriate limits; however, for cases when the classical solutions did not apply, the accuracy of the phase perturbation results could not be determined. In this paper we examine the validity of the phase perturbation technique for a region in parameter space when the two classical solutions fail. Numerical results for the bistatic scattering cross section are compared with exact numerical results for one-dimensional surfaces having a Gaussian roughness spectrum and satisfying a Dirichlet boundary condition. It is found that in the region considered the phase perturbation results agree with the exact results over all scattered angl...

Beam diffraction by half planes and wedges: uniform and asymptotic solutions

Abstract: The complex source point method converts an omnidirectional source diffraction solution into a beam solution by an appropriate choice of complex source coordinates. In so doing shadow and reflection boundary singularities of the geometrical theory of diffraction become non-singular, in general. Thus the suggestion that, for certain parameters, transition region functions are unnecessary. Here numerical results from uniform and asymptotic solutions for beam diffraction by half-planes and wedges indicate this is so only if diffraction is negligible. Convenient uniform expressions are shown to provide accurate far field values for all parameters.

Theoretical Models for Polarimetric Microwave Remote Sensing of Earth Terrain

Abstract: Using the two-layer anisotropic random medium, a mathematically rigorous, fully polarimetric model is developed to compute the Mueller and covariance matrices in the backscattering direction for various kinds of earth terrain. The electric field is first written in the form of an integral equation involving the unperturbed dyadic Green's function in the absence of the permittivity fluctuations. The integral equation is then solved by an iterative series known as the Born series. With only the first term of the series, which physically describes a single scattering process, the fully polarimetric backscattering coefficients are derived. Four different kinds of upgoing and downgoing waves exist due to the excitation of both ordinary and extraordinary waves in the anisotropic random medium. An averaging scheme over the azimuthal direction is used to simulate the effects on the radar backscattering due to the azimuthal randomness in the growth direction of leaves in tree and grass fields.

Computation of the propagation characteristics of TE and TM modes in arbitrarily shaped hollow waveguides utilizing the conjugate gradient method

Abstract: This paper describes the use of the conjugate gradient method in conjunction with the finite difference method for the calculation of the propagation characteristics of TE and TM modes, including cutoff wavenumbers and field distribution, of hollow conducting waveguides of arbitrary cross sections. This method is quite fast and accurate and can be applied in a straightforward fashion for the analysis of both TE and TM modes in waveguides of arbitrary cross sections. In order to check the accuracy of this method, the new approach has been applied to compute the cutoff wavelength of a rectangular waveguide as analytical results are available for this problem. This method has also been applied to compute the first six TE and TM modes for L-shaped, single ridge, vaned rectangular, T-septate and rectangular coaxial waveguides. Comparison of accuracy is made whenever data is available. Since the conjugate gradient method is an iterative method, computer storage is 6N instead of N2 for conventional matrix method...

Generalised space domain Green's dyadic for multilayered media with special application to microwave interconnections

Abstract: The eigenmode problem for multilayered structures with coplanar or non-coplanar strips is analysed using the space domain Green's dyadic of these structures as the kernel of an integral equation. The integral equation is solved using the method of moments combined with point-matching. The calculation of the Green's dyadic starts in the spectral domain. First, an efficient solution technique is presented to determine the spectral Green's dyadic. Special attention is then devoted to its behaviour for large values of the Fourier variable and to the contribution of this asymptotic part to the space domain Green's dyadic. The behaviour of the fields in the vicinity of the excitation is determined explicitly. The method is illustrated by two typical examples.

Lateral electromagnetic pulses generated on a plane boundary between dielectrics by vertical and horizontal dipole sources with Gaussian pulse excitation

Abstract: The exact lateral electromagnetic pulse generated by a vertical dipole excited by a Gaussian pulse is derived. A comparison with the previously derived approximate formula shows that the latter gives the correct field at all radial distances except for the nonappearance of the relatively small second pulse. Corresponding approximate formulas are derived for the electric field of a horizontal dipole. These should give the correct field except for the nonappearance of the small second pulse in some components.

Transient Analysis of Frequency-Dependent Transmission Line Systems Terminated with Nonlinear Loads

Abstract: A new method for analyzing frequency-dependent transmission line systems with nonlinear terminations is presented. The generalized scattering matrix formulation is used as the foundation for the time domain iteration scheme. Compared to the admittance matrix approach proposed in a previous paper, it has the advantage of shorter impulse response which leads to smaller computer memory requirement and faster computation time. Examples of a microstrip line loaded with nonlinear elements are given to illustrate the efficiency of this method.

Scattering from a Dielectric Cylinder Partially Embedded in a Perfectly Conducting Ground Plane

Abstract: A rigorous field analysis of the problem of scattering from a dielectric cylinder partially embedded in a perfectly conducting ground plane, and excited by a magnetic or electric line current in the free space outside the dielectric cylinder, is given in this paper. The dielectric medium is assumed to be linear, homogeneous, isotropic, although not necessarily free from losses. A field equivalence theorem is utilized to derive, for each excitation, an integral equation for the equivalent magnetic current on the dielectric interface, which is later solved using Galerkin's method. The equivalent magnetic currents are then used to determine the scattered field everywhere outside and inside the dielectric cylinder. Numerical results for the equivalent magnetic currents and far scattered field patterns are given. The resonances of the partially embedded dielectric cylinder are also defined and computed for both polarizations.

Electromagnetic coupling by a wire through a circular aperture in an infinite planar screen

Abstract: The problem of electromagnetic penetration on a wire passing through an infinite screen is considered. An electric field integral equation is formulated, and solutions are obtained using both a zeroth order approximation and the method of moments. Numerical results for both the equivalent admittance and the current on the wire are obtained using both methods. The two solutions are then compared to verify the accuracy of the zeroth order approximation. It is found that the zeroth order approximation is valid for aperture radii less than 1/10 of a wavelength. It is also found that the electromagnetic coupling through the aperture is enhanced strongly by the presence of the wire.

A hybrid method for solving time-domain integral equations in transient scattering

Abstract: The authors proposed a hybrid method that combines the advantages of the frequency-domain techniques and the marching-on-in-time method while avoiding their disadvantages. As in the marching-on-in-time method, the time-domain integral equations are discretized in space. This results in a system of linear time-domain equations of a fixed dimension. This system, in turn, is solved by the frequency-domain procedure of subjecting it to a temporal Laplace or Fourier transformation. Using this approach, the authors solved three scalar scattering problems for which benchmark results obtained by alternative methods were available.<>

A comparison of integral, differential and hybrid methods for TE-wave scattering from inhomogeneous dielectric cylinders

Abstract: Trade-off's between integral and differential equation formulations for electromagnetic wave scattering from highly inhomogeneous dielectric bodies are evaluated, via a comparison of three different frequency-domain formulations for TE-wave scattering from dielectric cylinders. The formulations considered include a volume integral equation, a volume differential equation combined with an approximate near-field radiation condition, and a hybrid method using both a surface integral and volume differential equation. Numerical results indicate that all three methods have similar accuracy for a given scatterer model, and that the methods incorporating differential equations have significant computational advantages over volume integral formulations.

An Exact Solution of Mie Type for Scattering by a Multilayer Anisotropic Sphere

Abstract: The purpose of this paper is to describe methods of resolving discrepancies between experimental observations of scattering by crystalline particles and attempts to explain these observations assuming that the electrical properties of these particles can be described by the use of scalar valued functions for the permittivity, conductivity, and permeability. We can develop coupled integral equations describing the interaction of electromagnetic radiation with a heterogeneous, penetrable, dispersive, anisotropic scatterer and can use several methods of solving these integral equations. The solution of the problem of describing scattering by an anisotropic sphere can be substituted into the integral equation to check the integral equation formulation of the problem. Conditions are given for the uniqueness of the solution of the associated transmission problem. Because of the multiple propagation constants in an anisotropic material, the trivial uniqueness arguments valid for isotropic scatterers do not have ...

E-polarization diffraction by a thick metal-dielectric join

Abstract: A solution of the diffraction from a dielectric-metallic join due to an incident E1 -polarized plane wave is presented. Direct diffraction, coupling, launching, and reflection subproblems associated with a loaded parallel-plate waveguide are first treated via the dual integral equation method. The results are subsequently combined in the context of the generalized scattering matrix formulation to obtain the diffraction from the truncated parallel-plate waveguide with a recessed stub and a dielectric loading extending to infinity. The stub is then restored to the waveguide mouth to obtain the diffraction by the dielectric-metallic join. As expected, the final expressions involve several Wiener-Hopf split functions and an efficient numerical technique for their evaluation is given in an appendix. The convergence of the solution with respect to the number of included modes is examined and a number of scattering patterns are presented.

Analysis of Optical and Millimeter Wave Dielectric Waveguide

Abstract: We analyze the rectangular dielectric waveguide for millimeter wave and integrated optics applications using a combination of numerical and analytical methods. The problem is solved numerically in one dimension, while in the other dimension it is treated with propagators, reflection operators and mode matching. We derive an equation for the propagation constant of the waveguide which can be solved efficiently. The method is demonstrated to be numerically efficient, and with a good choice of grid distribution it can give a good value of the propagation constant even near to cutoff. We also derive the field plots of the guided modes, and suggest a method for mode classification.

On Physical Optics for Calculating Scattering from Coated Bodies

Abstract: The familiar physical optics (PO) approximation is no longer valid when the perfectly conducting scatterer is coated with dielectric material. This paper reviews several possible PO formulations. By comparing the PO formulation with the moment method solution based on the impedance boundary condition for the case of the coated cone-sphere, a PO formulation using both electric and magnetic currents consistently gives the best numerical results. Comparisons of the exact moment method with the PO formulations using the impedance boundary condition and the PO formulation using the Fresnel reflection coefficient for the case of scattering from the cone-ellipsoid demonstrate that the Fresnel reflection coefficient gives the best numerical results in general.

E-field and H-field solutions of TE scattering from multiple conducting and dielectric cylinders of arbitrary cross-section

Abstract: A simple moment solution is given for the problem of electromagnetic scattering from two dimensional structures consisting of multiple perfectly conducting and lossy dielectric cylinders of arbitrary cross-section The system is excited by a plane wave polarized transverse electric to the axis of the cylinders The equivalence principle is used to replace the cylinders by equivalent electric and magnetic surface currents radiating into an unbounded medium Two different sets of coupled integral equations involving the surface currents are obtained by enforcing the boundary conditions on the tangential components of the total electric and magnetic fields The method of moments is used to solve the integral equations Pulses are used for both expansion and testing functions Some of the limitations of the method are briefly discussed Results for the surface currents and the scattering cross sections are presented Results computed using the E- field and/or the H- field formulation are in very good agreemen

Monte Carlo Calculations of Radar Backscatter from a Multi-Layer Random Medium

Abstract: This paper extends the Monte Carlo method developed in a previous paper [2] for calculating the radar backscatter from a medium of randomly distributed discrete scatterers This extension enables the effect of multiple layers of different types of scatterers to be included in the simulations The presence of a ground boundary is modelled by a plane lossy half-space Results of these simulations are compared with measurements from fields of wheat and soyabean at C-band, and with calculations using radiative transfer theory

Calculation of Filter Response of a Dielectric Slab Waveguide Having Multiperiodic Interface Corrugations via the Fundamental Matrix Method

Abstract: The coupled-mode equations of six interacting modes in a dielectric slab waveguide having weak spatially-modulated multiperiodic interface corrugations are derived via the perturbation method of multiple scales and then solved numerically by means of a novel numerical method for two-point boundary-value problems. This numerical method is particularly useful for stiff systems of differential equations which is characteristic of mode coupling in a multiperiodic guide. The power reflection coefficient of a filter section is calculated for the cases of constant amplitude, tapered and chirped corrugations when conditions of simultaneous resonance are nearly satisfied. The method is also applied to a thin film having aperiodic refractive index perturbations and shown to be more efficient when compared with other numerical methods.

Radar backscatter from a vegetation layer with rough ground boundary

Abstract: The problem of radar backscattering from a vegetation layer with a smooth or a rough ground boundary is formulated by a Monte Carlo method. The vegetation layer is assumed to contain a mixture of randomly distributed dielectric discs and thin prolate ellipsoids whose phase matrices are known and whose distributions of angular orientations can be prescribed independently. The ground boundary is modelled by a Fresnel reflection coefficient for a plane lossy surface or a Kirchhoff lossy surface as the case may be. Results from the Monte Carlo simulations are compared with calculations of a matrix-doubling method by [9], and also with measurements from fields of wheat, soyabean, milo and corn [7,20]. The results indicate that the Monte Cario method presented in this paper can give a good fit with experimental data, using parameters which are believed to be reasonable.

Power flow equation in real multimode waveguides

Abstract: Pour une excitation de puissance donnee a l'entree et dans le cas d'une fonction de couplage arbitraire, l'analyse presentee permet d'obtenir la reponse impulsionnelle d'un guide onde a modes multiples

Finite element computation of complex resonant frequencies for penetrable axisymmetric bodies

Abstract: A finite element based electromagnetic scattering program is used to identify the complex natural resonances for axisymmetric dielectric bodies. These resonances are found by way of a complex frequency s-plane search for the zeroes of the determinant of the global system matrix which represents the scattering solution. Examination of the behavior of the elements of this matrix also reveals the mode type, either TE or TM, the meridional order and the azimuth index. Computational examples are presented for the cases of a penetrable sphere, a 2:1 prolate spheroid and a 1:1 finite right circular cylinder, each composed of high density lossless dielectric.

A Finite-Difference Frequency-Domain (FD-FD) Approach To Electromagnetic Scattering Problems

Abstract: A finite-difference, frequency-domain (FD-FD) approach to electromagnetic wave scattering is presented. This approach evolved from recent progress that features the concept of generalized scattering amplitudes, the application of boundary-fitted curvilinear coordinate systems, and the use of Debye potentials for 3-D obstacle scatterings. The introduction of the radially non-oscillatory generalized scattering amplitudes circumvents the difficulties in dealing with oscillatory field quantities in the infinite exterior scattering region and allows the finite-difference method to be applied to scattering problems in an effective manner. The radiation condition in terms of the generalized scattering amplitude is very simple in form and can be enforced exactly in the far field. For a 3-D scattering problem the formulation in terms of Debye potentials, expressed as functions of body-fitted coordinates, not only decouples the vector scattering problem into a combination of two independent scalar scattering proble...

Radar cross section reduction by absorber covering

Abstract: Radar cross section (RCS) reduction by absorber covering is experimentally studied by employing microwave diversity imaging. Experimental results show that broadband absorber covering is not effective at reducing the co-polarized (the transmitting and receiving antennas have opposite sense of circular polarization) RCS of a plate when the incident wave approximates the edge-on direction but is effective at reducing the cross-polarized (both the transmitting and receiving antennas have the same sense of circular polarization) RCS for all incident directions. The surface current absorber covering is effective at reducing the nonspecular energy and multiple bounces regardless of the polarization status of the measurement.

The Huygens' Principle and Doppler Effect in the Presence of Time-Dependent Surfaces

Abstract: Kirchhoff's surface integral representation for the solution of the wave equation, also commonly referred to as the Huygens' principle, is presently considered for the case of time dependent (i.e., moving) surfaces. This is motivated by problems involving moving sources and scatterers prescribed on moving surfaces. A general formulation and discussion of simple examples are given here. The surface integral representation for the solution of the scalar and vector wave equations, for harmonic and arbitrary time dependence, are used as a starting point. The extension of these integrals to the case of time dependent surfaces and its validity are discussed. In general one can always extend the representations to arbitrarily moving surfaces, but the explicit integration with respect to the retarded time relevant to the sources on the moving surface cannot be performed in general. In the special case of motion of surface elements in the direction of the normal, it is shown that the integration is feasible. The r...

Finite and Infinite Frequency Selective Surfaces: Experiments and Models

Abstract: The scattered fields from several finite frequency selective surfaces (FSS's) are presented along with frequency response data for an FSS which is large enough to be considered infinite. Measurement techniques for both the infinite and finite FSS are discussed and the experimental results are compared with numerical data generated using both a moment method for the infinite FSS and the array factor for the finite case.

Analysis of Circularly Cylindrical Resonator Filled With Axially Magnetized Stratified Gyromagnetic Medium

Abstract: A rigorous analysis of a circularly cylindrical resonator containing an axially magnetized stratified gyromagnetic medium is presented. The full-wave mode matching method is used. The field inside a cavity is expanded into series of transverse mode functions of a layered gyromagnetic parallel-plate line. An exemplary ferrite-air resonator is investigated numerically and experimentally showing good agreement of computed resonant frequencies with measured values.

On the formulation and implementation of a conjugate gradient FFT method

Abstract: Criteria are established for choosing the best way to formulate and implement a conjugate gradient FFT (fast Fourier transform) method. Also, the issues of speed and convergence are addressed in co...