Electromagnetic scattering and radiation by surfaces of arbitraryshape in layered media. I. Theory

An accurate and general procedure for the analysis of electromagnetic radiation and scattering by perfectly conducting objects of arbitrary shape embedded in a medium consisting of an arbitrary number of planar dielectric layers is developed. The key step in this procedure is a formulation of the so-called mixed-potential electric field integral equation (MPIE) that is amenable to an existing advanced solution technique developed for objects in free space and that employs the method of moments in conjunction with a triangular-patch model of the arbitrary surface. Hence, the goal is to immediately increase analysis capabilities in electromagnetics, yet remain compatible with the large existing base of knowledge concerning the solution of surface integral equations. Three alternative forms of the MPIE in plane-stratified media are developed, and their properties are discussed. One of the developed MPIEs is used to analyze scatterers and antennas of arbitrary shape that penetrate the interface between contiguous dielectric half-spaces     

Electromagnetic scattering from grassland. II. Measurement andmodeling results

For pt.I see ibid., vol.38, no.1, p.339-48 (2000). The validity of a coherent, grassland scattering model is determined by comparing the model predictions with direct measurements of a representative grass canopy. A wheat field was selected as the test target, and polarimetric, multifrequency backscattering data were collected over an entire growing season, along with a complete set of ground-truth data. The L-band measured data demonstrated a strong dependence on azimuthal look direction in relation to the row direction of the wheat. The C-band measurements likewise showed an interesting backscattering response, wherein σ_νν⁰ actually increased with incidence angle for many cases. The coherent scattering model provides backscattering data that match and predict these measured data and most of the other measured data well. The model shows that at L-band, the incoherent scattering power alone is insufficient for predicting the measured results, as the coherent terms can dominate the total scattered energy. Additionally, the model, which accounts for this nonuniform illumination of the wheat elements, demonstrates the peculiar data observed for C-band. Likewise, it is demonstrated that the fidelity used to model grass constituents (e.g., curvature) is required to match the scattering measurements accurately     

Electromagnetic scattering from a buried cylinder in layered media with rough interfaces

A solution to scattering from a cylinder buried arbitrarily in layered media with rough interfaces based on extended boundary condition method (EBCM) and scattering matrix technique is developed. The reflection and transmission matrices of arbitrary rough interfaces as well as an isolated single cylinder are constructed using EBCM and recursive T-matrix algorithm, respectively. The cylinder/rough surface interactions are taken into account by applying the generalized scattering matrix technique. The scattering matrix technique is used to cascade reflection and transmission matrices from individual systems (i.e., rough surfaces or cylinders) in order to obtain the scattering pattern from the overall system. Bistatic scattering coefficients are then obtained by incoherently averaging the power computed from the resulting Floquet modes of the overall system. In numerical simulations, the bistatic scattering coefficients are first validated by comparing the simulation results with the existing solutions which are the limiting cases including scattering from two-interface rough surfaces without any buried object and from a buried cylinder beneath a single rough surface. Subsequently, the numerical simulations of scattering from a buried cylinder in layered rough surfaces are performed to investigate the relative importance and sensitivity of various physical parameters of layered rough surfaces to incoherent scattering coefficients. Results show layered rough interfaces can significantly alter the scattering behaviors of a buried cylinder.     

Electromagnetic scattering by multiple three-dimensional scatterersburied under multilayered media. II. Numerical implementations andresults

For pt.I see ibid., vol.36, no.2, p.526-34 (1998). In part I of this paper, coupled electric-field integral equations for dielectric objects, conducting objects, and multiple dielectric and/or conducting objects were derived when they were buried under one-dimensional (1D) multilayered media. In part II of this paper, numerical implementations for these integral equations are developed by use of the method of moments, in which the “self-actions” in the method are treated special because of the presence of singularity. Sample numerical results are presented for several cases of interest, which show the validity of the scheme     

Electromagnetic scattering by stratified inhomogeneous anisotropic media

An analytical formulation is presented for the computation of scattering and transmission by general anisotropic stratified material. This method employs a first-order state-vector differential equation representation of Maxwell's equations whose solution is given in terms of a4 times 4transition matrix relating the tangential field components at the input and output planes of the anisotropic region. The complete diffraction problem is solved by combining impedance boundary conditions at these interfaces with the transition matrix relationship. A numerical algorithm is described which solves the state-vector equation using finite differences. The validation of the resultant computer program is discussed along with example calculations.     

Optical theorems for electromagnetic scattering by inhomogeneitiesin layered dielectric media

The optical theorem, which relates the forward scattering amplitude to the total cross section of a scatterer in free-space, is extended to problems of scattering of an incident transverse electric plane wave or guided mode by inhomogeneities in lossless, waveguiding, dielectric interfaces or layers. The cases of a compact irregularity on either the interface between two unbounded dielectric media or in the waveguiding layer of a dielectric-slab waveguide are considered. Simple formulas that connect the scattered amplitudes of the different types of waves excited by the incident energy are derived. They can be used as an independent check of numerical codes when benchmark solutions are not available or are hard to obtain. In addition, a relationship between the scattered amplitudes and the spectral power of each excited wave is derived using the method of stationary phase     

Electromagnetic scattering by multiple three-dimensional scatterersburied under multilayered media. I. Theory

A general procedure is developed for the analysis of electromagnetic (EM) scattering by multiple three-dimensional (3D) dielectric and/or conducting objects buried under one-dimensional (1D) multilayered media. In this first part of a two-part paper, general closed-form formulations for the electric fields excited by an arbitrarily oriented electric dipole under the layered media are first presented, from which electric-field integral equations for the buried dielectric objects, pure conducting objects, and their combinations are then obtained, and the scattered electric fields in the upper space are formulated. Finally, the physical significance of the above formulations is discussed. In the second part, numerical implementations for these integral equations and the scattered fields are investigated     

Electromagnetic scattering by rough conducting circular cylinders.II. Axial corrugation

For pt.I see ibid., vol.36, no.5, p.651 (1988). The coherent and incoherent responses of conducting axially corrugated surfaces (which are on the average circular cylinders) are calculated. The calculation encompasses second-order perturbation. The general approach used is to apply the extinction theorem to write an integral equation for the surface current density, and then to use the perturbation theory to solve it. The results are recast by using Pade approximants to achieve a significant extension of the domain of validity of the original formulation     

Electromagnetic scattering and radiation from finite microstripstructures

Two techniques are presented for the analysis of electromagnetic radiation and scattering from finite microstrip structures. The two techniques are based on two different formulations, viz. the volume-surface and surface-surface formulations. In the volume-surface formulation the finite-sized dielectric is replaced by an equivalent volume polarization current whereas the conducting plates are replaced by equivalent surface currents. For the surface-surface formulation the surface covering the dielectric volume is replaced by equivalent electric and magnetic currents and the conducting plates by surface electric currents. Both techniques can be utilized for the analysis of arbitrarily shaped finite microstrip structures. The techniques are quite accurate, and they are utilized to validate each other. Typical numerical results are presented to demonstrate the agreement between these two solution techniques     

Sinusoidal reaction formulation for radiation and scattering from conducting surfaces

A piecewise-sinusoidal reaction technique is developed for scattering and radiation from perfectly conducting bodies of arbitrary shape. This paper presents the theory and numerical results for scattering patterns of rectangular plates and radiation patterns of corner-reflector antennas. In all cases, experimental measurements are included for comparison with the calculated data.     

Electromagnetic scattering by inhomogeneous dielectric bodies ofrevolution embedded within stratified media

A method of moments (MoM) solution for scattering by heterogeneous bodies of revolution (BOR) embedded within a multilayered environment is given. A modal volume integral equation (VIE) is formulated in the mixed potential form and solved with the use of the specialized basis functions     

Wave propagation and scattering in random media and rough surfaces

The author presents a comprehensive review highlighting historical as well as new developments in the area of random media. Both discrete and continuous media are considered as well as rough surfaces. The author discusses wave propagation in turbulence and in a random continuum where the refractive index is a random function of space and time. Examples are optical propagation in the atmosphere, microwaves in the troposphere, ionosphere, planetary atmosphere, and solar wind, and acoustic scattering in ocean turbulence. The author describes multiple scattering by random distributions of discrete scatterers. Examples are optical and microwave scattering by rain, fog, smog, snow, ice particles, and vegetation, optical and ultrasound scattering by tissues and blood, optical and acoustic scattering in the ocean, and scattering in composite materials. Scattering by rough surfaces and interfaces is discussed. Examples are acoustic scattering by ocean surfaces, microwave and optical scattering by vegetation, terrain, and snow cover, and ultrasound scattering by rough interfaces in biological media     

Electromagnetic scattering from extended wires and two- and three-dimensional surfaces

Efficient numerical solutions for the electromagnetic scattering for classes of electrically large one-, two-, and three-dimensional perfectly conducting scatterers are presented. The formulation is based on solution of the electric field integral equation (EFIE) using the method of moments (MM). An entire domain Galerkin representation is used for wires and two-dimensional surfaces and a combination of entire and subdomain representations is applied to surfaces in three dimensions. The analysis is extendable to corrugated surfaces formed from sections of surfaces of translation or rotation. Numerical results are presented for wires, infinite strips, and finite strips (or plates). The behavior of the solutions with the number of terms in the entire domain expansion is examined. The reconstruction of the traveling-wave contribution to the scattering cross section using various approximations is discussed, and representative examples are given.     

A comparison of scattering model results for two-dimensionalrandomly rough surfaces

Bistatic radar cross sections are calculated using two modern scattering models: the small slope approximation (both first- and second-order), and the phase perturbation technique. The problem is limited to scalar-wave scattering from two-dimensional, randomly rough Dirichlet surfaces with a Gaussian roughness spectrum. Numerical results for the cross sections are compared to those found using the classical Kirchhoff, or physical optics, approximation and perturbation theory. Over a wide range of scattering angles, the new results agree well with the classical results when the latter are considered to be accurate. A comparison between the new results shows that the phase perturbation method gives better results in the backscattering region for correlation lengths greater than approximately one wavelength, while both the first- and second-order small slope approximations yield greater accuracy in the forward scattering direction at low grazing angles     

Inverse scattering technique applied to remote sensing of layered media

An inverse scattering technique applied to a remote estimation of the dielectric and conductivity profile of an inaccessible layered medium is presented. The inaccessible region is illuminated by plane waves at normal incident, and the data are taken as the reflected power at a fixed remote location for a set of discrete frequencies. The problem of estimating the dielectric and conductivity profile from this set of data is posed as a nonlinear integral equation. This formulation based on reflected power is appealing for practical purpose, in that the phase information of the reflected field is not required. The equation is solved by developing a quasi-Newton iterative scheme in functional space which produces a dielectric and conductivity profile that fits the data. The Backus and Gilbert resolving-power theory is used to assess the reliability of the estimates and the resolving length of the data. Results are given for the numerical reconstruction of various dielectric and conductivity profiles from an artificial data set, together with local averages estimates and resolving kernels.     

金属衬底多层各向异性介质电波反射特性研究

通过分析和计算多层各向异性介质的电磁波传输矩阵,导出了金属衬底上多层各向异性介质的电磁波反射系数计算方法,举例验证了该计算方法的正确性.作为一个应用例子,初步分析了金属衬底上各向异性材料的极化转换特性,为复杂电磁材料的电磁散射近似计算提供了理论基础.     

Electromagnetic scattering from anisotropic materials, part II: Computer code and numerical results in two dimensions

The two-dimensional problem of oblique scattering by penetrable cylinders of arbitrary cross section made of materials which are linear, lossy, anisotropic and possibly inhomogeneous is considered. The materials are characterized by arbitrary tensor susceptibilitiesbar{x}_{ec}andbar{x}_{m}. The frequency-domain volume integrodifferential equations satisfied by the electric and magnetic fields and obtained in a previous paper (Part 1) are analyzed numerically. Optimal ordering of the unknowns and transverse electric-transverse magnetic (TE-TM) decomposition in the matrix formulation of the problem are discussed. The cross section of the scatterer is broken down into a triangular mesh. The field components at the vertices of the triangles are the unknowns; within each triangle, each field component is a linear combination of its values at the vertices. Computed field distributions inside the scatterer are found to be in excellent agreement with results obtained by other methods.     

Electromagnetic scattering from perfectly conducting rough surfaces in the resonance region

A rigorous integral formalism for the problem of scattering of electromagnetic radiation from a cylindrical, perfectly conducting rough surface of arbitrary shape is introduced. The computer code obtained from this theory enables us to show that the range over which the incident field affects the surface current density is of the order of the radiation wavelength. This phenomenon is explained using a new approximate theory, able to express the scattered field in the form of an integral whose integrand is known in closed form. Using the rigorous computer code, we show that the new approximate theory is better than the Kirchhoff approximation in the resonance region. Finally, it is shown that the phenomenon of short interaction range of the incident field permits the rigorous computation of the field scattered from a rough surface of arbitrary width.     

Local spectral analysis of short-pulse excited scattering fromweakly inhomogeneous media. II. Inverse scattering

For Pt.I see ibid., vol.47, no.7, p.1208-17 (July 1999). This paper is concerned with the reconstruction of a weakly inhomogeneous scattering profile from data generated by a short-pulse incident plane wave, which is postprocessed so as to localize the interrogated region to a space-time resolved scattering cell, The phase-space localization due to postprocessing is brought about by applying local (i.e., windowed) slant-stack transforms to the time-dependent scattered fields. In the domain of the scatterer, this processing corresponds to applying windowed Radon transforms to the induced field distribution, which, in turn, generates pulsed-beam (PB) wave packets traveling toward the observer. The forward analysis parameterizing this new form of time-domain (TD) diffraction tomography has been performed in a companion paper and furnishes the framework for the investigation here. Via the forward parameterization, the three-dimensional (3-D) global scattering phenomenology has been reduced to scattering from an equivalent one-dimensional (1-D) scattering cell oriented along the bisector between the direction of the incident plane pulse and the direction of the scattered pulsed beam (PB) to the observer. For the inverse problem, this process is reversed by windowing the scattered field and backpropagating the resulting PBs so as to form local images of any selected region in the scattering domain. The phase-space signature of the scattering cell is related to the Radon transform of the medium in the cell so that the local profile function can be recovered by Radon inversion. An illustrative numerical example is included. Also discussed is the ultimate localization achieved by incident PB excitation and PB postprocessing of the scattered field