Coupling Between Guided Surface Waves, Lateral Waves, and the Radiation Fields by Rough Surfaces--Full-Wave Solutions

In this paper explicit expressions are presented for the guided surface waves and lateral waves that are excited when radiation fields are incident upon rough surfaces. Similarly, expressions are presented for the radiation fields scattered by rough surfaces that are excited by surface waves and lateral waves. In addition, coupling between the surface waves and the lateral waves due to surface irregularities is considered in detail. The solutions, which are based on a full-wave approach to the problem, are subject to the exact boundary conditions at the irregular interface. These are shown to be consistent with the reciprocity relationship in electromagnetic theory. The validity of the approximate impedance boundary condition is examined and consideration is given to excitation at the grazing incidence, the Brewster angle, and to waves incident at the critical angle for total internal reflection. Optimum conditions are determined for coupling between the radiation fields, the surface waves, and the Iateral waves incident upon irregular boundaries. Thus this work is applicable to problems of radio wave propagation near an irregular interface between two media and excitation of guided waves by irregular dielectric structures.     

Mueller matrix elements that characterize scattering from coatedrandom rough surfaces

The Mueller matrix completely characterizes scattered electromagnetic waves. It relates the incident to the scattered Stokes vectors. The Mueller matrix, which contains intensity and relative phase data, is very useful for remote sensing. The Mueller matrix characterizing scattering from coated two-dimensional (2-D) random rough surfaces is obtained from full-wave solutions for the scattered fields considered in the companion paper. The general bistatic scattering case is considered in the analysis. However, for the numerical simulations presented here, the backscatter case is considered in particular, since backscatter is usually measured in remote sensing. The uniformly coated 2-D random rough surfaces are assumed here to be homogeneous and isotropic, with a Gaussian surface-height joint probability-density function. The diffuse incoherent and coherent contributions to the Mueller matrix elements are evaluated. The computer simulations of realistic models of relevant physical problems related to remote sensing of irregular stratified media can be used to determine the optimum modes of detection involving the selection of polarization, frequency, backscatter angle, and the specific Mueller matrix elements most sensitive to changes in medium parameters     

Full wave physical models of nonspecular scattering in irregularstratified media

A physical interpretation is given of each term in the full-wave expansion of the vertically or horizontally polarized electromagnetic fields scattered by irregular stratified media. These solutions provide a basis for the construction of physical models of nonspecular scatter in complex, irregular, layered structures. The full wave solutions involve a pair of nonspecular reflection scattering coefficients and a pair of nonspecular transmission scattering coefficients that reduce to the familiar Fresnel reflection and transmission coefficients for the specular case. The full-wave solutions are shown to satisfy the reciprocity and duality relationships in electromagnetic theory, and they are invariant to coordinate transformations. The relationships between the full-wave solution, the high-frequency physical optics solution, and the low-frequency perturbation solution are demonstrated. The analysis is relevant to problems of communication in irregular stratified media and to problems of remote sensing     

Depolarization and scattering of electromagnetic waves by irregular boundaries for arbitrary incident and scatter angles full-wave solutions

Explicit expressions are presented for the radiation fields scattered by rough surfaces. Both electric and magnetic dipole sources are assumed, thus excitations of both vertically and horizontally polarized waves are considered. The solutions are based on a full-wave approach which employs complete field expansions and exact boundary conditions at the irregular boundary. The scattering and depolarization coefficients axe derived for arbitrary incident and scatter angles. When the observation point is at the source these scattering coefficients are related to the backscatter cross section per unit area. Solutions based on the approximate impedance boundary condition are also given, and the suitability of these approximations are examined. The solutions are presented in a form that is suitable for use by engineers who may not be familiar with the analytical techniques and they may be readily compared with earlier solutions to the problem. The full-wave solutions are shown to satisfy the reciprocity relationships in electromagnetic theory, and they can be applied directly to problems of scattering and depolarization by periodic and random rough surfaces.     

Transmission Through Layered Media With Rough Boundaries: First-Order Perturbative Solution

We investigate analytically the fully polarimetric electromagnetic wave propagation through a 3-D layered structure. In the framework of the first-order limit of the perturbation theory, a transmission model for a layered structure with an arbitrary number of rough interfaces is developed and an elegant closed-form solution is obtained. The final expressions, in terms of generalized reflection/transmission coefficients, provide parametrically a direct characterization of the scattering properties of the layered structure in terms of the structure's (geometric and electromagnetic) parameters. In addition, we point out the complementary character of the obtained scattering solution with respect to the existing one. Finally, we demonstrate that our solution satisfies the reciprocity principle.      

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.     

Bistatic scattering from three-dimensional layered rough surfaces

An analytical method to calculate the bistatic-scattering coefficients of a three-dimensional layered dielectric structure with slightly rough interfaces is presented. The interfaces are allowed to be statistically distinct, but possibly dependent. The waves in each region are represented as a superposition of an infinite number of up- and down-going spectral components whose amplitudes are found by simultaneously matching the boundary conditions at both interfaces. A small-perturbation formulation is used up to the first order, and the scattered fields are derived. The calculation intrinsically takes into account multiple scattering processes between the boundaries. The formulation is then validated against known solutions to special cases. New results are generated for several cases of two- and three-layer media, which will be directly applicable for modeling of the signals from radar systems and subsequent estimation of a layered medium subsurface properties, such as moisture content and layer depths.     

Full-wave solutions for the depolarization of the scattered radiation fields by rough surfaces of arbitrary slope

Employing a variable coordinate system associated with the local features of two-dimensionally rough surfaces with arbitrary slope, full-wave solutions are derived for the depolarization of the scattered radiation fields. An outline of the analytical procedures used in the derivations of the solutions are presented. Furthermore, the engineer who is not familiar with them can also use the final result which is expressed as a definite integral whose integrand is given explicitly and in closed form. These full-wave solutions are compared with the quasi-optics solution and the iterative or perturbational solutions for slightly rough surfaces, and they are shown to bridge the wide gap that exists between them. The full-wave solutions are consistent with energy conservation, duality, and reciprocity relationships in electromagnetic theory. These solutions account for upward and downward scattering of the incident waves with respect to the horizontal reference plane, thus shadowing and multiple scattering are considered. Applications to two-dimensionally periodic structures and random rough surfaces are also presented. The fullwave solutions are examined for Brewster, grazing, and specular angles and backscatter. Special consideration is also given to good conducting boundaries.     

Full-wave solutions for the scattered radiation fields from rough surfaces with arbitrary slope and frequency

Full-wave solutions are derived for the scattered radiation fields from rough surfaces with arbitrary slope and electromagnetic parameters. These solutions bridge the wide gap that exists between the perturbational solutions for rough surfaces with small slopes and the quasi-optics solutions. Thus it is shown, for example, that for good conducting boundaries the backscattered fields, which are dependent on the polarization of the incident and scattered fields at low frequencies, become independent of polarization at optical frequencies. These solutions are consistent with reciprocity, energy conservation, and duality relations in electromagnetic theory. Since the full-wave solutions account for upward and downward scattering, shadowing and multiple scatter are considered. Applications to periodic structures and random rough surfaces are also presented.     

Renormalization of EM fields in application to large-angle scattering from randomly continuous media and sparse particle distributions

The conventional wave-integral equation in electromagnetic scattering, consisting of a sum of directly received vacuum field plus a scattered field that sums weighted vacuum spherical waves from each scatterer, is replaced by one in which renormalized fields containing part of the multiply scattered energy replace the vacuum fields. A first-order approximation in the renormalized equation is applied to bistatic (large-angle) scattering from weak random fluctuations of the permittivity in a distant volume, and to a sparse monodisperse distribution of isotropic particles to yield scattering cross sections with extended validity for the direct polarization. A similar correction is introduced for the cross polarization in the case of backscatter. Differences with other calculations are noted.     

The theory of functionals of stochastic backscattered fields

The theory of wave scattering by anisotropic statistically rough surfaces, which is an important part of statistical radiophysics, is considered. A new analytic method is developed and generalized for solving problems of radar imaging. The method involves analytic determination of the functionals of stochastic backscattered fields and can be applied to solve a wide class of physical problems with allowance for the finite width of an antenna’s pattern. The unified approach based on this method is used to analyze the generalized frequency response of a scattering radio channel, a generalized correlator of scattered fields, spatial correlation functions of stochastic backscattered fields, frequency coherence functions of stochastic backscattered fields, the coherence band of a spatial-temporal scattering radar channel, the kernel of the generalized uncertainty function, and the measure of noise immunity characterizing radar probing of the Earth’s surface or extended targets. The introduced frequency coherence functions are applied for thorough and consistent study of techniques for measuring the characteristics of a rough surface, aircraft altitude, and distortions observed when radar signals are scattered by statistically rough, including fractal, surfaces. To exemplify urgent applications, radiophysical synthesis of detailed digital reference radar terrain maps and microwave radar images that was proposed earlier is considered and improved with the use of the theory of fractals.     

Quasi-ray Gaussian beam algorithm for short-pulse two-dimensional scattering by moderately rough dielectric interfaces

We consider short-pulse (SP) time-domain (TD) two-dimensional (2-D) scattering by moderately rough interfaces, which separate free space from a slightly lossy dielectric half-space, and are excited by one-dimensional (1-D) SP-TD aperture field distributions. This study extends to the SP-TD in our previous investigation of time-harmonic high frequency 2-D scattering of Gabor-based quasi-ray Gaussian beam fields excited by 1-D aperture field distributions in the presence of moderately rough dielectric interfaces (Galdi et al.). The proposed approach is based on the Kirchhoff physical optics (PO) approximation in conjunction with the Gabor-based quasi-ray narrow-waisted Gaussian pulsed-beam (PB) discretization (Galdi et al.), which is applied to the SP-induced equivalent magnetic surface currents on the interface that establish the TD reflected/transmitted fields. We show that, for well-collimated truncated SP incident fields, the PO-PB synthesis of the reflected/transmitted fields yields an approximate explicit physically appealing, numerically efficient asymptotic algorithm, with well-defined domains of validity based on the problem parameters. An extensive series of numerical experiments verifies the accuracy of our method by comparison with a rigorously-based numerical reference solution, and assesses its computational utility. The algorithm is intended for use as a rapid forward solver in SP-TD inverse scattering and imaging scenarios in the presence of moderately rough dielectric interfaces.     

Excitation of Surface Waves and the Scattered Radiation Fields by Rough Surfaces of Arbitrary Slope

Surface waves as well as Iateral waves are excited when a rough surface is illuminated by the radiation fields. In view of shadowing, these terms of the complete field expansions contribute significantly to the total fields when the transmitter or receiver are near the rough surface. In this work explict expressions are derived for the coupling between the radiation fields and the surface waves which are guided at the irregular interface between two media. In the analysis, the slope of the rough surface is not restricted and the solutions for both the horizontally and vertically polarized waves are shown to satisfy reciprocity and duality relationships in electromagnetic theory. Special consideration is given to Brewster angles of incidence and scatter and stationary phase techniques. The fufl-wave solutions are also applied to random and periodic rough surfaces.     

Wave diffraction by a rough boundary of an arbitrary plane-layeredmedium

The problem of electromagnetic (EM) wave scattering by a slightly rough boundary of an arbitrary layered medium is solved by a small perturbation method. The bistatic amplitude of scattering as well as scattering cross sections for a statistically rough surface are calculated for linear and circular polarized waves. Along with the scattering into the upgoing waves in the homogeneous medium, the scattering cross sections in the downgoing waves into a layered medium are obtained. Analytical results are applied to the modeling of natural layered media (ice and sand layers) remote sensing problems employing global positioning system (GPS) technics     

Scattering From Layered Structures With One Rough Interface: A Unified Formulation of Perturbative Solutions

In this paper, we investigate analytically the connection between the existing first-order small perturbation method solutions for the scattering from a layered structure with one rough interface. First of all, by using effectively the concept of generalized reflection coefficients, we cast the existing models in a unified more compact formulation and point out the connection between the different analytical solutions. The obtained reformulations of the available analytical solutions allow us to subsequently prove the consistency of the considered models. Finally, a suitable expansion is performed that leads us to understand the physical meaning of the analytical expressions. The obtained unified formulation also opens the way toward a general closed-form solution for the problem of scattering by a layered structure with an arbitrary number of corrugated interfaces.     

Scattering cross sections for composite models of non-Gaussian rough surfaces for which decorrelation implies statistical independence

The full wave approach is used to determine the scattering cross sections for composite models of non-Gaussian rough surfaces. It is assumed in this work that the rough surface heights become statistically independent when they decorrelate, thus no delta function type specular term appears in the expressions for the scattered fields. The broad family of non-Gaussian surfaces considered range in the limit from exponential to Gaussian. It is seen that for small angles of incidence the like polarized cross sections have the same dependence on the specific form of the surface height joint probability density, but for large angles the scattering cross sections for the horizontally polarized waves are much more sensitive to the specific form of the joint probability density. On the other hand the shadow functions are rather insensitive to the specific form of the joint probability density.     

Numerical simulation of scattering from three-dimensional randomlyrough surfaces

Randomly rough surface patches in three dimensions are generated on the computer. The FD-TD method is used to compute scattering from surface patches by converting the Maxwell's equations into difference equations using a central difference approximation for the space and time derivatives. The volume of grids above the rough surface is divided into the total field and the scattered field regions. In between these two regions, obliquely incident waves are generated. To reduce computation, the volume of grids is chosen to be small, and a transformation is used to convert the scattered field into far zone fields for bistatic scattering coefficient calculations. Possible errors near the edge of the surface due to the use of a relatively small volume are suppressed by introducing a windowing function. Very good agreements are obtained between the results obtained by this method and those calculated by an integral equation method (IEM) for scattering from randomly rough perfectly conducting and dielectric surfaces     

Scattering from a Layered Medium Connected with Rough Interfaces: Matrx Doubling Method

A theoretical scattering model is developed that computes the scattered and transmitted intensities from an inhomogeneous layered medium above the half-space. A matrix doubling method technique is extended to handle multilayer scattering problems of which each scattering layer of spherical particles has rough boundary interfaces. Incoherent scattering is assumed in the formulation so that the Stokes vector representations are used to calculate the polarimetric multiple scattering effects. The scattering coefficients are computed for a two-layered Rayleigh scattering medium with a rough boundary. The developed scattering model of a radiative transfer approach is useful for scattering computations dealing with a random medium often encountered in active and passive microwave remote-sensing problems.     

机载正下视SAR探测极地冰川的回波数值模拟

建立了大尺度分层粗糙面散射物理模型, 基于Kirchhoff近似、几何光学和射线追踪方法, 推导给出粗糙面散射场的计算公式, 提出了一种快速模拟机载正下视合成孔径雷达(Synthetic Aperture Radar, SAR)探测冰川回波的数值仿真方法, 以帮助分析实测数据.对SAR系统设计、雷达回波信号处理算法研究都有很大帮助, 可以应用到星体地下结构探测回波的模拟.理论公式及数值仿真结果验证了此数值仿真方法的正确性.在不同的仿真场景和雷达系统参数下, 数值仿真模拟了冰川散射回波, 定量分析了冰层表面粗糙度、次表面粗糙度、山体倾斜度、雷达系统参数等对天底区域和非天底区域散射回波的影响.本文的仿真方法可以快速计算任意大尺度特定地形所对应的雷达探测仪回波数据.     

Characteristics of guided and leaky waves on multilayer thin-filmstructures with planar material gratings

This paper presents the characteristics of guided (surface) waves and leaky waves on multilayer structures with planar implanted periodic dielectric blocks. A three-dimensional (3-D) integral-equation formulation in conjunction with the method of moments (MoM's) is used to find the propagation constants of the surface-wave and leaky-wave modes. The analysis deals with layered structures with irregular implants. Photonic band-gaps of both guided waves and leaky waves for rectangular air-implants are identified. Anisotropic properties of the surface waves and leaky waves are investigated. The design of leaky-wave antennas with the information of mode characteristics is discussed. The analysis is validated through the comparison with a low-frequency effective-medium approach and results for linear gratings