Numerical simulations of the scattered field near a statistically rough air-ground interface

The two-dimensional problem of horizontally polarized wave scattering from an air-ground interface is considered. The diffraction problem is formulated by means of the extinction theorem, leading to a system of two simultaneous surface integral equations. The small-slope approximation has been used to solve this system. This solution was used as a fast forward solver in the Monte Carlo simulations of the scattered field near to the rough interface. Properties of the reflected field have been investigated for a single realization of the rough interface as well as for a statistical ensemble of such interfaces. Special attention has been paid to the phase of the reflected field (in the case of a single realization) and to the variance of the reflected field (in the case of a statistical ensemble), which has direct relation with the surface clutter in ground penetrating radars. A principal possibility to retrieve a surface profile from interferometric measurements of the reflected field near the surface is demonstrated.     

Extended boundary condition method for scattering and emission from natural surfaces modeled by fractals

The extended boundary condition method with the Weierstrass-Mandelbrot fractal function (WM-EBCM) has been recently employed to model and solve the problem of electromagnetic scattering from natural surfaces. In this paper we first of all show, on the basis of theoretical considerations and of numerical examples, that this method can be used also for the evaluation of electromagnetic emission from natural surfaces. In addition, a small roughness approximation of the WM-EBCM solution is presented to highlight the connection between EBCM and SPM, and to avoid matrix ill-conditioning in scattering problems. Achieved results show that the zero-order scattered field is the (deterministic) field reflected by the mean plane, and that the first-order (random) scattered field is directly proportional to surface roughness. Validity limits of the approximated method are discussed and verified by studying the scattered field behavior at different surface roughness conditions.     

Scattering of forward bulk magnetostatic waves by a defect of the surface of a ferromagnetic film magnetized at an arbitrary angle

The solution for the diffraction problem of scattering of magnetostatic waves by an arbitrary shallow defect situated under the surface of a ferromagnetic film magnetized at an arbitrary angle is obtained in the quasi-static approximation. Expressions for the energy flux density of scattered magnetostatic waves in the far-field zone are found. The results of computations of the time-averaged flux density of bulk magnetostatic waves reflected from rectangular and circular shallow irregularities are presented.     

Very high frequency radiowave scattering by a disturbed sea surface Part I: Scattering from a slightly disturbed boundary

This paper considers the scattering of very high frequency (VHF) electromagnetic waves from a random weakly corrugated surface by the perturbation method. The calculations show that the scattering has a resonant nature, i.e., only certain Fourier components of the surface shape are responsible for scattering in every given direction. Experiments carried out in a water basin confirmed the results of the calculations. The backscattered intensity is proportional to the spectral density of those Fourier components of the surface oscillation that have a resonant space period. In these experiments, resonant maxima of the reflected signal corresponding to the second-order approximation of the perturbation method were also observed. The frequency spectrum of the scattered electromagnetic field is also investigated. It is shown that the spectrum of the scattered radiation is shifted from the incident frequency by a certain value related to the phase velocity of the resonantly scattering Fourier component of the surface shape. The experimentally observed dependence of the scattered intensity on frequency and the theoretically predicted one are very much alike.     

A physical optics version of the geometrical theory of diffraction

The authors derive a diffraction coefficient which is suitable for calculating the filed diffracted by the vertices of perfectly conducting objects. This diffraction coefficient is used to calculate the field scattered by the corner of a metallic sheet. Two diffraction coefficients, one for edges and one for vertices, are derived by solving the appropriate canonical problems using the physical optics (PO) approximation. The diffraction coefficients are calculated by first using the PO approximation which consists of calculating the total field on the surface of an object from the incident field according to the laws of geometrical optics, and then calculating the scattered field by employing this total surface field in a vector diffraction integral. The validity of the diffraction coefficients has been investigated by comparing their predictions with experimental measurements of the scattered field from a single corner of a rectangular metal sheet, and good agreement was found     

Scattering by right angle dielectric wedge

An asymptotic solution of electromagnetic waves scattered by a right-angled dielectric wedge for plane wave incidence is obtained. Scattered far fields are constructed by waves reflected and refracted from dielectric interfaces (geometric-optical fields) and a cylindrical wave diffracted from the edge. The asymptotic edge diffracted field is obtained by adding a correction to the edge diffraction of physical optics approximation, where the correction field in the far-field zone is calculated by solving a dual series equation amenable to simple numerical calculation. The validity of this result is assured by two limits of relative dielectric constantvarepsilonof the wedge. The total asymptotic field calculated agrees with Rawlins' Neumann series solution for smallvarepsilon, and the edge diffraction pattern is shown to approach that of a perfectly conducting wedge for largevarepsilon. Calculated far-field patterns are presented and the accuracy of physical optics approximation is discussed.     

Plasmon Resonances in a Glass Nanowire Covered with a Silver Layer of Variable Thickness

A two-dimensional problem of diffraction of a plane electromagnetic wave by a silver shell with the boundaries formed by a circular and an elliptical cylinders is considered. The far fields and the scattering spectra are calculated by rigorous methods in the visible band. The dipole and quadrupole resonance frequencies for thin shells are determined in the quasi-static approximation. It is shown that the quadrupole resonances are degenerate and the dipole resonances are “split”; at the dip frequency, the scattered field can be directed perpendicularly to the direction of propagation of the incident plane wave.     

The scattering cross section of a composite cylinder, geometric optics

The optical analogue of the scattering cross section of a composite cylinder is developed from a representation of the forward scattered amplitude as a continuous spectrum of radial eigenfunctions. The Debye approximation for the Hankel functions, which is valid when their arguments are large compared to the order, leads to a series of integrals which can be evaluated asymptotically by the method of stationary phase. The final result, for a certain range of parameters, is a diffraction correction plus a double sum of terms, each of which can be interpreted as an optical ray. It is shown that if the angular displacement between the incoming and scattered ray directions is(2m + 1)pi, the ray must have been reflected at the conducting core of the cylinder at least2m + 1times. After the parameter ranges to which these results apply were determined, the nonlinear equations for the ray angles were solved on a large-scale digital computer and the scattering cross section of a number of composite cylinders was calculated as a function of frequency. The results are presented graphically.     

Shadow boundary incremental length diffraction coefficients appliedto scattering from 3-D bodies

Shadow boundary incremental length diffraction coefficients (SBILDCs) are high-frequency fields designed to correct the physical optics (PO) field of a three-dimensional (3-D) perfectly electrically conducting scatterer. The SBILDCs are integrated along the shadow boundary of the 3-D object to approximate the field radiated by the nonuniform shadow boundary current (the difference between the exact and PO currents near the shadow boundary). This integral is added to the PO field to give an approximation to the exact scattered field that takes into account both PO and nonuniform shadow boundary currents on the scatterer. Like other incremental length diffraction coefficients, any SBILDC is based on the use of a 2-D canonical scatterer to locally approximate the surface of the 3-D scatterer to which it is applied. Circular cylinder SBILDCs are, to date, the only SBILDCs that have been obtained in closed form. In this paper, these closed-form expressions are validated by applying them for the first time to a 3-D scatterer with varying radius of curvature-the prolate spheroid. The results obtained clearly demonstrate that for bistatic scattering the combined PO-SBILDC approximation is considerably more accurate than the PO field approximation alone     

Nonlinear scattering of microwaves by a travelling-wave density-modulated plasma column

A theory is presented which is based on the Born approximation of the nonlinear scattering of microwaves from a periodically density-modulated plasma column of finite length. It has been shown quantitatively that the scattered waves produce diffraction patterns and frequency shifts; these scattered waves form a set of sidebands which are separated from the incident wave by the modulation frequency of an oscillating plasma column.     

无规入射散射系数测量的研究

无规入射散射系数是在扩散声场中界面散射声能与总反射声能之间的比值,它是采用计算机模拟来对室内声场进行预测的重要参量。国际标准化组织(ISO)即将公布其对无规入射散射系数的定义及其在混响场中的测量方法。关于这一方法的有效实施以及准确地获得实验数据,显得尤为重要。根据测量的基本原理建立了完整的无规入射散射系数测量系统,并给出典型散射试件的测量结果,分析了测量中的一些技术问题。     

Scattering by a rectangularly corrugated surface: an approximatetheory

We address the problem of the scattering of a plane, TM-polarized electromagnetic wave by a two-dimensional rectangularly corrugated surface. The height of the corrugation is measured by a characteristic length D and its period by Λ. We take the ordering of these scales to be D~Λ~λ where λ is the wavelength of the incident wave. We apply a radiation condition (strictly valid only in the far-field) in the aperture above a rectangular notch. This approximation allows the determination of an explicit representation of the reflection coefficients, the scattered field, and the field within a corrugation. Numerical results are presented which are in excellent agreement with a published finite difference approximation for diffraction gratings     

A three-wave FDTD approach to surface scattering with applicationsto remote sensing of geophysical surfaces

A major difficulty in physical interpretation of radio wave scattering from geophysical surfaces is the lack of detailed information on the signatures of geologically plausible discrete objects. Although the aggregate response will never be dominated by any single object, differences in the population of discrete objects on or near the surface (their sizes and shapes, for example) can change the character of a radio echo markedly. When the average surface is modelled as a flat, homogeneous half-space, the field that “drives” the scattering process is a composite consisting of the incident plane wave and the reflected and transmitted plane waves, all of which are known quantities; the total field can then be defined as the sum of the driving field and the scattered field. When a discrete object is near the surface, the total field can be calculated using finite-difference time-domain (FDTD) techniques, and the scattered near field can be calculated accordingly. The Green's functions for electric and magnetic currents above and below the surface, obtained by Sommerfeld theory and employed in conjunction with Huygens' principle, transform the local scattered fields to the far field. The FDTD implementation accommodates discrete lossy dielectric and magnetic scatterers in the vicinity of a dielectric surface; extension to a lossy half-space is straightforward. Two-dimensional results for scattering from perfectly conducting circular cylinders above and below a dielectric surface agree with moment method solutions within a few percent. Results for scattering from a dielectric wedge exhibit expected forward diffraction and internal reflection phenomena     

On the far-field approximation for scattering from randomly rough surfaces

Various authors have justified the far-fields approximation for rough surface scattering using one of the classical approximations for the scattered fields, usually considering either the coherent scattered field or the incoherent scattered intensity. An exact expression for the field scattered from a perfectly conducting rough surface is considered. The expression for the incoherent scattered intensity is formally derived, and a condition under which the far-field approximation is valid is found, independent of specific approximations for the surface or scattered fields or for the surface height statistics. The condition so derived is, under many circumstances, substantially less restrictive than that derived before in the general case. Furthermore, the previous results may be easily recovered by further specialization of our result.     

On the degrees of freedom of scattered fields

Starting from the observation that fields differing less than a prescribed error cannot be resolved as distinct entities, the degrees of freedom of the scattered field are introduced and then computed. The degrees of freedom are shown to be practically equal to the Nyquist number appropriate to the effective (spatial) bandwidth of the scattered field and to the extension of the observation domain. Accordingly, a finite number of elements of information can be used to determine the scattered field to a prescribed approximation error. It is also shown that the field representation can be made in terms of field values and simple sampling functions, provided that a marginal increase in the approximation error is tolerated. The results not only completely justify the use of sampling interpolation for representing scattering fields, but also demonstrate that such representation is practically an optimal one. An algorithm for the reconstruction of scattered fields, given the maximum allowed error, is then produced     

Scattering from a hyperboloidal reflector in a cassegrainian feed system

The scattered field from a hyperboloidal reflector is calculated by integrating the induced current density over the front of the hyperboloid. The resulting integral expressions for the fields possess a stationary term which, when evaluated, yields the geometrical ray-optics approximation to the scattering problem. The complete field, including diffraction effects, may be obtained by numerical evaluation of the integrals. The formulas are applied to a hyperboloid illuminated by an idealized, sharply cut off uniform feed pattern. Characteristic diffraction phenomena are reduced with increasingD/lambdauntil the geometrical ray-optics result is obtained in the limit of vanishing wavelength. Theoretical field patterns are also obtained for a horn-fed hyperboloidal subreflector in a Cassegrainian feed system; they indicate that for moderately large hyperboloidal reflectors spillover may be reduced to an acceptable level, but there is a tendency toward increased forward spillover. The results of 9600-Mc model tests compare favorably with the theoretical patterns.     

基于倾斜地面上分形树的电磁散射研究

本文用随机Ｌ系统产生具有自相似发形结构的分形树,基于ＭｏｎｔｅＣａｒｌｏ模拟的方法,用相干中近似、树的独立散射近似和独立散射近似研究了倾斜粗糙面为下垫面的分形树的电磁散射、计算结果表明,相干叠加近似和树的独立散射近似具有比较好的一致性,而独立散射近似在低频时不能给出好的结果,倾斜粗糙面的存在使得交叉极化分量与同极化分量相差减小。     

Scattering from apertures in infinite ground planes using FDTD

A scattered field version of FDTD for scattering from an aperture in an infinite ground plane is presented. In this formulation the fields reflected from the infinite ground plane are computed analytically, not as FDTD scattered fields. This is necessary to eliminate scattering from the edges of the ground plane, where it is terminated at the FDTD outer boundary. Also, the fields scattered by the ground plane are usually of much higher amplitude than the desired aperture-scattered fields. In this formulation these fields need not be absorbed by the FDTD outer boundary. This provides more accurate calculation of low amplitude scattering from the aperture. The formulation can include materials in the aperture and on both sides of the infinite ground plane. For example, scattering from an aperture antenna with a dielectric cover backed by an aperture filled with lossy dielectric can be computed with this formulation     

A UGO/EUTD solution for the scattering and diffraction from cubicpolynomial strips

A combined uniform geometrical optics (UGO) and extended uniform geometrical theory of diffraction (EUTD) solution is developed for scattering and diffraction by perfectly conducting cubic polynomial strips. The new solution overcomes the difficulties of the classic GO/UTD solution near caustics and composite shadow boundaries. The approach for constructing the UGO/EUTD solution is based on a spatial domain physical optics (PO) radiation integral representation for the scattered field, which is then reduced using a uniform asymptotic procedure. New uniform reflection, zero-curvature diffraction, and edge diffraction coefficients are derived and involve the ordinary and incomplete Airy integrals as canonical functions. The UGO/EUTD solution is very efficient and provides useful physical insight into the various scattering and diffraction processes. It is also universal in nature and can be used to effectively describe the scattered fields from flat, strictly concave or convex, and concave-convex boundaries containing edges. Its accuracy is confirmed via comparison with some reference moment method (MM) results     

Scattering of a Plane Wave on a Ferrite Cylinder at Normal Incidence

The scattered field is given as a series of cylinder functions. If the ferrite cylinder is magnetized along its axis the scattering pattern becomes asymmetrical about the direction of incidence. Approximation formulas for the thin cylinder and the far field zone are given. It is shown that in the first approximation the amplitude is an even function and the phase angle of the field is an odd function of the scattering angle. Exact numerical results have been obtained with a Univac digital computer. By a suitable arrangement of the ferrite cylinders, a unidirectional pattern can be obtained which is controlled by the applied magnetic dc field.