Quasi-ray Gaussian beam algorithm for time-harmonic two-dimensionalscattering by moderately rough interfaces

Gabor-based Gaussian beam (GB) algorithms, in conjunction with the complex source point (CSP) method for generating beam-like wave objects, have found application in a variety of high-frequency wave propagation and diffraction scenarios. Of special interest for efficient numerical implementation is the noncollimated narrow-waisted species of GB, which reduces the computationally intensive complex ray tracing for collimated GB propagation and scattering to quasi-real ray tracing, without the failure of strictly real ray field algorithms in caustic and other transition regions. The Gabor-based narrow-waisted CSP-GB method has been applied previously to two-dimensional (2-D) propagation from extended nonfocused and focused aperture distributions through arbitrarily curved 2-D layered environments. In this 2-D study the method is applied to aperture-excited field scattering from, and transmission through, a moderately rough interface between two dielectric media. It is shown that the algorithm produces accurate and computationally efficient solutions for this complex propagation environment, over a range of calibrated combinations of the problem parameters. One of the potential uses of the algorithm is as an efficient forward solver for inverse problems concerned with profile and object reconstruction     

高斯介质粗糙面电磁散射的小斜率近似方法

基于小斜率近似方法推导了极坐标系下介质粗糙面的双站散射系数和后向散射系数计算公式.为验证小斜率近似方法的准确性,针对二维高斯介质粗糙面,计算了双站散射系数并将得到的数值结果与实验测量数据和基尔霍夫近似方法计算结果进行了对比分析,结果表明:小斜率近似方法的结果和实验数据吻合较好.同时对不同入射角下散射系数的角分布及粗糙度和均方根斜率对散射系数的影响进行了讨论分析.     

Moderately rough surface underground imaging via short-pulse quasi-ray Gaussian beams

An adaptive framework is presented for ultra-wideband ground penetrating radar imaging of shallow-buried low-contrast dielectric objects in the presence of a moderately rough air-soil interface. The proposed approach works with sparse data and relies on recently developed Gabor-based narrow-waisted quasi-ray Gaussian beam algorithms as fast forward scattering predictive models. First, a nonlinear inverse scattering problem is solved to estimate the unknown coarse-scale roughness profile. This sets the stage for adaptive compensation of clutter-induced distortion in the underground imaging problem, which is linearized via Born approximation and subsequently solved via various pixel-based and object-based techniques. Numerical simulations are presented to assess accuracy, robustness and computational efficiency for various calibrated ranges of problem parameters. The proposed approach has potential applications to antipersonnel land mine remediation.     

Forward-backward method for scattering from dielectric rough surfaces

The iterative forward-backward (FB) method is a recently proposed efficient technique for numerical evaluation of scattering from perfectly conducting rough surfaces. Extension of the method to include scattering from imperfect conducting surfaces, with a high imaginary part of the complex dielectric constant, has also been proposed. The FB method is further generalized to analyze scattering from dielectric rough surfaces with arbitrary complex dielectric constant. Electric and magnetic equivalent surface currents are split into forward and backward components and equations governing these current components are obtained. As a solution, an iterative scheme is proposed and its convergence rate is analyzed. Finally, the effectiveness of the method is assessed by comparing the obtained scattering results with "exact" ones, computed by employing the usual method of moments (MoM).     

Bistatic specular scattering from rough dielectric surfaces

An experimental investigation was conducted to determine the nature of bistatic scattering from rough dielectric surfaces at 10 GHz. This paper focusses specifically on the dependence of coherent and incoherent scattered fields on surface roughness for the specular direction. The measurements, which were conducted for a smooth surface with ks<0.2 (where k=2π/λ and s is the RMS surface height) and for three rough surfaces with ks=0.5, 1.39, and 1.94, included observations over the range of incidence angles from 20° to 65° for both horizontal and vertical polarizations. For the coherent component, the reflectivity was found to behave in accordance with the prediction of the physical optics model, although it was observed that the Brewster angle exhibited a small negative shift with increasing roughness. The first-order solution of physical optics also provided good agreement with observations for hh-polarized incoherent scattering coefficient, but it failed to predict the behavior of the vv-polarized scattering coefficient in the angular range around the Brewster angle. A second-order solution is proposed which appears to partially address the deficiency of the physical optics model     

MMW scattering by rough lossy dielectric cylinders and tree trunks

The millimeter-wave (MMW) radar backscatter response of a rough, lossy, dielectric cylinder is examined both analytically and experimentally. Models for both the coherent and incoherent components of the scattered field are developed based on the geometric-optics approximation. The accuracy of the analytical models and their applicability in predicting the backscatter response of tree trunks are determined experimentally by measuring the radar backscatter at 95 GHz from a rough conducting cylinder and from a section of a tree trunk. In both cases, very good agreement was achieved between the model predictions and the measurements     

Scattering of a Gaussian beam by a dielectric rectangular cylinder

For purpose of finding the dielectric constant, a new expression of the beam scattering is obtained by using the boundary element method (BEM) with extended boundary conditions. Comparison between with and without the resonant condition was made for the total scattered power. To find the accuracy, convergence property of the total scattered power versus divided number has been examined. To check the boundary conditions at the corner of the scatter, the electric field difference between inner and outer side has also been calculated and confirmed. The total electric field distributions in space are illustrated for the plane and beam wave. Microwave experiments was also performed     

Electromagnetic scattering from slightly rough surfaces withinhomogeneous dielectric profiles

Remote sensing of soil moisture using microwave sensors require accurate and realistic scattering models for rough soil surfaces. In the past, much effort has been devoted to the development of scattering models for either perfectly conducting or homogeneous rough surfaces. In practice, however, the permittivity of most soil surfaces is nonuniform, particularly in depth, for which analytical solution does not exist. The variations in the permittivity of a soil medium can easily be related to its soil moisture profile and soil type using the existing empirical models. In this paper, analytical expressions for the bistatic scattering coefficients of soil surfaces with slightly rough interface and stratified permittivity profile are derived. The scattering formulation is based on a new approach where the perturbation expansion of the volumetric polarization current instead of the tangential fields is used to obtain the scattered field. Basically, the top rough layer is replaced with an equivalent polarization current and, using the volumetric integral equation in conjunction with the dyadic Green's function of the remaining stratified half-space medium, the scattering problem is formulated. Closed-form analytical expressions for the induced polarization currents to any desired order are derived, which are then used to evaluate the bistatic scattered fields up to and including the third order. The analytical solutions for the scattered fields are used to derive the complete second-order expressions for the backscattering coefficients as well as the statistics of phase difference between the scattering matrix elements. The theoretical results are shown to agree well with the backscatter measurements of rough surfaces with known dielectric profiles and roughness statistics     

High frequency scattering of a Gaussian beam by a conducting cylinder

When the radius of the cylinder is much larger than the wavelength, an approximate expression for the scattering of a Gaussian beam by a conducting cylinder is obtained by using Watson transformation. The beam fields in shadow region and illuminated region are, respectively, derived from residue theorem and stationary phase method. In order to check the theory, comparisons for scattering pattern and field variation in space were made. Numerical examples of the scattering patterns forw/lambda geqleq a_{0}/lambda gg 1 (w, a_{0} lambdabeing the beamwidth, the radius of cylinder, and the wavelength) are also illustrated.     

Electromagnetic scattering by a two-dimensional wedge composed ofconductor and lossless dielectric

Electromagnetic scattering by two-dimensional wedges composed of perfectly conducting and lossless dielectric material is considered. Heuristic geometrical theory of diffraction type diffraction coefficients are presented and a hybrid moment-method/physical-optics technique is developed to verify the accuracy of the proposed diffraction coefficients. The purpose is to show that the heuristic approach can yield acceptably accurate results for a number of composite wedge geometries, rather than to present rigorous diffraction coefficients for the composite wedge per se. Calculated results are presented in which the results obtained by means of the two methods are compared. Very good agreement is achieved for a variety of wedge geometries     

三维介质粗糙面上导体目标散射的解析-数值混合算法

推导出二维介质粗糙面与其上三维导体目标复合散射的耦合积分方程,提出目标散射的数值矩量法(Method of Moment,MoM)与粗糙面散射的基尔霍夫解析近似法(Kirchhoff Approximation,KA)相结合的混合迭代算法.理论推导表明:当目标距离粗糙面的高度满足条件时,目标的离散单元在粗糙面上任意一点的散射场满足局部平面波关系,利用粗糙面局部面元的反射和透射关系,得出粗糙面感应场的KA解析计算式.由于粗糙表面的感应场用KA解析计算,只需对目标的感应电流进行一次数值积分,无需数值求解粗糙面的积分方程,节省大量的存储空间和运算时间,能在理论上十分简明、数值计算上十分有效地求解三维体目标与面目标组合的复合散射问题.讨论了目标与粗糙面相互作用的互耦迭代算法的有效性和收敛性.结合Monte-Carlo方法产生随机粗糙面样本,数值分析Gauss介质粗糙面上方的规则导体球或任意不规则六面体的散射,讨论了粗糙面的介电参数和目标几何形状等对双站散射的影响.     

Transient scattering from two-dimensional dielectric cylinders ofarbitrary shape

The problem of transient scattering by arbitrarily shaped two-dimensional dielectric cylinders is solved using the marching-on-in-time technique. The dielectric problem is approached via the surface equivalence principle. Two coupled integral equations are derived by enforcing the continuity of the electric and magnetic fields which are solved by using the method of moments. Numerical results are presented for two cross sections, viz. a circle and a square, and compared with inverse discrete Fourier transform (IDFT) techniques. In each case, good agreement is obtained with the IDFT solution     

A hybrid FEM-based procedure for the scattering from photoniccrystals illuminated by a Gaussian beam

We provide an efficient numerical procedure for evaluating the field scattered by two-dimensional (2-D) photonic crystals when they are illuminated by Gaussian beams. In particular, the incident Gaussian beam is interpreted as a spectrum of both homogeneous and inhomogeneous plane waves. The scattering of each plane wave is analyzed by resorting to a hybrid technique combining the finite-element method (FEM) with a Floquet modal expansion. Moreover, by applying the standard saddle point method, the evaluation of the field at a specific point of the exterior medium is reduced to the contribution of the fundamental Floquet mode of a single plane wave belonging to the incident spectrum, strongly enhancing the numerical efficiency     

A new theory for scattering of electromagnetic waves fromconducting or dielectric rough surfaces

The problem of electromagnetic scattering from a conducting or dielectric rough surface with arbitrary shape is studied. An exact solution, using a differential method, is provided for a plane wave with one-dimensional irregularity of the interface. The problem is reduced to the resolution of a linear system of partial differential equations with constant coefficients, and to the computation of eigenvalues and eigenvectors of a truncated infinite matrix. Numerical application is made to show the angular distribution of energy density in the case of an arbitrary profile of the scattering surface and its evolution when the nonperiodic profile tends to become periodic. The near field is computed on the interface and its enhancement in the illuminated region is observed. It increases with the height of the irregularity and with the frequency     

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.     

Generation of complex Gaussian beam modes in beam interaction with a planar dielectric interface

The problem of Gaussian beam interaction with a planar interface separating two semi-infinite homogeneous isotropic lossless media is considered for regular incidence, i.e., excluding the case of total internal reflection. The reflected and refracted fields are expressed in terms of the fundamental and higher order complex beam modes. These newly identified complex beam modes differ from the conventional beam modes and they describe the structure of the reflected and transmitted fields in a more convenient manner.     

A combined steepest descent-fast multipole algorithm for the fastanalysis of three-dimensional scattering by rough surfaces

A new technique, the steepest descent-fast multipole method (SDFMM), is developed to efficiently analyze scattering from perfectly conducting random rough surfaces. Unlike other prevailing methods, this algorithm has linear computational complexity and memory requirements, making it a suitable candidate for analyzing scattering from large rough surfaces as well as for carrying out Monte Carlo simulations. The method exploits the quasiplanar nature of rough surfaces to efficiently evaluate the dyadic Green's function for multiple source and observation points. This is achieved through a combination of a Sommerfeld steepest descent integral and a multilevel fast multipole-like algorithm based on inhomogeneous plane wave expansions. The fast evaluation of the dyadic Green's function dramatically speeds up the iterative solution of the integral equation for rough surface scattering. Several numerical examples are presented to demonstrate the efficacy and accuracy of the method in analyzing scattering from extremely large finite rough surfaces     

Two-dimensional scattering of a Gaussian beam by a periodic array of circular cylinders

The two-dimensional scattering of a Gaussian beam by a periodic array of circular cylinders is studied. The incident Gaussian beam is expressed as a superposition of plane waves of different amplitudes and different incident angles, using the plane-wave spectrum technique based on Fourier optics. For each plane wave, the scattered field is calculated with the T-matrix of an isolated circular cylinder and its lattice sums characterizing a periodic arrangement of the circular cylinders. The circular cylinders may be perfect conductors, dielectric or gyrotropic cylinders, as long as their T-matrices are known.     

Electromagnetic inverse scattering of two-dimensional perfectlyconducting objects by real-coded genetic algorithm

Shape reconstruction of two-dimensional perfectly conducting objects using noisy measured scattering data is considered. The contour of each conducting object is denoted by a shape function in the local polar coordinate which is approximated by a trigonometric series. A point-matching method is used to solve the scattering problem. The main idea of the inversion algorithm is to cast the inverse problem into a restrained minimization problem and to solve it by the real-coded genetic algorithm (RGA). The performance of this algorithm is demonstrated by numerically reconstructing arbitrarily shaped objects and by a detailed comparison with both the standard genetic algorithm (SGA) and the Newton-Kantorovitch method