Hybrid method for investigation of electromagnetic scattering from conducting target above the randomly rough surface

A current based hybrid method (HM) is proposed which combines the method of moment (MOM) with the Kirchhoff approximation (KA) for the analysis of scattering interaction between a two-dimensional (2D) infinitely long conducting target with arbitrary cross section and a one-dimensional (1D) Gaussian rough surface. The electromagnetic scattering region in the HM is split into KA region and MOM region. The electric field integral equation (EFIE) in MOM region (target) is derived, the computational time of the HM depends mainly on the number of unknowns of the target. The bistatic scattering coefficient for the infinitely long cylinder above the rough surface with Gaussian roughness spectrum is calculated, and the numerical results are compared and verified with those obtained by the conventional MOM, which shows the high efficiency of the HM. Finally, the influence of the size, location of the target, the rms height and correlation length of the rough surface on the bistatic scattering coefficient with different polarizations is discussed in detail.     

Electromagnetic scattering from two-layer rough interfaces in the Kirchhoff approximation

Electromagnetic wave scattering from multilayers consisting of two two-layer Gaussian rough surfaces with lossless media is investigated in the Kirchhoff approximation (KA), with consideration of the shadowing effects. The tapered incident wave is introduced into the classic KA, and the bistatic scattering coefficient is redetermined. The advantage of this method is that it is faster in computation than the exact numerical methods. The numerical results show that the bistatic scattering coefficient calculated in the KA is in good agreement with that obtained by using the method of moment (MOM) over a most angular range, which indicates the validity of the KA proposed in our paper. Finally, the effects of the relative permittivity, the root-mean-square (RMS) height, the correlative length, and the average height between the two interfaces on the bistatic scattering coefficient are discussed in detail.     

三维随机粗糙面上导体目标散射的解析-数值混合算法

提出三维导体目标与导体粗糙面复合散射的解析-数值混合迭代算法,推导出三维目标与粗糙面的耦合积分方程,以及粗糙面散射的Kirchhoff近似(KA)计算式.粗糙面的KA解析计算大大降低了粗糙面求解的复杂度,与目标矩量法的混合迭代保证了计算结果的精度,使得三维体-面目标复合散射计算变得可行.由于体-面两者的高阶耦合作用明显减小,保证了该混合迭代算法的收敛性.与镜像Green函数方法的比较表明该混合算法的有效性,并讨论了粗糙面长度选择对计算结果的影响.结合Monte-Carlo方法,数值分析了理想导体Gauss 关键词： 复合散射 Kirchhoff近似 共轭梯度法 互耦迭代     

高斯分层介质粗糙面光波透射问题的微扰法研究

运用微扰法研究平面波入射分层介质粗糙面的光波透射问题,推出了不同极化状态的透射光波散射系数公式。采用高斯粗糙面来模拟实际的分层介质粗糙面,结合高斯粗糙面的功率谱导出了平面波入射高斯分层介质粗糙面的透射系数计算公式。通过数值计算得到HH极化透射系数随透射光波散射角变化的曲线,讨论底层介质介电常数、中间介质介电常数和厚度、粗糙面参数及入射光波长对透射系数的影响。数值计算结果表明：底层介质介电常数、中间介质介电常数和厚度、粗糙面参数及入射光波长对透射系数的影响是非常复杂的。     

Scattering from very rough metallic and dielectric surfaces: a theory based on the modified Kirchhoff approximation

This paper presents a theory of scattering from very rough metallic and dielectric surfaces using the first- and second-order Kirchhoff approximations (KA) modified with the angular and propagation shadowing. The shadowing functions limit the single and double scattered waves which are illuminated and not shadowed by the surface. The theoretical results are compared with the Monte Carlo simulations showing the range of validity of the theory. The theory is applicable to the range where the RMS height is close to a wavelength and the RMS slope is close to unity, and the second medium is lossy. The second-order scattering includes two waves travelling in opposite directions on the surface, giving a physical explanation of the enhanced backscattering.     

Scattering of a plane wave by one-dimensional dielectric random rough surfaces—study with the curvilinear coordinate method

We present a method giving the bi-static scattering coefficient of a one-dimensional dielectric random rough surface illuminated by a plane wave. The theory is based on Maxwell's equations written in a nonorthogonal coordinate system. For each medium, this method leads to an eigenvalue system. The scattered field is expanded as a linear combination of eigensolutions satisfying the outgoing wave condition. The boundary conditions allow the diffraction amplitudes to be determined. The Monte Carlo technique is applied and the bi-static scattering coefficient is estimated by averaging the scattering amplitudes over several realizations. The results of a Gaussian random process with a Gaussian roughness spectrum are compared to published experimental and numerical data. Comparisons are conclusive.     

粗糙面重构问题的混合算法研究

基于Desanto的谱表示法,采用数值和近似算法相结合的混合算法对一维粗糙面的重构问题进行了研究.对于正问题,采用数值算法——矩量法(MOM)得到一维粗糙面的相关散射数据,对于逆问题,考虑不同粗糙度的粗糙面,分别采用两种近似算法——微扰近似(SPA)、基尔霍夫近似(KA)与矩量法的混合算法,对粗糙面轮廓进行了重构;数值结果以高斯粗糙面为例,给出了混合算法对不同粗糙度粗糙面的重构算例,并进行了数据比较和分析. 关键词： 粗糙面重构 矩量法 微扰近似 基尔霍夫近似     

Scattering of an electromagnetic wave from a slightly random cylindrical surface: horizontal polarization

The scattering of an electromagnetic wave from a random cylindrical surface ir studied for a plane-wave incidence with S-(TE) polarization, by means ofthe stochastic scattering theory developed by Nakayama, Ogura. Sakati et al. The theory is based on the Wiener-Ito stochastic functional calculus combined with the group-theoretic consideration concerning the homogeneity of the random surface. The random surface is assumed to be a homogeneous Gaussian random field on the cylinder C, homogeneous with respect to the group of motiolrs on C: translations along the axis and rotations around the axis. An operator D operating on a random field on C is introduced in such a way that D keeps the homogeneous random surface invariant This gives a reprerentation of the cylbdrical group and commutes with the boundary condition and the Maxwell equation. Thus, for an injection of the mth cylindrical TE or TM wave, which is a vector eigenfunction of the D operator, the scattered random wave field is an eigenfunctiou with the same eigenvalue: it satisfies the Maxwell equation and is a stoch-tic Iunctional of the Gaussian random surface, BO that it can be expressed in a vector form of the Wiener-Ito expansion in t e m of TE and TM waves and orthogonal functional. of the Gaussian random measures associated with the random cylindrical surface. In the analysis the random surface is modelled by an approximate boundaiy condition representing a perfectly conducting cylindrical surface with a slight roughness. The boundary condition on the random cylinder is transformed into a hierarchy of equations for the Wiener kernels which can be solved approximately. The random wave field for a plane-wave injection is obtained by summing these fields over m. From the stochastic representation of the electromagnetic field so obtained, various statistical characteristics can be calculated the coherent scattering amplitude. total coherent power flow, incoherent power flow, differential sections for coherent rcatlerhig and incoherent scattering, etc. The power conservation law is cast into a stochastic electromagnetic version of the optical theorem stating that the total scatteiing cross section is given by the imaginary part of the forward coherent scattering amplitude. Numerical calculations are made for a planewave injection with S-(TE) polarization. The case of p-(TM) polarization can be treated in a similar manner.     

Parameters Extraction of Millimeter Wave Circuits by Hybrid Vector Finite Element and Moment Method Combined with SOC Technique

This paper presents a hybrid method, which couples the vector finite element method (FEM) and method of moment (MOM) for analyzing the field and current distribution of the millimeter wave circuits. The FEM is applied to handle the interior region of dielectric bodies and MOM is used to solve surface integral equations. Then, These integral expressions are coupled into the FEM equations through the continuity of the tangential fields across the connection boundaries. Simultaneously, the short-open calibration (SOC) technique is used for predicting accurately the scattering parameters of the circuits. Numerical results are well compared with those published in the previous literatures.     

粗糙海面及其上方导体目标复合电磁散射的混合算法研究

利用基于电流计算的矩量法结合高频算法基尔霍夫近似的混合算法,分析了一维PM谱粗糙海面及其上方二维无限长任意截面导体目标的双站复合电磁散射特性.混合算法将粗糙面和目标分别划分到KA区域和MOM区域,由于无需数值求解粗糙海面区域的表面极化电流,该算法的运算时间和对计算机内存的需求主要取决于粗糙面上方目标的网格划分情况.数值结果以无限长导体圆柱为例计算了其与一维下垫PM谱粗糙海面的复合双站散射截面,并将计算结果与经典MOM结果进行了比对和验证,结果表明混合方法具有较高的计算效率.最后应用混合方法讨论了不同极化状态、海上不同风速以及目标不同尺寸和位置对复合散射截面的影响. 关键词： 粗糙海面 电磁散射 混合算法 矩量法     

Scattering of an electromagnetic wave from a planar waveguide structure with a slightly 2D random surface

This paper deals with the scattering of an electromagnetic (EM) wave from a waveguide structure with a slightly rough surface. The waveguide structure is a dielectric film on a planar, perfectly conductive surface, and the top of the film is a two-dimensional (2D) homogeneous Gaussian random surface. The treatment is based on the stochastic functional theory where the random EM field is represented in terms of a Wiener - Hermite functional of the random surface. Numerical calculations show that enhanced backscattering and cross-polarization occur, but that no enhanced satellite peak appears for a 2D random surface, in contrast to the case of a 1D surface. The enhanced backscattering is caused by the interference of two double-scattering processes and is attributed to the existence of guided waves in the scattering structure.     

随机粗糙表面光散射场分布特性的机理研究

为了研究随机粗糙表面光散射分布特性机理,采用线性滤波法生成高斯分布随机粗糙表面,以基尔霍夫近似作为电磁场边界条件,采用蒙特卡罗方法数值计算了一组金属和一组电介质粗糙表面在S偏振光和P偏振光照射下的散射光强度空间分布。计算结果显示:金属表面与电介质表面的散射光分布宽度、散射峰值、散射峰位置三个散射特征存在显著差异,经过分析发现这种特征差异的产生机理是由表面面元的斜率分布和面元反射率共同因素导致,与数值计算结果对比,二者具有良好的一致性。     

Scattering of an electromagnetic wave from a slightly random cylindrical surface: horizontal polarization

Abstract

The scattering of an electromagnetic wave from a random cylindrical surface ir studied for a plane-wave incidence with S-(TE) polarization, by means ofthe stochastic scattering theory developed by Nakayama, Ogura. Sakati et al. The theory is based on the Wiener-Ito stochastic functional calculus combined with the group-theoretic consideration concerning the homogeneity of the random surface. The random surface is assumed to be a homogeneous Gaussian random field on the cylinder C, homogeneous with respect to the group of motiolrs on C: translations along the axis and rotations around the axis. An operator D operating on a random field on C is introduced in such a way that D keeps the homogeneous random surface invariant This gives a reprerentation of the cylbdrical group and commutes with the boundary condition and the Maxwell equation. Thus, for an injection of the mth cylindrical TE or TM wave, which is a vector eigenfunction of the D operator, the scattered random wave field is an eigenfunctiou with the same eigenvalue: it satisfies the Maxwell equation and is a stoch-tic Iunctional of the Gaussian random surface, BO that it can be expressed in a vector form of the Wiener-Ito expansion in t e m of TE and TM waves and orthogonal functional. of the Gaussian random measures associated with the random cylindrical surface. In the analysis the random surface is modelled by an approximate boundaiy condition representing a perfectly conducting cylindrical surface with a slight roughness. The boundary condition on the random cylinder is transformed into a hierarchy of equations for the Wiener kernels which can be solved approximately. The random wave field for a plane-wave injection is obtained by summing these fields over m. From the stochastic representation of the electromagnetic field so obtained, various statistical characteristics can be calculated the coherent scattering amplitude. total coherent power flow, incoherent power flow, differential sections for coherent rcatlerhig and incoherent scattering, etc. The power conservation law is cast into a stochastic electromagnetic version of the optical theorem stating that the total scatteiing cross section is given by the imaginary part of the forward coherent scattering amplitude. Numerical calculations are made for a planewave injection with S-(TE) polarization. The case of p-(TM) polarization can be treated in a similar manner.     

Scattering from a slightly random, one-dimensional metal surface: 45° linearly polarized incidence, backscattering enhancement and degree of polarization

The scattering of an electromagnetic wave from a slightly random metal surface which supports the surface plasmon mode at optical frequencies is studied theoretically by means of a stochastic functional approach. In order to investigate the Stokes matrix or the state of polarizations, as well as the intensity of the scattered waves, the rough surface is assumed to be one dimensional, and is illuminated by a+45° linearly polarized plane electromagnetic (light) wave whose plane of incidence is perpendicular to the grooves of the surface. The stochastic wave fields are represented in terms of the Wiener-Hermite functionals, and the approximate solutions of the Wiener kernels are obtained for both TM- and TE-polarized components, from which the Stokes matrix elements can be determined. The dressed or perturbed plasmon mode in the presence of surface roughness is obtained by a mass operator involved in the solutions, and the enhanced backscattering closely related to the plasmon mode is studied in connection with the enhanced peak width and the mass operator for the dressed plasmon mode. The Stokes parameters and the degree of polarization are calculated numerically from various polarized components of the incoherent scattering distribution. To clarify the surface plasmon's association with the scattering characteristics, calculations are made for two kinds of random surfaces, a random surface with a centred Gaussian spectrum and a random grating with twin spectral peaks at the plasmon spatial frequency.     

Regions of validity of geometric optics and Kirchhoff approximations for reflection from Gaussian random rough dielectric surfaces

In this paper, the effects of characteristics of incident light and the geometrical parameters to the reflectivity of dielectric Gaussian random rough surfaces are presented. The behaviors of the reflectivity vs. several parameters are quantified using approximate methods: the geometric optics approximation (GOA) and the Kirchhoff approximation (KA) and an exact method called integral method (IM). Finally, we determine the limits of validity of approximate methods by comparisons with IM results. The regions of validity of approximate methods depending of many geometrical and physical parameters: roughness, Brewster and shadowing effects, multiple reflections, surface materials, and nature of polarization. The broader domain of validity (DV) is for KA, at normal TE-polarized incident light, for the higher dielectric permittivity. However, the narrowed DV is for GOA, at normal TM-polarized incident light for lower dielectric permittivity.     

An improved technique on the stochastic functional approach for randomly rough surface scattering –Numerical-analytical Wiener analysis

This paper proposes an improved technique on the stochastic functional approach for randomly rough surface scattering. Its first application is made on a TE plane wave scattering from a Gaussian random surface having perfect conductivity with infinite extent. The random wavefield becomes a ‘stochastic Floquet form’ represented by a Wiener–Hermite expansion with unknown expansion coefficients called Wiener kernels. From the effective boundary condition as a model of the random surface, a series of integral equations determining the Wiener kernels are obtained. By applying a quadrature method to the first three order hierarchical equations, a matrix equation is derived. By solving that matrix equation, the exact Wiener kernels up to second order are numerically obtained. Then the incoherent scattering cross-section and the optical theorem are calculated. A prediction is that the optical theorem always holds, which is derived from previous work is confirmed in a numerical sense. It is then concluded that the improved technique is useful.     

Study of MPI based on parallel MOM on PC clusters for EM-beam scattering by 2-D PEC rough surfaces

This paper firstly applies the finite impulse response filter (FIR) theory combined with the fast Fourier transform (FFT) method to generate two-dimensional Gaussian rough surface. Using the electric field integral equation (EFIE), it introduces the method of moment (MOM) with RWG vector basis function and Galerkin's method to investigate the electromagnetic beam scattering by a two-dimensional PEC Gaussian rough surface on personal computer (PC) clusters. The details of the parallel conjugate gradient method (CGM) for solving the matrix equation are also presented and the numerical simulations are obtained through the message passing interface (MPI) platform on the PC clusters. It finds significantly that the parallel MOM supplies a novel technique for solving a two-dimensional rough surface electromagnetic-scattering problem. The influences of the root-mean-square height, the correlation length and the polarization on the beam scattering characteristics by two-dimensional PEC Gaussian rough surfaces are finally discussed.     

Scattering of electromagnetic waves from two-dimensional perfectly conducting random rough surfaces - study with the curvilinear coordinate method

We present a method giving the bi-static scattering coefficient of two-dimensional (2-D) perfectly conducting random rough surface illuminated by a plane wave. The theory is based on Maxwell's equations written in a nonorthogonal coordinate system. This method leads to an eigenvalue system. The scattered field is expanded as a linear combination of eigensolutions satisfying the outgoing wave condition. The boundary conditions allow the scattering amplitudes to be determined. The Monte Carlo technique is applied and the bi-static scattering coefficient is estimated by averaging the scattering amplitudes over several realizations. The random surface is represented by a Gaussian stochastic process. Results are compared to published numerical and experimental data. Comparisons are conclusive.     

任意形状凸粗糙物体高斯光束相干散射研究

研究了任意形状凸粗糙物体对高斯光束的相干散射特性。由平面波谱展开法推导出粗糙面高斯波束散射场表达式．并根据物理光学近似和稳相法原理得到相干散射截面的理论公式。与平面波解不同的是,在公式中引入了波束因子这一表征波束作用的重要参量,该参量与束腰半径、束腰中心与物体中心距离和物体照射面积以及入射、散射方向有关。最后数值计算了1．06μm激光波束对粗糙球的散射,分析了波束因子．介电常量和极化状态对红外激光相干散射截面的影响,重点讨论了波束因子的变化规律。分析表明．当波束半径远大于物体尺寸时,波束入射的结果可退化到平面波情况。