Eigenvalue system for the scattering from rough surfaces - Saving in computation time by a physical approach

The curvilinear coordinate method is an efficient theoretical tool for analysing rough surfaces. It consists on solving Maxwell’s equations written in a nonorthogonal coordinate system. The C method leads to eigenvalue systems and the scattered fields can be expanded as a linear combination of eigensolutions. The boundary conditions allow the combination coefficients to be determined. The dominant computational cost for the C method is the eigenvalue problem solution which is of order of N³ where N is the size of eigenvalue systems. In this paper, we propose a new approach based on the association of the C method with the beam simulation method (BSM) in order to reduce the computational time. The BSM is based on decomposing a large incident beam into narrower subbeams and then synthesizing the large beam by coherent superposition. The adopted procedure consists of two stages. First, the surface fields are obtained by the C method associated with each elementary beam illuminating smaller surfaces. Second, the total surface field is deduced from a coherent superposition of elementary surface current densities. The far-field and the scattering coefficients are derived from the Huygens principle applied to the total surface fields. We confirm the efficiency and the validity of the approach and show that the BSM applied with the C method allows a significant saving in computation time.     

Rigorous and approximate methods for modeling wave scattering from a locally perturbed perfectly conducting surface

Rigorous and approximate methods are considered for solving the problem of harmonic plane wave scattering from a plane surface arbitrarily perturbed along one dimension on a finite interval. This problem is treated using the Fredholm integral equations of the second kind and the Kirchhoff and Rayleigh approximations. The estimates of the computational efficiency of the integral equation method and the Rayleigh approximation are compared by calculating fields scattered from random rough surfaces in the resonance region (i.e., when the roughness height is comparable to or smaller than the incident wavelength) for an arbitrary incidence of a plane wave. Scattering patterns calculated using the integral equations and the Kirchhoff approximation are discussed in the case of large-scale random rough surface scattering. Particular attention is paid to scattering at near-grazing incidence.     

Babinet's principle in the Fraunhofer diffraction by a finite thin wire

The scattered waves by a thin finite wire are evaluated by using the Rayleigh-Sommerfeld integral in the Fraunhofer approximation. The scattered fields by the complementary thin wire are also obtained with the aid of the Babinet's principle. The scattering integrals are evaluated directly. It is shown that Babinet's principle holds excellently for this problem. The scattered fields are examined numerically.     

Tilt-invariant theory of rough-surface scattering: I

Abstract

The small-slope approximation (SSA) in rough-surface scattering theory uses the surface slope as a small parameter of expansion. But, from the physical point of view, the slope may not be a restrictive parameter because we can change the slope of a surface simply by tilting the coordinate system. We present the theory of rough-surface scattering in a coordinate-invariant form. The new method, tilt-invariant approximation (TIA), leads to a different expansion that does not require that the slope of a surface be small. For a small Rayleigh parameter this approximate solution provides the correct perturbation theory, for a large Rayleigh parameter it provides the Kirchhoff approximation with several correcting terms.     

Comparisons of the discrete-dipole approximation and modified double interaction model methods to predict light scattering from small features on surfaces

Two numerical methods to model light scattering from illuminated features on surfaces are presented. The discrete-dipole approximation (DDA) method is considered, as well as the modified double interaction method (MDIM). The DDA method models electromagnetic scattering of continuous features using discrete dipoles placed on a lattice structure. Sommerfeld integral terms are used to model dipole/surface interaction in the near-field. The MDIM method first computes scattering from the features based in free space using other methods such as Mie theory or other standard light scattering codes (including DDA). The surface interaction is modeled as a first approximation by means of a geometrical shadowing effect and the Fresnel coefficients. Comparisons of the methods will be shown for light scattering from spherical features. The material properties of dielectric and metallic materials will be considered and the feature sizes will be varied. The prediction accuracy and computational requirements of each method will be investigated. For most cases, the studies will show that the DDA method is more accurate than the MDIM method for dielectric materials since the modeling of the feature and surface electromagnetic interaction is more accurate; however, the modified double interaction method may be advantageous over the discrete-dipole approximation method for metallic features because of lesser computational times and memory requirements.     

Tilt-invariant theory of rough-surface scattering: I

The small-slope approximation (SSA) in rough-surface scattering theory uses the surface slope as a small parameter of expansion. But, from the physical point of view, the slope may not be a restrictive parameter because we can change the slope of a surface simply by tilting the coordinate system. We present the theory of rough-surface scattering in a coordinate-invariant form. The new method, tilt-invariant approximation (TIA), leads to a different expansion that does not require that the slope of a surface be small. For a small Rayleigh parameter this approximate solution provides the correct perturbation theory, for a large Rayleigh parameter it provides the Kirchhoff approximation with several correcting terms.     

海面与其上方双矩形截面柱复合散射的混合算法研究

采用Pierson-Moscowitz(PM)海谱和Monte Carlo方法模拟实际的粗糙海面, 基于矩量法和基尔霍夫近似的混合算法研究了海面与其上方双矩形截面导体柱的复合电磁散射特性, 得出了复合散射系数的角分布曲线, 计算了复合散射系数随海面参数、矩形截面柱参数以及入射波参数的变化情况, 并做了详细分析与讨论, 得到了PM谱海面与其上方双矩形截面柱复合散射特性. 结果表明, 与单纯的矩量法相比较, 采用基于矩量法和基尔霍夫近似的混合算法, 既可获得较高的准确性, 同时又可减少计算时间和内存占用量, 而且粗糙面尺度越大该优势越明显.     

Unconventional application of the two-flux approximation for the calculation of the Ambartsumyan-Chandrasekhar function and the angular spectrum of the backward-scattered radiation for a semi-infinite isotropically scattering medium

It is commonly accepted that the Schwarzschild-Schuster two-flux approximation (1905, 1914) can be employed only for the calculation of the energy characteristics of the radiation field (energy density and energy flux density) and cannot be used to characterize the angular distribution of radiation field. However, such an inference is not valid. In several cases, one can calculate the radiation intensity inside matter and the reflected radiation with the aid of this simplest approximation in the transport theory. In this work, we use the results of the simplest one-parameter variant of the two-flux approximation to calculate the angular distribution (reflection function) of the radiation reflected by a semi-infinite isotropically scattering dissipative medium when a relatively broad beam is incident on the medium at an arbitrary angle relative to the surface. We do not employ the invariance principle and demonstrate that the reflection function exhibits the multiplicative property. It can be represented as a product of three functions: the reflection function corresponding to the single scattering and two identical h functions, which have the same physical meaning as the Ambartsumyan-Chandrasekhar function (H) has. This circumstance allows a relatively easy derivation of simple analytical expressions for the H function, total reflectance, and reflection function. We can easily determine the relative contribution of the true single scattering in the photon backscattering at an arbitrary probability of photon survival Λ. We compare all of the parameters of the backscattered radiation with the data resulting from the calculations using the exact theory of Ambartsumyan, Chandrasekhar, et al., which was developed decades after the two-flux approximation. Thus, we avoid the application of fine mathematical methods (the Wiener-Hopf method, the Case method of singular functions, etc.) and obtain simple analytical expressions for the parameters of the scattered radiation. Note that the simplicity of the expressions is supplemented with unexpectedly high accuracy. The results demonstrate the unknown possibilities offered by the two-flux approximation, which is the simplest approximate method to solve the equations of transport theory. We assume that the method can be employed in the calculations of the angular characteristics of the reflected radiation for media whose single scattering is described using complicated (in comparison with isotropic) laws.     

Factors influencing electromagnetic scattering from the dielectric periodic surface

The scattering characteristics of the periodic surface of infinite and finite media are investigated in detail.The Fourier expression of the scattering field of the periodic surface is obtained in terms of Huygens' s principle and Floquet's theorem.Using the extended boundary condition method(EBCM) and T-matrix method, the scattering amplitude factor is solved,and the correctness of the algorithm is verified by use of the law of conservation of energy.The scattering cross section of the periodic surface in the infinitely long region is derived by improving the scattering cross section of the finite period surface.Furthermore, the effects of the incident wave parameters and the geometric structure parameters on the scattering of the periodic surface are analyzed and discussed.By reasonable approximation, the scattering calculation methods of infinite and finite long surfaces are unified.Besides, numerical results show that the dielectric constant of the periodic dielectric surface has a significant effect on the scattering rate and transmittance.The period and amplitude of the surface determine the number of scattering intensity peaks, and, together with the incident angle, influence the scattering intensity distribution.     

二维导体微粗糙面与其上方金属平板的复合电磁散射研究

研究了二维导体微粗糙面与其上方金属平板复合电磁散射特征.应用互易性原理使求解二次散射场简化为求解包含平板上的极化电流和微粗糙面散射场的积分方程，从而降低了求解难度.应用物理光学近似和微扰法分别求解了平板上的极化电流和粗糙面的电磁散射场，得到了复合散射截面计算公式并进行了数值计算.尤其对该复合模型后向耦合电磁散射结果进行了详细分析和讨论. 关键词： 互易性原理 复合电磁散射 微粗糙面 平板     

Application of the method of equivalent edge currents to composite scattering from the cone-cylinder above a dielectric rough sea surface

Compared with scattering from a rough surface only, composite scattering from a target above a rough surface has become so practical that it is a subject of great interest. At present, this problem has been solved by some numerical methods which will produce an enormous calculation amount. In order to overcome this shortcoming, the reciprocity theorem (RT) and the method of equivalent edge currents (MEC) are used in this paper. Due to the advantage of RT, the difficulty in computing the secondary scattered fields is reduced. Simultaneously, MEC, a high-frequency method with edge diffraction considered, is used to calculate the scattered field from the cone-cylinder target with a high accuracy and efficiency. The backscattered field and the polarization currents of the rough sea surface are evaluated by the Kirchhoff approximation (KA) method and physical optics (PO) method, respectively. The effects of the backscattering radar cross section (RCS) and the Doppler spectrum on the size of the target and the windspeed of the sea surface for different incident angles are analysed in detail.     

Second-order small perturbation method for transmission from dielectric rough surfaces

Although the small perturbation method (SPM) for rough surface scattering has been studied extensively in problems in optics, remote sensing and propagation, there are fewer studies on rough surface transmission by the SPM. In this paper, from Huygens’ principle and the extinction theorem, the SPM is used to derive the transmitted field to the second order, and expressions for the bidirectional transmission coefficient and the total surface transmittance to the second order are developed for the random rough surface. The refined expressions can be applied to the situations where the transmission characteristics of a random rough surface need to be more accurately calculated. For example, to calculate the brightness temperature of stratified rough media by the incoherent method, we have to know the bidirectional transmission coefficient or transmittance of random rough surface as accurately as possible. The accuracy of the presented expressions is verified through the conservation of energy. It is shown that the transmission characteristics calculated by SPM to the first order violate conservation of energy, whereas solutions to the second order conform to energy conservation much better. This is particularly important for the calculation of transmittance or emissivity.     

The simulation of the origin and propagation of speckle field generated through a plane wave and Gaussian beam and its verification by speckle correlation method

This paper presents a simulation model of the origin and propagation of speckle field within the Fresnel approximation and verification of the model through a speckle correlation method for determination of in-plane object's translation. There is used a convolution form of the Fresnel–Kirchhoff diffraction integral in the simulation model instead of often used Fast Fourier Transform approach. A possible way of simulation of the light scattering by object's surface and in-plane translation of the illuminated surface is mentioned, whereas two types of illumination (plane wave and Gaussian beam) are used. Finally, results of numerical correlation of generated displaced speckle fields are shown and compared with the results obtained by theoretical relations.     

Multiple scatter of vector electromagnetic waves from rough metal surfaces with infinite slopes using the Kirchhoff approximation

This paper presents calculations of a new formulation of the three‐dimensional Kirchhoff approximation which allows calculation of the scattering of vector waves from two-dimensional (2D) metal and dielectric rough surfaces containing infinite slopes. Results are presented for scattering from metal surfaces with rectangular surface structures. This type of surface has applications, for example, in remote sensing and in testing or imaging of printed circuits. Some calculations for rectangular-shaped grooves in a plane are presented for the 2D surface method and are compared to previously published results using a different method of calculation. Good agreement is found between the results for the different calculation methods.     

The use of the virtual source technique in computing scattering from periodic ocean surfaces

In this paper the virtual source technique is used to compute scattering of a plane wave from a periodic ocean surface. The virtual source technique is a method of imposing boundary conditions using virtual sources, with initially unknown complex amplitudes. These amplitudes are then determined by applying the boundary conditions. The fields due to these virtual sources are given by the environment Green's function. In principle, satisfying boundary conditions on an infinite surface requires an infinite number of sources. In this paper, the periodic nature of the surface is employed to populate a single period of the surface with virtual sources and m surface periods are added to obtain scattering from the entire surface. The use of an accelerated sum formula makes it possible to obtain a convergent sum with relatively small number of terms (～40). The accuracy of the technique is verified by comparing its results with those obtained using the integral equation technique.     

Extension of the local curvature approximation to third order and improved tilt invariance

The second-order local curvature approximation (LCA2) is a theory of rough surface scattering that reproduces fundamental low and high frequency limits in a tilted frame of reference. Although the existing LCA2 model provides agreement with the first order small perturbation method up to the first order in surface tilt, results reported in this paper produce a new formulation of the model that achieves consistency with perturbation theory to first order in surface height and arbitrary order in surface tilt. In addition, extension of the modified LCA to third order is presented, and allows the theory to match the second-order small perturbation method to arbitrary order in surface tilt. Crucial to the development of the theory are a set of identities involving relationships among the small perturbation method (i.e. low frequency) and Kirchhoff approximation (i.e. high frequency) kernels; a set of new identities obtained in our derivations is also presented. Sample results involving 3D electromagnetic scattering from penetrable rough surfaces, as well as 2D scattering from Dirichlet sinusoidal gratings, are provided to compare the new results with the existing LCA2 model and with other rough surface scattering theories.     

Scattering of Rayleigh waves by a statistical inhomogeneity of the mass density

The problem of the scattering of a Rayleigh wave by a surface inhomogeneity of the mass density of an isotropic solid is solved in the Born approximation of perturbation theory. The inhomogeneity is statistical with a Gaussian correlation function in the plane parallel to the surface and is deterministic with an exponentially decaying dependence on the coordinate perpendicular to the surface. Expressions are derived for the displacement fields in the scattered longitudinal (P), transverse (SV and SH), and Rayleigh (R) waves at large distances from the inhomogeneity. The Rayleigh wave energy scattering coefficients are calculated as functions of the wavelength λ, the correlation length a of the inhomogeneity, the depth d of the defective layer, and the Poisson ratio of the medium, σ. The angular distribution of the scattered Rayleigh wave energy is determined. Asymptotic expressions are obtained for the scattering coefficient in various limiting cases with respect to the parameters a/λ and λ/d. The relation between the energies in the scattered P, SV, SH, and R waves is established. The resulting equations are used to calculate the scattering coefficients numerically over a wide range of variation of the parameters a/λ, λ/d, and σ; the results are presented in the form of graphs and a table. A physical pattern of the scattering process is constructed and used as a basis for interpreting the results of the study. Fiz. Tverd. Tela (St. Petersburg) 39, 267–274 (February 1997)     

Exclusion principle effects in pion-nucleus scattering in the region of the 3, 3 resonance

Chew-Low theory for pion scattering is examined for a nucleon immersed in a Fermi sea. All exclusion principle effects, including those internal to the pion-nucleon scattering amplitude, are considered, and the modifications of the 3, 3 resonance in nuclei are studied. An optical model is constructed in a local density approximation. Results are compared with recent data on pion scattering from ¹²C.     

各向异性圆锥体的平面光波散射特性

基于通用的矢量电位和标量电位与介电常数张量无关的原理,由激发的电偶极子与位函数的关系得到了任意各向异性目标散射场的表达式。得到了通用的介电常数张量的变换关系,具体地给出了介电常数张量在球坐标系中的表达式,将目标的内外电场展为级数,得到了各向异性晶体圆锥体一级散射场的解析表达式。理论结果与文献一致,验证了算法的正确性。在光波波长与粒子尺寸相近的情况下,对所得结果进行了仿真,表明各向异性圆锥体的散射具有偶极辐射的特点。所得结果简单、通用,为研究形状更为复杂的各向异性目标、纳米粒子等的光散射研究提供了理论基础。     

Extension of the local curvature approximation to third order and improved tilt invariance

The second-order local curvature approximation (LCA2) is a theory of rough surface scattering that reproduces fundamental low and high frequency limits in a tilted frame of reference. Although the existing LCA2 model provides agreement with the first order small perturbation method up to the first order in surface tilt, results reported in this paper produce a new formulation of the model that achieves consistency with perturbation theory to first order in surface height and arbitrary order in surface tilt. In addition, extension of the modified LCA to third order is presented, and allows the theory to match the second-order small perturbation method to arbitrary order in surface tilt. Crucial to the development of the theory are a set of identities involving relationships among the small perturbation method (i.e. low frequency) and Kirchhoff approximation (i.e. high frequency) kernels; a set of new identities obtained in our derivations is also presented. Sample results involving 3D electromagnetic scattering from penetrable rough surfaces, as well as 2D scattering from Dirichlet sinusoidal gratings, are provided to compare the new results with the existing LCA2 model and with other rough surface scattering theories.