Dielectric Rough Surface Research Articles

A study of electromagnetic scattering from conducting targets above and below the dielectric rough surface

The composite scattering from the conducting targets above and below the dielectric rough surface using the extended Propagation-Inside-Layer Expansion (EPILE) combined with the Forward-Backward method (FBM) is studied. The established integral equations are approved by comparing with the related theory. The accuracy and efficiency of the EPILE + FBM are compared with the method of moments (MOM). The influences of target size, target height/depth, target position, and the rms height, the correlation length, as well as the incident angle on the bistatic scattering coefficient (BSC) for different polarizations are also investigated. The presented algorithm is of generality for the target-rough surface composite scattering problems.

Fast numerical method for electromagnetic scattering from an object above a large-scale layered rough surface at large incident angle: vertical polarization

A fast numerical method has been proposed in this paper for calculating the electromagnetic scattering from a perfectly electric conducting object above a two-layered dielectric rough surface. The focus in this study is large incidence. The parallel fast multipole method is combined with the method of moments for fast implementation of the scattering from this composite model. The biconjugate gradient method is adopted to solve the unsymmetrical matrix equation and parallelized. The simulating time and parallel speedup ratio with different processors are provided. Several numerical results are shown and analyzed to discuss the influences of the parameters of the rough surface, the object, and the intermediate medium on the bistatic scattering.

A Fast Numerical Method for Electromagnetic Scattering From Dielectric Rough Surfaces

In this paper we propose an efficient and accurate iterative numerical approach to analyze EM scattering from 1-D dielectric rough surfaces. It is based on a new splitting of the impedance matrix Z to improve the asymptotic convergence rate of the resultant iterative system. The structure of split matrix is then fully explored, in combination with the application of an identity for inverse of block matrix, to further reduce the computational and storage complexity. The embedded matrix-vector product is computed using the spectral acceleration technique. Extensive numerical simulations demonstrate a couple of appealing features of this proposed method for Gaussian surface with Gaussian spectrum: (1) It converges faster than both forward-backward method (FBM) and FBM with spectral acceleration (FBM-SA); (2) For HH polarization, the proposed method is about twice as fast as FBM-SA. For VV polarization, the proposed method is better when the rms slope is not larger than 16° or interestingly when rms height is beyond 2.0 wavelengths. Moreover, it converges for cases where FBM-SA fails for both polarizations. These features indicate that the proposed method can be effectively used to analyze EM scattering from 1-D dielectric Gaussian surface with Gaussian spectrum.

ITERATIVE HYBRID METHOD FOR ELECTROMAGNETIC SCATTERING FROM A 3-D OBJECT ABOVE A 2-D RANDOM DIELECTRIC ROUGH SURFACE

An iterative hybrid method combining the Kirchhofi approximation (KA) and the multilevel fast multipole algorithm (MLFMA) is studied for electromagnetic scattering from a three- dimensional (3-D) object above a two-dimensional (2-D) random dielectric rough surface. In order to reduce the computational costs, some treatments have been studied. Firstly, the fast far-fleld approximation (FAFFA) is utilized to speed up the electromagnetic coupling interaction process between the rough surface and the object. Secondly, based on the scattering mechanism of the rough surface, a truncation rule on moderate rough surface for bi-static scattering is proposed under the plane wave illumination, which can further speed up the iteration. Compared with the conventional methods, the hybrid method with the above treatments is very e-cient to analyze the scattering of a 3-D object above random rough surfaces. Simulation results validate the efiectiveness and accuracy of the iterative hybrid method.

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.

BISTATIC SCATTERING FROM TWO-DIMENSIONAL DIELECTRIC OCEAN ROUGH SURFACE WITH A PEC OBJECT PARTIALLY EMBEDDED BY USING THE G-SMCG METHOD

An e-cient approach called general sparse matrix canonical grid (G-SMCG) method is proposed to analyze the electromagnetic scattering from 2-D dielectric rough surface with a conducting object partially buried. In this paper, the scattering of 3-D arbitrarily shaped object is computed by using the traditional method of moments (MoM) with RWG basis function, and the scattering of rough surface is analyzed by using the SMCG method. The coupling interactions between an object and rough surface are calculated by iterative method. Combing the ocean rough surface with Pierson Moskowitz (PM) spectrum, the bistatic scattering coe-cients of typical objects buried in the ocean surface have been computed by using the proposed method. Then the accuracy and e-ciency of this method are discussed. Finally, the bistatic scattering coe-cients of a ship located on ocean surface are calculated, and the in∞uence of sea state and wind direction on the scattering coe-cients is indicated.

Numerical Analysis of Scattering by Dielectric Random Rough Surfaces Using Modified SMCG Scheme and Curvilinear RWG Basis Functions

An augmented sparse-matrix canonical-grid (SMCG) approach for numerical analysis of scattering by dielectric random rough surfaces is developed. It is an extension of the previous modified SMCG scheme for perfect-electric-conducting (PEC) surfaces to dielectric cases, and is enhanced by adopting curved triangulation modeling. By using the curved modeling with curvilinear Rao-Wilton-Glisson basis functions (CRWG bases), the number of unknowns can be reduced substantially to extract results of the same accuracy, compared with using the planar triangular discretization with planar RWG bases. Numerical results for Gaussian and ocean-like dielectric rough surfaces are provided to confirm the validity and efficacy of the proposed method.

FDTD Investigation on Electromagnetic Scattering from Two-Layered Rough Surfaces under UPML Absorbing Condition

Electromagnetic scattering from one-dimensional two-layered rough surfaces is investigated by using finite-difference time-domain algorithm (FDTD). The uniaxial perfectly matched layer (UPML) medium is adopted for truncation of FDTD lattices, in which the finite-difference equations can be used for the total computation domain by properly choosing the uniaxial parameters. The rough surfaces are characterized with Gaussian statistics for the height and the autocorrelation function. The angular distribution of bistatic scattering coefficient from single-layered perfect electric conducting and dielectric rough surface is calculated and it is in good agreement with the numerical result with the conventional method of moments. The influence of the relative permittivity, the incident angle, and the correlative length of two-layered rough surfaces on the bistatic scattering coefficient with different polarizations are presented and discussed in detail.

Numerical studies of Lifshitz interactions between dielectrics

We study numerically the fluctuation-derived interaction between dielectrics in both two and three dimensions. We demonstrate how sparse matrix factorizations enable one to study torsional interactions in three dimensions. In two dimensions we study the full crossover between nonretarded and retarded interactions as a function of separation. We use constrained factorizations in order to measure the interaction of a particle with a rough dielectric surface and compare with a scaling argument.

NUMERICAL CHARACTERIZATION OF BISTATIC SCATTERING FROM PEC CYLINDER PARTIALLY EMBEDDED IN A DIELECTRIC ROUGH SURFACE INTERFACE: HORIZONTAL POLARIZATION

Scattering from a two-dimensional (2-D) perfectly electri- cally conducting (PEC) cylinder partially embedded in a random di- electric rough surface interface is studied using the method of moments (MoM) with pulse basis functions and the point matching technique, for the case of horizontal polarization. The random rough surface is modeled using Gaussian statistical characteristic for the rough surface height and surface correlation function, and generated by the spectral- method. The tapered plane-wave incidence is used to avoid artificial edge diffraction due to the truncation of the rough surface into finite- length rough surface in the numerical simulations. With the developed algorithms, the interactions between the dielectric rough surface and the partially buried PEC cylinder are investigated using the Monte Carlo simulation, and are expressed as a function of the root mean square (rms) height of a random dielectric rough surface and the mois- ture content of the soil. The numerical results show that the bistatic scattering coefficients are dependent upon the moisture content, the rms height of a rough surface, and other parameters.

有耗介质高斯随机粗糙面对光波散射的矩量法和基尔霍夫近似的统一

The optical wave scattering from one-dimensional (1D) lossy dielectric Gaussian random rough surface is studied. The tapered incident wave is introduced into the classical Kirchhoff approximation (KA), and the shadowing effect is also taken into account to make the KA results have a high accuracy. The definition of the bistatic scattering coefficient of the modified KA and the method of moment (MOM) are unified. The characteristics of the optical wave scattering from the lossy dielectric Gaussian random rough surface of different parameters are analyzed by implementing MOM.

A NUMERICAL METHOD FOR ELECTROMAGNETIC SCATTERING FROM DIELECTRIC ROUGH SURFACES BASED ON THE STOCHASTIC SECOND DEGREE METHOD

In this paper, we propose an iterative numerical approach based on the stochastic second degree (SSD) algorithm in combination with a new splitting of the impedance matrix to analyze electromagnetic scattering from 1-D dielectric rough surfaces. The embedded matrix-vector product is computed using the banded matrix iterative approach/canonical grid (BMIA/CAG) and the spectral acceleration (SA) technique. For Gaussian surface with Gaussian spectrum, through extensive numerical simulation, it is observed that for HH polarization, the proposed method requires roughly one half number of iterations as needed by the forward-backward method with spectral acceleration (FBM-SA). When the rms height is small, the proposed method takes more run time; when the rms slope is no less than 0.33 and rms height is no less than 1:0‚, where ‚ is the wavelength, the proposed method is more e-cient. More importantly, it obviously improves the convergence properties over FBM-SA by changing cases from divergent to convergent when rms height is no less than 2:0‚ and rms slope is no less than 0.55 except for one extreme case. For VV polarization, the proposed method is less computationally e-cient in terms of run time and number of iterations than FBM-SA. However, as far as convergence properties are considered, similar to HH polarization, the proposed method improves over FBM-SA when the rms height and rms slope are large. Hence for both polarizations, the proposed method demonstrates its suitability when dealing with truly rough surfaces.

Investigation on the characteristics of electromagnetic scattering from 2-D fBm rough surface of layered medium

The electromagnetic scattering from the rough surface of layered medium with plane wave incidence is investigated. A 2-D fBm fractal rough surface is used to simulate the natural rough surface of layered medium, and the formulae of the scattering coefficient of the 2-D fBm fractal dielectric rough surface of layered medium with the plane wave incidence is derived by using the small perturbation method in association with the power spectrum density of 2-D fBm fractal rough surface. The angular distribution of the bistatic-scattering coefficient of HH polarization are obtained by numerical computation, the influence of fractal dimension, the permittivity of substrate medium, the permittivity and the mean layer thickness of intermediate medium, the surface roughness parameters and the frequency of the incident wave on the bistatic-scattering coefficient is discussed. The fractal characteristics, the basic characteristics, the zonal characteristics and the characteristics with varying frequency of the scattering coefficient from 2-D fBm fractal rough surface are obtained.

Implementation and validation of the curvilinear coordinate method for the scattering of electromagnetic waves from two-dimensional dielectric random rough surfaces

The curvilinear coordinate method is applied for analysing 2-D dielectric random rough surfaces. The theory is based on Maxwell's equations written in a non-orthogonal coordinate system. For each medium, this method leads to an eigenvalue system. The scattered fields within two media are expanded as linear combinations of eigensolutions satisfying the outgoing wave condition. The boundary conditions allow the scattering amplitudes to be determined. The coherent and incoherent intensities are estimated by averaging the scattering amplitudes over several realizations. The theory is verified by comparison with results obtained by other exact method. A discussion on the C-method and the Sparse-Matrix CAnonical Grid method is proposed in terms of accuracy and computation time.

Solution of scattering from rough surface with a 2D target above it by a hybrid method based on the reciprocity theorem and the forward–backward method

This paper proposes a hybrid method based on the forward–backward method (FBM) and the reciprocity theorem (RT) for evaluating the scattering field from dielectric rough surface with a 2D target above it. Here, the equivalent electric/magnetic current densities on the rough surface as well as the scattering field from it are numerically calculated by FBM, and the scattered field from the isolated target is obtained utilizing the method of moments (MOM). Meanwhile, the rescattered coupling interactions between the target and the surface are evaluated employing the combination of FBM and RT. Our hybrid method is first validated by available MOM results. Then, the functional dependences of bistatic and monostatic scattering from the target above rough surface upon the target altitude, incident and scattering angles are numerically simulated and discussed. This study presents a numerical description for the scattering mechanism associated with rescattered coupling interactions between a target and an underlying randomly rough surface.

On the Scattering of Electromagnetic Waves by Periodic Rough Dielectric Surfaces: A BOA Solution

A new approach for the scattering of electromagnetic (EM) waves from periodic dielectric rough surfaces is addressed. The method is an extension of the buried object approach (BOA), which is developed for rough surfaces of infinite extend, to the present problem. The BOA allows to model the original problem as the scattering of EM waves from cylindrical objects located in a two-half-space medium with planar interface. Then, the problem is reduced to the solution of a Fredholm integral equation of second kind through the periodic Green's function of two-half-space medium. The periodic Green's function of two-half-space medium is calculated via the Floquet mode expansion, whose numerical evaluation can be accelerated by using effective methods. The method can also be used to solve the scattering problems of rough surfaces of infinite extend and having a localized roughness. Numerical simulations show that the method yields effective and accurate results for surfaces of arbitrary variation.

Fractal characteristics investigation on electromagnetic scattering from 2-D Weierstrass fractal dielectric rough surface

A normalized two-dimensional band-limited Weierstrass fractal function is used for modelling the dielectric rough surface. An analytic solution of the scattered field is derived based on the Kirchhoff approximation. The variance of scattering intensity is presented to study the fractal characteristics through theoretical analysis and numerical calculations. The important conclusion is obtained that the diffracted envelope slopes of scattering pattern can be approximated as a slope of linear equation. This conclusion will be applicable for solving the inverse problem of reconstructing rough surface and remote sensing.

A hybrid KA‐MoM algorithm for computation of scattering from a 3‐D PEC target above a dielectric rough surface

A new hybrid analytical‐numerical iterative algorithm, which combines the Kirchhoff approximation (KA) and the Method of Moment (MoM), is developed for computing the electromagnetic scattering from a three‐dimensional (3‐D) perfect electric conducting (PEC) target above a 2‐D infinite randomly rough dielectric surface. The equations of difference scattering due to the target presence above the rough surface are derived. The induced difference fields on the rough surface due to the interactions between the target and the rough surface are calculated by using the KA method. The excitation term on the right‐hand‐side (RHS) of target's surface integral equation (SIE), which contains the difference scattering of the rough surface, is then updated for calculating new target currents with the Conjugate Gradient (CG) procedure. Then the target currents are used to compute the difference field induced on the rough surface with the KA method. Multiple iterations take account of the multiorder interactions between the target and the underlying rough surface. Numerical quadrature upon the rough surface is performed only once to compute the coupling scattering field from the rough surface to the target, and it takes N steps (N is the discretized mesh number of rough surface). By using this hybrid KA‐MoM algorithm, the requirements of memory and CPU time can be reduced significantly. Moreover, the validity conditions and the convergence performance of this hybrid algorithm are also discussed. With Monte‐Carlo generations of randomly rough surfaces, bistatic scattering from different‐shaped targets above a Gaussian rough surface is numerically simulated. Finally, dependence of bistatic scattering pattern on the surface dielectric property and the target geometry is discussed.

INVESTIGATION ON THE SCATTERING CHARACTERISTICS OF GAUSSIAN BEAM FROM TWO DIMENSIONAL DIELECTRIC ROUGH SURFACES BASED ON THE KIRCHHOFF APPROXIMATION

The scattering characteristic of paraxial gaussian beam from two dimensional dielectric rough surfaces is studied in this paper. The modification of the Kirchhoff approximation theory for rough surface scattering by an incident gaussian beam instead of a plane wave are developed based on conventional Kirchhoff scattering theory and plane wave spectrum expansion method. The coherent and incoherent scattered intensity and cross section of two dimensional dielectric rough surfaces is derived in detail. As a application, under incidence wave length λ =1 .06 µm, we calculate the coherent and incoherent scattered intensity and cross section of Gaussian beam scattering from plating aluminium dielectric rough surfaces change with the scattering zenith angles in different rough surface correlation length, rough surface height root mean square and other conditions. In the same scattering conditions, we compare the coherent and incoherent scattered section between the gaussian beam and plane wave to prove that our methods and programming cods is correct. The numerical results are shown

Electromagnetic Scattering From Rough Surface Using Single Integral Equation and Adaptive Integral Method

An efficient algorithm for electromagnetic wave scattering from rough dielectric surfaces is developed. The algorithm is based on the single magnetic field integral equation (SMFIE) and the surface is discretized using Rao-Wilton-Glisson (RWG) triangular basis functions. The new feature of the algorithm is the application of the adaptive integral method (AIM) with SMFIE for speeding up the calculation. The developed new method utilizes the flexibility of RWG functions to model arbitrary rough surface and the speed of FFT, enabling accurate simulations over large surfaces.