A heuristic model approximation for scattering from perfectly conducting one-dimensional random rough surfaces

Abstract

We propose a model for scattering from one-dimensional, perfectly conducting, slightly rough surfaces. A possible method for solving the scattering equations is examined which, with some assumptions, suggests the final result. The approximation is relatively simple and is comparable in computational effort with most first-order theories. We compare the bistatic scattering cross section for TE waves predicted by the present model for Gaussian randomly rough surfaces with numerical simulations and with some first-order theories. The comparison shows that the model is remarkably accurate for slightly rough surfaces and TE polarization.     

Multiple scattering of plasmons at rough surfaces

We investigated the polarization and angle dependence of the scattered light intensity of surface plasma oscillations (SPO) propagating along rough silver surfaces. The rough silver films were prepared using the methods of pre-evaporating CaF₂ and silver on heated substrates. The scattered light intensity of both systems is explained by surface scattering effects. Differences of the light intensities between the rough silver films prepared by the two methods mainly were observed in “restlight intensities”, which cannot be described by first-order scattering theories. We explain these differences by higher order scattering effects.     

Numerical, analytical, and experimental studies of scattering from very rough surfaces and backscattering enhancement

This paper Presents numerical simulations, theoretical analysis, and millimeter wave experiments for scattering from one-dimensional very rough surfaces. First, numerical simulations are used to investigate the effects of roughness spectrum, height variation, interface medium, polarization, and incident angle on the backscattering enhancement. The enhanced backscattering due to rough surface scattering is divided into two cases; the RMS height close to a wavelength and RMS slope close to unity, and RMS height much smaller than a wavelength with surface wave contributions. Results also show that the enhancement is sensitive to the roughness spectrum. Next, a theory based on the first- and second-order Kirchhoff approximation modified with angular and propagation shadowing is developed. The theoretical solutions provide a physical explanation of backscattering enhancement and agree well with the numerical results. In addition to the scattering of a monochromatic wave, the analytical results of the broadening and lateral spreading of a pulsed beam wave scattering from rough surfaces are also discussed. Finally, the existence of backscattering enhancement from one-dimensional very rough conducting surfaces with exact Gaussian statistics and Gaussian roughness spectrum is verified by a millimeter-wave experiment. Experimental results which show enhanced backscattering for both TE and TM polarizations for different angles of incidence are presented.     

Optical backscattering measurements from fractal surfaces and their possible relevance to radar scattering from the sea surface

In spite of recent progress, existing theories of electromagnetic wave scattering by rough surfaces cannot yet explain several important features of microwave sea echo, particularly in grazing incidence geometries. To explain them it is necessary to develop scattering models that can reproduce the features in a robust way. The aim of this paper is to report laboratory optical frequency experiments designed to aid achievement of this objective. In particular, polarization sensitive measurements of the backscattered intensity are reported for a range of characterized fractal surfaces using visible laser radiation. The appearance of enhanced backscattering peaks are observed even quite close to grazing incidence for some types of surfaces and indicate the importance of multiple scattering. It is also shown that the dependence of the backscattering cross-section on incidence angle bears some gross similarities to that obtained from microwave scattering from the sea surface for high index fractal surfaces that exhibit intermittency.     

Wave diffraction by rough interfaces in an arbitrary plane-layered medium

Abstract

The problem of electromagnetic wave scattering by a slightly rough interface in an arbitrarily layered medium is solved by a small-perturbation method. The bistatic amplitude of scattering as well as the scattering cross sections for statistically rough surfaces are calculated for linear polarized waves. Along with scattering into up-going waves in a homogeneous medium and scattering cross sections in down-going waves into a layered medium, scattering amplitudes from a rough interface in the arbitrarily layered medium are obtained.     

Numerical,analytical, and experimental studies of scattering from very rough surfaces and backscattering enhancement

Abstract

This paper Presents numerical simulations, theoretical analysis, and millimeter wave experiments for scattering from one-dimensional very rough surfaces. First, numerical simulations are used to investigate the effects of roughness spectrum, height variation, interface medium, polarization, and incident angle on the backscattering enhancement. The enhanced backscattering due to rough surface scattering is divided into two cases; the RMS height close to a wavelength and RMS slope close to unity, and RMS height much smaller than a wavelength with surface wave contributions. Results also show that the enhancement is sensitive to the roughness spectrum. Next, a theory based on the first- and second-order Kirchhoff approximation modified with angular and propagation shadowing is developed. The theoretical solutions provide a physical explanation of backscattering enhancement and agree well with the numerical results. In addition to the scattering of a monochromatic wave, the analytical results of the broadening and lateral spreading of a pulsed beam wave scattering from rough surfaces are also discussed. Finally, the existence of backscattering enhancement from one-dimensional very rough conducting surfaces with exact Gaussian statistics and Gaussian roughness spectrum is verified by a millimeter-wave experiment. Experimental results which show enhanced backscattering for both TE and TM polarizations for different angles of incidence are presented.     

Brewster's scattering angle in scattered waves from slightly rough metal surfaces

Brewster's scattering angle in electromagnetic wave scattering from slightly random metal surfaces is investigated by means of the stochastic functional approach. While there are dips due to Brewster's scattering angle in scattering profiles from dielectric surfaces, Brewster's scattering angle does not exist in scattering from metal surfaces. However, the dips can exist in scattering from rough metal surfaces with the optically denser medium to convert evanescent wave into radiative wave.     

蒙特卡洛法研究随机粗糙表面的光散射特性

本文采用蒙特卡洛(M-C)数值模拟,生成起伏高度满足高斯分布的随机粗糙表面。借助Kirchhoff近似,并在综合考虑辐射传输、光学及电磁学有关理论的基础上,利用M-C方法计算了符合高斯分布的一维随机粗糙表面的单次和多次光散射分布,模型结合射线追踪法考虑了粗糙表面的遮蔽效应。结果表明在考虑多次散射时,存在后向散射增强现象,该结论与实验结果相吻合,证明本文数值模拟方法的正确性。     

Low-grazing angles scattering of electromagnetic waves from one-dimensional natural surfaces: Rigorous and approximate theories

We present a rigorous model, based on a specific boundary integral formalism for the wave scattering from rough, one-dimensional, dielectric or conducting surfaces at low-grazing incidence and scattering angles. Even though this so-called Grazing Method of Moment is, from a numerical cost point of view, independent of the incidence, it remains very numerically demanding. We thus propose an extrapolation technique for faster monostatic diagram computation, based on the theoretical behavior of the scattering amplitude at low-grazing angles. This technique is compared to the GMoM and to some approximate models, for surfaces with Gaussian spectrum as well as for sea surface.     

Bistatic scattering and depolarization by randomly rough surfaces: application to the natural rough surfaces in X-band

Abstract

The scattering of waves by random rough surfaces has important applications in the remote sensing of oceans and land. The problem of developing a model for rough surfaces is very difficult since, at best, the scattering coefficient σ⁰ is dependent upon (at least) the radar frequency, geometrical and physical parameters, incident and observation angles, and polarization. The problem of electromagnetic scattering from a randomly rough surface is analysed using the Kirchhoff approximation (stationary phase, scalar approximation), the small-perturbation model and the two-scale models. A first major new consideration in this paper is the polarimetric signature calculations as a function of the transmitter location and receiver location for a bistatic radio-link. We calculate the like- and cross-polarized received power directly using the scattering coefficients, without calculating the Mueller matrix. Next, a study of the regions of validity of the Kirchhoff and small-perturbation rough surface scattering models (in the bistatic case) is presented. Comparisons between the numerical calculations and the models are made for various surface rms heights and correlation lengths both normalized to the incident wavenumber (denoted by σ and L, respectively). By using these two parameters to form a two-dimensional space, the approximate regions of validity are then established. The second major new consideration is the development of a theoretical two-scale model describing bistatic reflectivity as well as the numerical results computed for the bistatic radar cross section from rough surfaces especially from the sea and snow-covered surfaces. The results are used to show the Brewster angle effect on near-grazing angle scattering.     

Bistatic scattering and depolarization by randomly rough surfaces: application to the natural rough surfaces in X-band

The scattering of waves by random rough surfaces has important applications in the remote sensing of oceans and land. The problem of developing a model for rough surfaces is very difficult since, at best, the scattering coefficient σ⁰ is dependent upon (at least) the radar frequency, geometrical and physical parameters, incident and observation angles, and polarization. The problem of electromagnetic scattering from a randomly rough surface is analysed using the Kirchhoff approximation (stationary phase, scalar approximation), the small-perturbation model and the two-scale models. A first major new consideration in this paper is the polarimetric signature calculations as a function of the transmitter location and receiver location for a bistatic radio-link. We calculate the like- and cross-polarized received power directly using the scattering coefficients, without calculating the Mueller matrix. Next, a study of the regions of validity of the Kirchhoff and small-perturbation rough surface scattering models (in the bistatic case) is presented. Comparisons between the numerical calculations and the models are made for various surface rms heights and correlation lengths both normalized to the incident wavenumber (denoted by σ and L, respectively). By using these two parameters to form a two-dimensional space, the approximate regions of validity are then established. The second major new consideration is the development of a theoretical two-scale model describing bistatic reflectivity as well as the numerical results computed for the bistatic radar cross section from rough surfaces especially from the sea and snow-covered surfaces. The results are used to show the Brewster angle effect on near-grazing angle scattering.     

Theoretical and computational aspects of scattering from rough surfaces: one-dimensional perfectly reflecting surfaces

We discuss the scattering of acoustic or electromagnetic waves from one-dimensional rough surfaces. We restrict the discussion in this report to perfectly reflecting Dirichlet surfaces (TE polarization). The theoretical development is for both infinite and periodic surfaces, the latter equations being derived from the former. We include both derivations for completeness of notation. Several theoretical developments are presented. They are characterized by integral equation solutions for the surface current or normal derivative of the total field. All the equations are discretized to a matrix system and further characterized by the sampling of the rows and columns of the matrix which is accomplished in either coordinate space (C) or spectral space (S). The standard equations are referred to here as CC equations of either the first (CC1) or second kind (CC2). Mixed representation, or SC-type, equations are solved as well as SS equations fully in spectral space.

Computational results are presented for scattering from various periodic surfaces. The results include examples with grazing incidence, a very rough surface and a highly oscillatory surface. The examples vary over a parameter set which includes the geometrical optics regime, physical optics or resonance regime, and a renormalization regime.

The objective of this study was to determine the best computational method for these problems. Briefly, the SC method was the fastest, but it did not converge for large slopes or very rough surfaces for reasons we explain. The SS method was slower and had the same convergence difficulties as SC. The CC methods were extremely slow but always converged. The simplest approach is to try the SC method first. Convergence, when the method works, is very fast. If convergence does not occur with SC, then SS should be used, and failing that CC.     

Polarization characteristics of an electromagnetic wave scattered from a slightly random surface: +45° polarized incidence

Abstract

The present paper deals with the scattering of an obliquely polarized electromagnetic (EM) wave from a slightly rough surface, which is assumed to be a two-dimensional (2D), homogeneous and isotropic Gaussian random field. In contrast to the cases of TE(s) and TM(p) polarized incidence, the scattering profile for an obliquely polarized incidence is not symmetric with respect to the incident plane, despite the fact that the random surface is statistically isotropic.     

A critical survey of approximate scattering wave theories from random rough surfaces

This review is intended to provide a critical and up-to-date survey of the analytical approximate methods that are encountered in scattering from random rough surfaces. The underlying principles of the different methods are evidenced and the functional form of the corresponding scattering amplitude or cross-section is given. The reader is referred to the original papers in order to obtain the explicit expressions of the coefficients and kernels. We have tried to identify the main strengths and weaknesses of the various theories. We provide synthetic tables of their respective performances, according to a dozen important requirements a valuable method should meet. Both scalar acoustic and vector electromagnetic theories are equally addressed.     

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.     

Theoretical and computational aspects of scattering from rough surfaces: one-dimensional perfectly reflecting surfaces

Abstract

We discuss the scattering of acoustic or electromagnetic waves from one-dimensional rough surfaces. We restrict the discussion in this report to perfectly reflecting Dirichlet surfaces (TE polarization). The theoretical development is for both infinite and periodic surfaces, the latter equations being derived from the former. We include both derivations for completeness of notation. Several theoretical developments are presented. They are characterized by integral equation solutions for the surface current or normal derivative of the total field. All the equations are discretized to a matrix system and further characterized by the sampling of the rows and columns of the matrix which is accomplished in either coordinate space (C) or spectral space (S). The standard equations are referred to here as CC equations of either the first (CC1) or second kind (CC2). Mixed representation, or SC-type, equations are solved as well as SS equations fully in spectral space.

Computational results are presented for scattering from various periodic surfaces. The results include examples with grazing incidence, a very rough surface and a highly oscillatory surface. The examples vary over a parameter set which includes the geometrical optics regime, physical optics or resonance regime, and a renormalization regime.

The objective of this study was to determine the best computational method for these problems. Briefly, the SC method was the fastest, but it did not converge for large slopes or very rough surfaces for reasons we explain. The SS method was slower and had the same convergence difficulties as SC. The CC methods were extremely slow but always converged. The simplest approach is to try the SC method first. Convergence, when the method works, is very fast. If convergence does not occur with SC, then SS should be used, and failing that CC.     

The Rayleigh hypothesis in scattering off photonic crystal interfaces

We examine the Rayleigh hypothesis in the context of scattering of light off photonic crystal interfaces. First, the hypothesis - which was initially suggested for scattering of waves off rough surfaces between homogeneous media - is rephrased to apply to photonic crystal interfaces. Next, an exact and explicit functional form is presented that maps plane photonic crystal surfaces to periodic rough surfaces in free space, so that known criteria for the validity of the Rayleigh hypothesis for scattering at rough surfaces can be applied directly to scattering at the photonic crystal surfaces. The same map also allows the scattering problem to be solved exactly.     

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.