Showing papers in "Waves in Random Media in 1991"
TL;DR: In this paper, 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 is presented.
Abstract: 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.
94 citations
TL;DR: In this paper, it was shown numerically that for rough one-dimensional surfaces with small roughness, the Kirchhoff approximation is valid except at low grazing angles, and one must sum the first three orders of perturbation theory to obtain the correct result.
Abstract: Numerical simulations, using both exact and approximate methods, are used to study rough surface scattering in both the smd and large roughness regimes. This study is limited lo scattcring lrom rough one-dimensional surfaces that obey the Dirichlet boundary condition and have a Gaussian roughness spectrum. For surfdces with small roughness (kh≪1, where k is the radiation wavenumber and h is the root-mean-square (RMS) Surface height), perturbation theory is known to be valid. However, it is shown numerically that when kh≪1 and kl≳6 (where I is the surface correlation length) the Kirchhoffapprorimation is valid except at low grazing angles, and one must sum the first three orders of perturbation theory obtain the correct result. For kh≪1 and kl≅1, first-order perturbation theory is accurate. In this region, the accuracy of the first two terms of the iterative series solution of the exact integral equation is examined; the first term a1 this series is the Kirchhoff approximation, It is shown numeric...
90 citations
TL;DR: In this paper, the effects of roughness spectrum, height variation, interface medium, polarization, and incident angle on the backscattering enhancement were investigated, and a theory based on the first and second-order Kirchhoff approximation modified with angular and propagation shadowing was developed.
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 ...
51 citations
TL;DR: In this paper, the angular distribution of four wavelengths of light scattered by a one-dimensional random rough surface, whose probability density function is Gaussian with a standard deviation σ=1.22±0.02μm and whose lateral correlation function is also Gaussian, with 1/e width τ=3.17± 0.07μm.
Abstract: Measurements are presented of the angular distribution of four wavelengths of light scattered by a one-dimensional random rough surface, whose probability density function is Gaussian with a standard deviation σ=1.22±0.02 μm and whose lateral correlation function is also Gaussian with 1/e width τ=3.17±0.07 μm. The wavelengths used are 0.63, 1.15, 3.39 and 10.6 μm. The surface is used in two forms: coated with gold and as an almost lossless dielectric. The results are compared to those predicted by a double scattering form of the Kirchhoff formulation. Agreement is good at small angles of incidence but less good at larger angles of incidence.
51 citations
TL;DR: In this paper, the finite element method (FEM) of Monte Carlo simulations of random rough surface scattering is extended to penetrable rough surface scatterings, which yields a system of linear algebraic equations which is solved by a direct sparse symmetric matrix inversion.
Abstract: The finite element method (FEM) of Monte Carlo simulations of random rough surface scattering is extended to penetrable rough surface scattering. The attraction of the method is the banded nature of the resulting matrix equation. The method yields a system of linear algebraic equations which is solved by a direct sparse symmetric matrix inversion. Convergence and accuracy of the method is demonstrated and established by varying various input parameters such as the number of evanescent waves, the number of sampling points and the surface lengths. Results with incident plane wave TE polarization are presented for both the mean reflected scattered intensity and the mean transmitted scattered intensity as a function of surface parameters such as RMS surface heights and correlation lengths. The numerical results are compared against the tapered wave integral equation (TWIE) method. The results of a tapered wave solution of the integral equation averaging over many realizations are in good numerical ag...
43 citations
TL;DR: In this article, a general expression valid for propagation through a thick layer of turbulence, which includes as a particular case that of a path completely filled with turbulence, is given, and numerical results are derived.
Abstract: Wandering and correlation of wandering of two parallel laser beams after crossing atmospheric turbulence are theoretically and experimentally investigated. A general expression is given, valid for propagation through a thick layer of turbulence, which includes as a particular case that of a path completely filled with turbulence. Two different models of isotropic atmospheric turbulence are considered and numerical results are derived. The results of an experimental test through the atmosphere are also described.
43 citations
TL;DR: A summary of the theoretical and computational approaches to rough surface scattering is presented in this paper, where the Dirichlet field on the surface is modeled by the normal derivative of the field and coherent and incoherent intensities as a function of angle and surface height.
Abstract: A summary of the theoretical and computational approaches to rough surface scattering is presented. For the Dirichlet problem new computational results are presented for the behaviour of the normal derivative of the field on the surface as well as the behaviour of coherent and incoherent intensities as a function of angle and surface height. Examples are given for surface reconstruction using scattered data as a function of surface height and as the scattered data window is narrowed.
32 citations
TL;DR: In this article, the authors derived analytical expressions for the probability density and the spacetime correlation functions of the grain noise complex envelope, assuming statistical independence between any pair of grains, and showed that the parameters of the distribution may be related to the material characteristics (grain density, grain size distribution, propagation velocity).
Abstract: Many materials present an internal grain microstructure. When these materials are subjected to ultrasonic non-destructive testing, the grains behave like scattering centres producing unwanted backscattered noise that can make the detection of true defects difficult. This paper is devoted to the modelling of the probability density and the spacetime correlation functions of the grain noise complex envelope. Assuming statistical independence between any pair of grains, the authors derive analytical expressions for the above functions. Specifically, the envelope comes to be K-distributed, the parameters of the distribution may be related, under reasonable simplifying assumptions, to the material characteristics (grain density, grain size distribution, propagation velocity). The spacetime correlation function is a separable function. It may be expressed as the product of a spatial factor due to the spatial correlation introduced by the non-zero beamwidth, and a time factor due to the time correlation...
29 citations
TL;DR: In this article, a theoretical method is described for calculating the bidirectional scattering characteristic for any given thin-film multilayer geometry in which the surfaces and interfaces are assumed to be rough, and where statistical inhomogeneities in the optical permittivities may also exist in each layer.
Abstract: A theoretical method is described for calculating the bidirectional scattering characteristic for any given thin-film multilayer geometry in which the surfaces and interfaces are assumed to be rough, and where statistical inhomogeneities in the optical permittivities may also exist in each layer. The light energy scattered in any direction depends on geometrical thickness, the permittivities of the ideal layer stack and also on the corresponding auto- and cross-correlation functions. The expressions that are obtained for the scattered field are completely general in the sense of the Born approximation of first order in the imperfections and the exciting fields. The contributions of interface and volume scattering can be assumed arbitrarily because both are derived in a unique way. The main new result consists in the occurrence of four different possibilities of coupling between the scattered and exciting waves due to the standing wave character of both light waves. It is easy to show that the cas...
27 citations
TL;DR: In this article, a critical review of the various theoretical models used for handling the problem of scattering by randomly rough surfaces is given, and a description of their approach to this problem is given.
Abstract: After a critical review of the various theoretical models used for handling the problem of scattering by randomly rough surfaces, we give a description of our approach to this problem. This approac...
26 citations
TL;DR: In this paper, the authors present theoretical and experimental results bearing on the conditions under which enhanced backscattering occurs, and the way in which this phenomenon depends on the nature of the random surface roughness.
Abstract: The enhanced backscattering of light from a random surface is manifested by a well defined peak in the retro-reflection direction in the angular distribution of the intensity of the incoherent component of the light scattered from such a surface. In this paper we present several new theoretical and experimental results bearing on the conditions under which enhanced backscattering occurs, and the way in which this phenomenon depends on the nature of the random surface roughness, both in the case that the random surface bounds a semi-infinite scattering medium and in the case that it bounds a film, either free-standing or on a reflecting substrate. In addition, we present new results on the transmission of light through thin metallic films bounded by random surfaces, which display the phenomenon of enhanced transmission, namely a well defined peak in the antispecular direction in the angular distribution of the intensity of the incoherent component of the light transmitted through such films.
TL;DR: In this paper, a new approach to asymptotic analysis of related problems is introduced based on the concept of main/additional coherence channels expansion, which is applied to the analysis of the quasi-plane wave variance.
Abstract: A complete set of asymptotes for the flux fluctuation variance or finite-size source scintillation index is obtained, starting from the path integral representation for a field in a random medium. A new approach to asymptotic analysis of related problems is introduced based on the concept of main/additional coherence channels expansion. This new technique was applied to asymptotic analysis of the quasi-plane wave variance.
TL;DR: In this article, the scattering of s-polarized electromagnetic waves by a cloud of small particles above an interface is numerically studied, accounting for multiple scattering, and the backscattering effect is first observed.
Abstract: The scattering of s-polarized electromagnetic waves by a cloud of small particles above an interface is numerically studied, accounting for multiple scattering. The backscattering effect is first o...
TL;DR: In this article, an approximate analytical solution for the high-frequency propagator obtained by applying the multiscale expansion asymptotic procedure to the partial differential equation governing the propagation is presented.
Abstract: In location and remote sensing experiments there arise a number of effects related to the double passage of the backscattered field through the same random inhomogeneities as the incident one. To account for the correlation of the forward–backward propagating events, there is a need for a measure in which the random information along the propagation path is preserved. For the generation of even statistical moments, the relevant measure defined in the recently formulated stochastic geometrical theory of diflraction is the two-point random function (TPRF)—a paired field measure which is propagated along the geometrical rays of the deterministic background medium. From this function all even statistical moments can be generated. Here we present an approximate analytical solution for the high-frequency propagator obtained by applying the multiscale expansion asymptotic procedure to the partial differential equation governing the propagation a1 the TPRF. The test of the solution is performed on canoni...
TL;DR: In this article, the authors used Gaussian random numbers for the values of parameters specifying the arrangements of the line segments in a generator of Koch curves to obtain diffraction patterns of unusual appearance.
Abstract: Some properties of diffraction patterns produced by randomized triadic Koch curves are investigated. Randomization is realized by employing Gaussian random numbers for the values of parameters specifying the arrangements of the line segments in a generator of Koch curves. Laser diffraction experiments were performed using the randomized fractals as objects. It is shown that only a slight deviation from the regularity of object fractals causes a considerable degree of randomization in their diffraction patterns. For a sufficient degree of randomization, the diffraction patterns become speckle patterns of unusual appearance. Angular-average intensity distributions obtained experimentally change gradually from a function with many peaks to a relatively smooth function with an increase of randomness of the object fractals. For a sufficiently random object, the angular-average intensity takes the form of the power law as expected.
TL;DR: In this paper, the authors studied the scattering of a beam of p-polarized light from a small RMS slope one-dimensional random surface on a semi-infinite metal or n-type semiconductor to which a constant magnetic field is applied.
Abstract: By means of numerical simulations the authors study the scattering of a beam of p-polarized light from a small RMS slope one-dimensional random surface on a semi-infinite metal or n-type semiconductor to which a constant magnetic field is applied. The surface is defined by the equation x 3=ξ(x 1), where the surface profile function ξ(x 1) is a stationary stochastic Gaussian process. The plane of incidence is the x 1 x 3 plane, and the magnetic field is directed along the x 2-axis. In the presence of the magnetic field the dispersion curve for the surface polaritons supported by the surface in the absence of the random roughness becomes non-reciprocal, i.e. the wavenumber k +(ω) for a surface polariton of frequency ω propagating in the +x 1-direction is unequal to the (magnitude of the) wavenumber k −(ω) for a surface polariton of the same frequency propagating in the −x 1-direction. As a consequence of this they find that the peak in the angular distribution of the intensity of the incoherent com...
TL;DR: In this paper, a theory for the propagation of electromagnetic waves in inhomogeneous solids made of anisotropic crystallites is developed in the framework of the effective medium approach, where the macroscopic dielectric tensor can explicitly be expressed by characteristic integrals containing the radial distribution function and a single anisotropy parameter.
Abstract: A theory for the propagation of electromagnetic waves in inhomogeneous solids made of anisotropic crystallites is developed in the framework of the effective medium approach. The macroscopic dielectric tensor can explicitly be expressed by characteristic integrals containing the radial distribution function and a single anisotropy parameter. The phase mismatch of the waves scattered from misoriented crystallites leads to absorption and refraction effects that are calculated using a self-consistent approach in the sense of the distorted-wave approximation. For higher frequencies resonance structures occur which can be interpreted as an interference effect between disturbed and undisturbed waves in the effective medium.
TL;DR: In this article, a closed hierarchy of coupled moment equations for the forward and back-scattered wavefields was obtained by using the Novikov-Furutsu theorem for wave propagation in continuous random media.
Abstract: The analysis of wave propagation in continuous random media typically proceeds from the parabolic wave equation with back scatter neglected. A closed hierarchy of moment equations can be obtained by using the Novikov–Furutsu theorem. When the same procedure is applied in the spatial Fourier domain, one obtains a closed hierarchy of coupled moment equations for the forward- and back-scattered wavefields that is not restricted to narrow scattering angles nor to small local perturbations. The general equations are difficult to solve, but a Markov-like approximation is suggested by the form of the scattering terms. Simple algebraic solutions can be obtained if a narrow-angle-scatter approximation is then invoked. Thus, three distinct approximations are explicit in this analysis, namely closure, Markov and narrow-angle scatter. The results show that the extinction of the coherent wavefield has a distinctly different form from the corresponding result for propagation in a sparse distribution of discret...
TL;DR: In this article, three types of statistical fourth moments of acoustic waves forward scattered by a randomly rough ocean surface are derived and numerically evaluated: scintillation index, two-position intensity correlation and four-moment coherence.
Abstract: Three types of statistical fourth moments of acoustic waves forward scattered by a randomly rough ocean surface are derived and numerically evaluated. The first one is related to the scintillation index which characterizes intensity fluctuations. The second one is the two-position intensity correlation function which describes the spatial correlation of wave intensity. The third is the fourth-moment two-position coherence function which carries information on the phase fluctuations of the scattered wave. In the range of weak scattering, the ratio of the absolute value of the fourth-moment two-position coherence function over the two-position intensity correlation exactly describes the mean-square fluctuation of the relative phase between the two positions. The acoustic frequency is high so that the Kirchhoff approximation can be used. Two types of spectral functions for surface-height fluctuations are considered: a Gaussian spectrum and the Donelan-Pierson spectrum. The latter is obtained from a ...
TL;DR: In this paper, the concept of Fresnel zones for modes is introduced, which is analogous to the usual Fresnel zone introduced for rays, and the analysis of mode scattering at large-scale and random inhomogeneities of a medium in waveguides is simplified.
Abstract: The notion of Fresnel zones for modes is introduced, which is analogous to the usual Fresnel zones introduced for rays. It is shown that using Fresnel zones for modes one can simplify the analysis of mode scattering at large-scale and random inhomogeneities of a medium in waveguides. Simple formulae to calculate fluctuations of mode amplitudes are obtained. They are similar to well-known formulae of geometrical optics and to those of the Rytov method used to calculate fluctuations of ray complex amplitudes. Relations deduced can be used for calculating field fluctuations both at regular waveguide points and at caustics.
TL;DR: In this article, a review is presented of some new and exciting phenomena regarding the multiple scattering of optical waves in random systems and the important role played by the vector nature of the wave on memory effects, correlations and statistical fluctuations.
Abstract: A review is presented of some new and exciting phenomena regarding the multiple scattering of optical waves in random systems. In particular, the author develops the important role played by the vector nature of the wave on memory effects (the ‘polarization memory effect’), correlations and statistical fluctuations (‘microstatistics’). He also describes the recent progress on the effect of a restricted geometry on correlation phenomena and nonRayleigh statistics.
TL;DR: In this paper, a numerical study is done on light scattering from one-dimensional random rough surfaces supporting both dielectrics and metals, and the influence of the corrugation on the Brewster angle is investigated.
Abstract: A numerical study is done on light scattering from one-dimensional random rough surfaces supporting both dielectrics and metals. The influence of the corrugation on the Brewster angle as well as on...
TL;DR: Sakati et al. as mentioned in this paper studied the scattering of an electromagnetic wave from a random cylindrical surface by means of the stochastic scattering theory developed by Nakayama, Ogura.
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 eigenfunctio...
TL;DR: In this article, a new representation of the Green function of a wave equation is developed as modified path integrals, and the mean-squares value of the wavefield is calculated by the complex Monte Carlo method of a layer of chaotically distributed three-dimensional scatterers with a random scatter of permittivity.
Abstract: A new representation of the Green function of a wave equation is developed as modified path integrals. The mean-squares value of the wavefield is calculated by the complex Monte Carlo method of a layer of chaotically distributed three-dimensional scatterers with a random scatter of permittivity. Collective resonance events in wave scattering have been detected.
TL;DR: In this paper, second-order polarization correlation functions, both theoretical and experimental, are presented for optical waves propagating through a highly random multiple-scattering two-dimensional (2D) medium.
Abstract: Second-order polarization correlation functions, both theoretical and experimental, are presented for optical waves propagating through a highly random multiple-scattering two-dimensional (2D) medium. For normal incidence and scattering, a 2D medium is found to be fully described by two material parameters, one of which is complex. Simple formulae are developed for these parameters in terms of the anisotropy of the medium and the scattering mean free path. General theoretical expressions are given for polarized and unpolarized correlation functions and also for the intensity statistics of the scattered light for arbitrary input polarization states. Experimental data are presented for both types of correlation function and for the intensity statistics, and are found to be in reasonably good agreement with the theory.
TL;DR: In this article, the stationary and non-stationary problem of a plane-wave incident on a randomly inhomogeneous medium is considered and the time asymptotic of the averaged intensity on the boundary slab is also obtained for a finite-thickness slab.
Abstract: In the framework of the embedding method the authors consider the stationary and non-stationary problem of a plane-wave incident on a randomly inhomogeneous medium. For the stationary problem there are three regions of sufficiently different behaviour of the wavefield intensity moments inside a weakly dissipative medium. For the non-stationary problem they succeeded in calculating the average intensity at t→+∞ by means of analytical prolongation of the stationary problem solution with respect to the absorption parameter. The time asymptotic of the averaged intensity on the boundary slab is also obtained for a finite-thickness slab.
TL;DR: In this paper, an experimental and theoretical study of two enhancement effects that occur in the transmission of light through a thin metal film whose illuminated surface is a one-dimensional random surface while its back surface is planar is presented.
Abstract: We present an experimental and theoretical study of two enhancement effects that occur in the transmission of light through a thin metal film whose illuminated surface is a one-dimensional random surface while its back surface is planar. The first is a well defined peak in the antispecular direction in the angular distribution of the intensity of the incoherent component of the transmitted light (enhanced transmission). The second is an additionally well defined peak in the forward direction in the angular distribution of the intensity of the incoherent component of the transmitted light, when the illuminated surface is not only randomly rough but has even symmetry as well (enhanced refraction). A fully automated bidirectional reflectometer has been used to measure the intensity of the incoherent component of He-Ne laser light transmitted through gold and silver films of these two types and the results are compared with the predictions of theoretical calculations of the enhancement effects.
TL;DR: In this paper, two alternative models are investigated, and it is shown that while some features of the statistics of the scattered waves are more sensitive to the spectrum of the fluctuations in the medium than to the basic statistical model, in general significantly different properties are predicted using the alternative models.
Abstract: In calculating the properties of waves scattered by random media it is almost always assumed that variations of the media constitute a joint Gaussian process. In this paper two alternative models are investigated. It is shown that whilst some features of the statistics of the scattered waves are more sensitive to the spectrum of the fluctuations in the medium than to the basic statistical model, in general significantly different properties are predicted using the alternative models.
TL;DR: In this article, the distribution of average backscattered intensity coincides with the correlation function of the intensity fluctuation of a virtual point source located at the mirror and observed from the real source plane.
Abstract: The connection between diffraction characteristics of the scatterer and distribution of average backscattered intensity of a spherical wave is considered. In experiments with an ‘infinite’ plane mirror it is shown that the distribution of average backscattered intensity coincides with the correlation function of the intensity fluctuation of a virtual point source located at the mirror and observed from the real source plane. Non-monotonic dependence (with a minimum at the Fresnel number of scattered mirror≃1) between the enhancement factor and the size of reflected mirror is observed in experiments.