Backscattering of s-polarized light from a cloud of small particles above a dielectric substrate

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 observed without the interface and the influence of the index of the particles is shown. In the case of a dilute system of particles with a low index such that no backscattering peak appears without the interface, it is shown that the introduction of an interface restores the backscattering effect. A physical mechanism responsible for this peak is described. In conclusion, a comparison of this model with scattering by rough surfaces is made.     

Scattering of an electromagnetic wave from a slightly random dielectric surface: Yoneda peak and Brewster angle in incoherent scattering

Abstract

The scattering of an electromagnetic wave from a two-dimensional, slightly rough dielectric surface is studied based on the stochastic functional approach. It is shown that in the case of TM(p)-polarized incidence there exists a zero in the incoherent scattering at the angle we call the ‘Brewster scattering angle’, which depends on the incident angle in contrast to the Brewster angle of coherent reflection which is independent of the incident angle, that a ‘quasi-anomalous scattering’ can generally occur in the optically denser medium at the critical angle of total reflection in both TE(s)- and TM(p)-polarized incidence, regardless of which side of the random surface is illuminated, and that the Yoneda peak in the x-ray scattering can be interpreted as a special case of the quasi-anomalous scattering which becomes sharper when the relative refractive index becomes closer to unity as in the x-ray region. Cross-polarized scattering and enhanced backscattering due to the second-order effect are also calculated.     

The scattering matrix of transparent particles of random shape in the geometrical optics approximation

A numerical model that allows one to calculate elements of the scattering matrix for transparent particles of random shape in the geometrical optics approximation is presented. It is shown that a deviation from sphericity, which, in particular, is modeled by a reduction of the number of triangular facets approximating a sphere, essentially affects the magnitude, position, and width of peaks of the photometric and polarimetric indicatrices. Thus, when 1500 facets were used for the approximation, the amplitude of the polarimetric peak associated with the first rainbow, which is located close to the scattering angle 160°, decreases by a factor of two. Calculations showed that, in the region of backscattering, for particles of an arbitrary shape, the linear polarization ?F ₁₂/F ₁₁ has no negative branch, which is well observed for spherical particles. In going from spherical to nonspherical particles, the backscattering peak also disappears. The indicatrices for particles of irregular shape that were calculated for small distances from the center of a particle noticeably differ from the indicatrices at infinity. Thus, when simulating multiple scattering in dense powderlike media, the use of particle scattering indicatrices that were calculated for infinite distances is incorrect even in the geometrical optics approximation.     

Interference effects in backscattering of light by a layer of a discrete random medium

Multiple backscattering of light by a layer of a discrete random medium is considered. A brief derivation of equations for describing the coherent and incoherent components of scattered light is presented. These equations are solved numerically in the approximation of doubled scattering of light by a semi-infinite medium of spherical scatterers having a size comparable with the wavelength in order to study the effect of the properties of particles on the angular dependence of interference effects. Calculations show that the half-width of the interference peak decreases upon an increase in lateral scattering by particles and that the degree of polarization has a complex angular dependence on the properties of the particles. For an optically thin layer of the medium, the relations defining the interference peak half-width and the scattering angle upon extreme linear polarization as functions of the effective refractive index are given.     

Incoherent and coherent backscattering of light by a layer of densely packed random medium

The problem of light scattering by a layer of densely packed discrete random medium is considered. The theory of light scattering by systems of nonspherical particles is applied to derive equations corresponding to incoherent (diffuse) and interference parts of radiation reflected from the medium. A solution of the system of linear equations describing light scattering by a system of particles is represented by iteration. It is shown that the symmetry properties of the T-matrices and of the translation coefficients for the vector Helmholtz harmonics lead to the reciprocity relation for an arbitrary iteration. This relation is applied to consider the backscattering enhancement phenomenon. Equations expressing the incoherent and interference parts of reflected light from statistically homogeneous and isotropic plane-parallel layer of medium are given. In the exact backscattering direction the relation between incoherent and interference parts is identical to that of sparse media.     

Electromagnetic wave scattering from a random medium layer with a random interface

Abstract

The problem of electromagnetic wave scattering from a random medium layer with a random interface is considered. The layer has planar boundaries on average. Assuming that both the random perturbations of the interface and the random fluctuations of permittivity of the medium are small, a first-order perturbation solution to the scattered field is obtained. Using this solution, the bistatic scattering coefficients γ_αβ are calculated and expressed in a compact and meaningful form. The various terms that constitute γ_αβ are identified with distinct scattering processes. Since it is often of particular interest, the special case of backscattering is considered. Finally, the results are compared with those of others.     

Application of a coherent model in simulating the backscattering coefficient of a mangrove forest

Abstract

In this paper, a single scattering model is presented for a coherent forest scattering simulation. It is tested on the backscattering coefficient of mangrove forests, which are known to involve large coherent effects. Analysis of branches, leaves and ground contributions is done to understand the backscattering coefficient composition. Finally the sensitivity of the code is investigated.     

Influence of the boundary of a medium on the coherent backscattering of light

The multiple scattering of light from an inhomogeneous medium occupying a half-space is investigated on the basis of the Bethe-Salpeter equation. The latter is integrated over the spatial variables to obtain an identity having the significance of the energy balance of the incident and scattered radiations. This relation is then used to derive a length parameter that plays the role of the Milne interpolation length. The use of this parameter in the method of mirror images for describing the shape of the coherent backscattering peak in isotropic single scattering yields results in almost perfect agreement with the predictions of the Milne theory. The application of the given approach for an anisotropic single-scattering diagram yields quantitative agreement of the theory with experiments on the angular dependence of coherent backscattering. The new approach is generalized to an electromagnetic (vector) field, and backscattering polarization effects are investigated. Zh. éksp. Teor. Fiz. 116, 1912–1928 (December 1999)     

Theoretical study of the Kirchhoff integral from a two-dimensional randomly rough surface with shadowing effect: application to the backscattering coefficient for a perfectly-conducting surface

Abstract

In this paper, the backscattering coefficient of a two-dimensional randomly rough perfectly-conducting surface is investigated using the Kirchhoff approach with a shadowing function. The rough surface height/slope correlations assumed to be Gaussian are accounted for in this analysis. The scattering coefficient is then formulated in terms of a characteristic function for the integrations over the surface heights, in terms of expected values for the integrations over the surface slopes. Numerical comparisons of Kirchhoff's approach (KA) with the stationary-phase (SP) approximation are made with respect to the choice of the one-dimensional surface height autocorrelation function and the shadowing effect. For an isotropic surface the results show that SP underestimated the incoherent backscattering coefficient compared with KA. Moreover, when the correlation between the slopes and the heights is neglected, the shadowing effect may be ignored.     

Universal behaviour of scattering amplitudes for scattering from a plane in an average rough surface for small grazing angles

Abstract

It is shown that for scattering from a plane in an average rough surface, the scattering cross section of the range of small grazing angles of the scattered wave demonstrates a universal behaviour. If the angle of incidence is fixed (in general it should not be small), the diffusive component of the scattering cross section for the Dirichlet problem is proportional to θ² where θ is the (small) angle of elevation, and for the Neumann problem it does not depend on θ. For the backscattering case these dependences correspondingly become θ⁴ and θ°. The result is obtained from the structure of the equations that determine the scattering problem rather than by use of an approximation.     

Effects of nondiffusive wave propagation upon coherent backscattering by turbid media

The nondiffusive contribution to the coherent backscattering intensity is calculated for the media with relatively large particles (size a is greater than wavelength λ). The results are in good agreement with the experimental data at the wings of the angular spectrum of the coherent backscattering. The shape of the backscattering peak is analyzed for strongly absorbing media. The correlation function of the intensity fluctuations is calculated for the scattering by Brownian particles at relatively large time shifts.     

Weak localization effects in the second-harmonic light scattered by random systems of particles

We report rigorous numerical simulations that show the presence of coherent backscattering effects in the second-harmonic generation and scattering of light by random systems of two-dimensional particles. Since the medium composing the particles is assumed to be homogeneous and isotropic, the second-harmonic field is generated mainly by surface effects. For the fundamental frequency, the results present a clear enhanced backscattering peak. In contrast, the second-harmonic scattering patterns present an intensity dip in the backscattering direction.     

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.     

Influence of the nonlocal nature of fluctuations on coherent effects in multiple scattering

We solve the Bethe-Salpeter equation that describes radiation transfer in highly inhomogeneous media with an anisotropic scattering with allowance for the contributions of Legendre polynomials of the zeroth, first, and second degrees. An analytical expression for the radiation-transfer propagator is derived. We show that as the average value of the second-degree Lagrange polynomial increases, the region where the diffusion approximation is valid shifts toward large distances. Within this approach we calculate the coherent backscattering intensity and study the effect of higher-order moments on the angular dependence of this intensity. Finally, we show that it is possible to experimentally detect the coherent backscattering peak in the critical region. Zh. éksp. Teor. Fiz. 113, 2022–2033 (June 1998)     

Multiple reflections in backscattering by a single scatterer near a perfectly reflecting surface

The scattering of a plane electromagnetic wave by a solitary scatterer randomly positioned near a perfectly reflecting surface is investigated in the dipole approximation taking into account infinite multiplicity of scattering. It is shown that the presence of multiply reflected waves increases the “effective” polarizability of the particle and adds another component of the dipole moment along the normal to the surface. As a result, the backscattering enhancement effect becomes stronger, and the angle of incidence at which amplification of the p-polarized wave vanishes becomes smaller. The influence of multiply scattered waves increases as the particle approaches the boundary in this case. Zh. Tekh. Fiz. 67, 72–75 (September 1997)     

Scattering from a layer of discrete random medium over a random interface: application to microwave backscattering from forests

Abstract

The distorted Born approximation is used to calculate the bistatic scattering coefficients from a layer of sparsely distributed discrete dielectric scatterers over a random interface. After specializing to the backscatter case, the scattering coefficient is determined as a sum of direct, direct reflected and interface scatter contributions. The direct reflected term contains contributions from the average interface and the interface fluctuations. These direct reflected terms include both incoherent and coherent or enhancement terms. The results are applied to backscattering from a mature hemlock forest over a roughened ground. The model results show that the direct reflected surface fluctuation terms give the dominant contribution to backscatter at P band and are equal in magnitude to the volume scatter at L band. Use of these new results brings the model predictions and experimental results into agreement.     

Enhanced backscattering and blazing effect from gratings,quasi-gratings and randomly rough surfaces

Abstract

The blazing effect is probably the most important property of diffraction gratings used for spectroscopic purposes. On the other hand, the enhanced backscattering phenomenon has been generally studied in the framework of scattering from randomly rough surfaces. Using numerical results from rigorous theories, it will be shown that these phenomena, which have very different origins, should have more precise definitions. In a special case of a randomly rough surface formed by random corners, it will be shown that the effects of these phenomena are sometimes very difficult to distinguish.     

Multiscattering effects in the far-field region for two small particles on a flat conducting substrate

Abstract

The scattered field in the far-field region for two small metallic particles on a conducting substrate is analysed as a function of both their separation and the angle of incidence. Special attention is paid to multiple scattering, which appears when the particles are very close, as well as to its related effects such as its influence on the enhanced backscattering phenomenon and depolarization of the incident beam in the plane of incidence.     

Enhanced backscattering and transmission of light from random surfaces on semi-infinite substrates and thin films

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.     

Studies of scattering theory using numerical methods

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 numerically that lor very small kh these first two terms reduce to first-order perturbation theory. However, lor this reduction to occur, kh must be made smaller than necessdry lor first-order perturbation theory to be accurate. In the regime of large roughness (kh?1) backscattering enhancement occurs when the RMS slope is on the order of unity. Several investigators have recently shown that the second term of the iterative series solution (the double-scattering term) replicates the properties of backscattering enhancement reasonably well. However, the double-scattering term has a lundamental flaw: predictions lor the scattering cross section per unit length based on the double-scattering term increase as the surfdce length is increased. This is shown here with numerical simulations and with an approximate analytical result based on the high frequency limit. The physical significance of this finding is also discussed. The final topic is the use of the double-scattering approximation to study the mechanism for backscattering enhancement with the Dirichlet boundary condition. This mechanism is usually assumed to be interference between reciprocal scattering paths. When the interlerence between reciprocal scattering paths is removed, the enhancement is eliminated. This shows that interference between reciprocal paths is almost certainly the dominant mechanism for backscattering enhancement in the scattering regime studied.