Gaussian beam scattering from arbitrarily shaped objects with rough surfaces

Abstract

The scattered field of Gaussian beam scattering from arbitrarily shaped dielectric objects with rough surfaces is investigated for optical and infrared frequencies by using the plane wave spectrum method and the Kirchhoff approximation, and the formulae for the coherent and incoherent scattering cross sections are obtained theoretically based on geometrical optics and tangent plane approximations. The infrared laser scattering cross sections of a rough sphere are calculated at 1.06 μm, and the influence of the beam size is analysed numerically. It is shown that when the beam size is much larger than the size of the object, the results in this paper will be close to those of an incident plane wave.     

Small-slope approximation for electromagnetic wave scattering at a rough interface of two dielectric half-spaces

Abstract

The small-slope approximation (SSA) for wave scattering at the rough interface of two homogeneous half-spaces is developed. This method bridges the gap between two classical approaches to the problem: the method of small perturbations and the Kirchhoff (or quasi-classical) approximation. In contrast to these theories, the SSA is applicable irrespective of the wavelength of radiation, provided that the slopes of roughness are small compared with the angles of incidence and scattering.

The resulting expressions for the SSA are given for the entries of an S-matrix that represents the scattering amplitudes of plane waves of different polarizations interacting with the rough boundary. These formulae are quite general and are valid, in fact, for waves of different origins. Apart from the shape of the boundary, some functions in these formulae are coefficients of the expansion of the S-matrix into a power series in terms of elevations. These roughness independent functions are determined by a specific scattering problem. In this paper they are calculated for the case of electromagnetic scattering at the interface of two dielectric half-spaces. In contrast to an earlier paper by the author, where only the formulae for the reflected field were presented, in this paper both reflected and transmitted fields are considered in detail.

The a priori symmetry relations that this scattering problem should obey (reciprocity and energy conservation) are formulated in terms of the S-matrix.

The statistical moments of scattering amplitudes are directly related to the mean-reflection coefficient and scattering cross sections, which are usually determined experimentally. The corresponding formulae are given here for the case of Gaussian space-homogeneous statistics of roughness.     

Bistatic scattering by arbitrarily shaped objects with rough surface at optical and infrared frequencies

The scattering cross sections for arbitrarily shaped dielectric objects with rough surface are determined for optical and infrared frequencies using the Kirchhoff approximation. The formula of the coherent scattering cross section is derived, and numerical method of incoherent scattering cross section is given. As a specific example, the infrared laser scattering cross sections of rough spheres are calculated at 1.06 m.     

Calculations of Infrared Laser Beam Scattering from Rough Dielectric Objects

The coherent and incoherent scattering cross sections of Infrared Laser Gaussian beam scattering from arbitrarily shaped convex dielectric objects with rough surfaces are investigated by using plane wave spectrum method and physical optics approximation. In the paper, the infrared laser scattering cross sections of rough sphere are calculated at 10.6 m , and the influence of the beam size, permittivity, and polarization as well as roughness parameters is analyzed numerically. When the beam size is much larger than the size of object, the results in the paper can reduce to those of an incident plane wave. On the other hand, for the case of roughness statistical parameter close to zero, only the forward scattering has a parent difference compared with the result of gaussian beam scattering from smooth sphere.     

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.     

Theory of light scattering from rough surfaces and interfaces and from volume inhomogeneities in an optical layer stack

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 case of a columnar structure reduces the theoretical effort and leads to a similarity of this volume case to that of normal interface scattering. The matrix formalism used in analogy to the normal calculations of reflection and transmission coefficients allows a simple physical interpretation of the light propagation through the layer system and straightforward numerical calculations.     

Gaussian beam scattering from arbitrarily shaped objects with rough surfaces

The scattered field of Gaussian beam scattering from arbitrarily shaped dielectric objects with rough surfaces is investigated for optical and infrared frequencies by using the plane wave spectrum method and the Kirchhoff approximation, and the formulae for the coherent and incoherent scattering cross sections are obtained theoretically based on geometrical optics and tangent plane approximations. The infrared laser scattering cross sections of a rough sphere are calculated at 1.06 μm, and the influence of the beam size is analysed numerically. It is shown that when the beam size is much larger than the size of the object, the results in this paper will be close to those of an incident plane wave.     

X-ray scattering from a randomly rough surface

Abstract

On the basis of the method of reduced Rayleigh equations we present a simple and reciprocal theory of the coherent and incoherent scattering of x-rays from one- and two-dimensional randomly rough surfaces, that appears to be free from the limitations of earlier theories of such scattering based on the Born and distorted-wave Born approximations. In our approach, the reduced Rayleigh equation for the scattering amplitude(s) is solved perturbatively, with the small parameter of the theory η(ω) = 1 - ε(ω), where ε(ω) is the dielectric function of the scattering medium. The magnitude of η(ω) for x-rays is in the range from 10^?6 to 10^?3, depending on the wavelength of the x-rays. The contributions to the mean differential reflection coefficient from the coherent and incoherent components of the scattered x-rays are calculated through terms of second order in η(ω). The resulting expressions are valid to all orders in the surface profile function. The results for the incoherent scattering display a Yoneda peak when the scattering angle equals the critical angle for total internal reflection from the vacuum-scattering medium interface for a fixed angle of incidence, and when the angle of incidence equals the critical angle for total internal reflection for a fixed scattering angle. The approach used here may also be useful in theoretical studies of the scattering of electromagnetic waves from randomly rough dielectric-dielectric interfaces, when the difference between the dielectric constants on the two sides of the interface is small.     

The scattering of electromagnetic waves in fractal media

Abstract

The scattering of electromagnetic waves in fractal media is studied. The fractal dimension is naturally involved in the formulation of two physical problems studied in this paper. The general theory of multiple scattering of electromagnetic wave in fractal media is developed by modifying Twersky's theory. Statistical quantities, such as the average field and average intensity of the multiple scattered wave, are studied for a wave propagating in a fractal medium. The scattering cross section of the medium is deduced. The backscattering of electromagnetic waves is also studied. The results showing the range of dependence of the backscattered signals are in agreement with numerical simulations by Rastogi and Scheucher (1990). It also suggests a method of measuring the fractal dimension of the fractal embedded media using radar sounding. The theory developed in this paper can also be used for problems related to multiple scattering of other kinds of waves, such as acoustic waves, elastic waves etc, in fractal media.     

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

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 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.     

Elastic scattering of an electron by the negative lithium ion

In the framework of the many-body theory, the differential and total cross sections of elastic scattering of slow electrons by the negative lithium ion Li⁻ are obtained. Calculations are performed both in the Hartree-Fock single-particle approximation and with regard to many-electron correlations, which take into account the dynamic polarization of the core. Features observed in the behavior of the phases and cross sections for p and d partial waves are associated with resonance scattering of electron waves. Considering the dynamic polarization of the core by an incident electron heightens the diffraction character of the scattering. The real process is compared with particle scattering in models with a repulsive potential.     

Radar scatter cross sections for two-dimensional random rough surfaces – full wave solutions and comparisons with experiments

Abstract

In this paper, the full wave expressions for the radar scattering cross sections for two-dimensional random rough surfaces are obtained. The rough-surface height/slope correlations are accounted for in this analysis. Analytical and numerical comparisons of the full wave solution with the small perturbation and physical optics solutions are made for isotropic, homogeneous random rough surfaces with Gaussian probability density function. The full wave results are also compared with experimental results.     

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.     

Microwave sea return at moderate to high incidence angles

Abstract

Bragg scattering is widely recognized as the dominant mechanism by which the ocean surface backscatters microwave radiation, but efforts to identify other, non-Bragg sources of this scattering have been pursued for many years. Non-Bragg backscattering from the sea surface is known to occur at incidence angles close to 0° and 90°. In this paper Bragg scattering is shown to explain most features of sea surface backscatter for incidence angles between about 20° and 80°, except when it predicts very small mean cross sections. The often-quoted evidence for non-Bragg scattering in this incidence angle range is that σ _o (HH) is occasionally found to be larger than or equal to σ _o (VV) for short integration times. We show that because of fading this is not evidence of non-Bragg scattering. For incidence angles up to about 50°, standard Bragg/composite surface scattering theory yields probabilities of finding σ _o (HH)>σ _o (VV) that are only slightly smaller than those found experimentally. As the incidence angle increases, greater differences between theoretical and experimental probabilities are found. The addition of Bragg scattering from bound, tilted waves brings theory into excellent agreement with experiment at incidence angles near 45° but still cannot account adequately for the probability of σ _o (HH)>σ _o (VV) or observed σ _o (HH) cross sections at higher incidence angles. We show that the addition of a small, non-Bragg cross section that is independent of the incidence angle and polarization, brings simulated cross sections and probability distributions into good agreement with data. A possible source of this small, non-Bragg sea return is sea spray just above the air/sea interface.     

Investigation on electromagnetic scattering from rough soil surface of layered medium using the small perturbation method

Electromagnetic scattering from a rough surface of layered medium is investigated, and the formulae of the scattering coefficients for different polarizations are derived using the small perturbation method. A rough surface with exponential correlation function is presented for describing a rough soil surface of layered medium, the formula of its scattering coefficient is derived by considering the spectrum of the rough surface with exponential correlation function; the curves of the bistatic scattering coefficient of HH polarization with variation of the scattering angle are obtained by numerical calculation. The influence of the permittivity of layered medium, the mean layer thickness of intermediate medium, the roughness surface parameters and the frequency of the incident wave on the blstatic scattering coefficient is discussed. Numerical results show that the influence of the permittivity of layered medium, the mean layer thickness of intermediate medium, the rms and the correlation length of the rough surface, and the frequency of the incident wave on the bistatic scattering coefficient is very complex.     

The effect of a local field on Raman scattering in a uniaxial crystal

This paper discusses the Raman scattering of light in an anisotropic crystal in the crystal optics approximation, taking into account local fields acting on the molecules. It shows that the effect of the local field reduces to the introduction of the effective Raman polarizability tensor of the molecules, which depends both on the properties of the molecules themselves and on the characteristics of the crystal at the frequencies of the incident and scattered waves. Raman scattering cross sections are obtained in a uniaxial crystal for various types of incident waves. It is shown that, in the case of an extraordinary incident wave, the local field substantially affects how the cross section depends on the direction of incidence. Zh. éksp. Teor. Fiz. 112, 180–191 (July 1997)     

Helium ionization with excitation of the atom accompanied by absorption and scattering of high-energy photons

We calculate analytically the cross sections for ionization of the helium atom with absorption and scattering of high-energy photons. The electrons are assumed to be moving in the Coulomb field of the nucleus. The electron-electron interaction is taken into account in the first order of perturbation theory. The high-frequency limits for the ratios of these cross sections to the single-electron ionization cross sections are obtained for s-excitations in absorption and for s-and p-excitations in scattering. Zh. éksp. Teor. Fiz. 111, 862–870 (March 1997)     

Transmission scatter cross sections across two-dimensional random rough surfaces – full wave solutions and comparison with numerical results

Abstract

In this paper, the full wave expressions for the bistatic transmission scattering cross sections across two-dimensional random rough surfaces are obtained. The full wave analysis accounts for the surface height/slope correlations. Analytical and numerical comparisons of the full wave solutions with the small perturbation and physical optics solutions are made for isotropic random rough surfaces. The full wave results are also compared with the numerical results based on Monte Carlo simulations of one-dimensional random rough surfaces. Detailed consideration is given to illustrating the relationship between these full wave solutions and the original full wave solutions including the impact of accounting for the height/slope correlations in this analysis.     

Effect of turning of rays on scattering of light in a layered medium

The problem of the scattering of light by random inhomogeneities in a layered medium whose characteristic scale is large compared to the wavelength of light is considered. The attention is mainly focused on the effect that the turning of incident and scattered waves has on light scattering in such a medium. In the mixed (q _⊥, z) Fourier representation, expressions for normal waves, and Green’s function are found, which can be used both far from the turning point, where the fields are described in the WKB approximation, and near this point, where the fields are described using the Airy function. Based on these expressions and using the Kirchhoff method, a general expression for the scattering intensity in the far field of the sample is obtained, which takes into account the turning of the incident and scattered waves in the fluctuating medium. Physical consequences of the calculation results are analyzed. In particular, it is shown that even a comparatively small gradient of the refractive index in the layer leads to a rather appreciable redistribution of the scattering intensity between the forward and backward hemispheres. In this case, the shape of the scattering indicatrix is rather exotic with sharp discontinuities, peaks, and dips whose amplitude is on the order of the intensity itself. Original Russian Text ? A.Yu. Val’kov, A.A. Zhukov, V.P. Romanov, 2008, published in Optika i Spektroskopiya, 2008, Vol. 105, No. 4, pp. 647–666.     

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.