Scattering and diffraction of a plane wave by a randomly rough half-plane

The scattering and diffraction of a TE (transverse electric) plane wave by a randomly rough half-plane are studied by a combination of three techniques: the Wiener-Hopf technique, the small perturbation method and a probabilistic method based on the shift-invariance of a homogeneous random function. By use of the D^a-Fourier transformation based on the shift-invariance, it is shown that the scattered wave is written by an inverse Fourier transformation of a homogeneous random function with a complex parameter. For a small rough case, such a random function with a complex parameter is expanded in a perturbation series and then the first-order solution is obtained exactly in an integral form. The first-order solution involves two physical processes such that the edge-diffracted wave is scattered by the randomly rough plane and the scattered wave, due to roughness, is diffracted by the half-plane. The solution is transformed into a sum of the Fresnel integrals with complex arguments, an integral along the steepest descent path and a branch-cut integral, which are evaluated numerically. Then, intensities of the coherently scattered wave and incoherent wave are calculated in the region near the edge and illustrated in figures.     

Scattering and diffraction of a plane wave from a randomly rough strip*

Abstract

This paper deals with plane wave scattering and diffraction from a randomly rough strip using a combination of three tools: the perturbation method, the Wiener-Hopf technique and a group-theoretic consideration based on the shift-invariant property of the homogeneous random surface. The D ^a -Fourier transformation associated with the shift invariance is defined instead of the conventional complex Fourier transformation. For a slightly rough case, Wiener-Hopf equations for the zero-, first- and second-order perturbed fields are derived. They are reduced to a common Wiener-Hopf equation, an exact solution of which is obtained formally by means of the Wiener-Hopf technique. Using the inverse D ^a -Fourier transformation, the scattered wavefield is obtained as a stochastic field. When the strip width is large compared with the wavelength, a uniformly asymptotic representation of the scattered far field is obtained by the saddle point method. For a Gaussian roughness spectrum, several numerical results are calculated and illustrated in figures, based on which the characteristics of scattering and diffraction are discussed.     

Scattering and diffraction of a plane wave from a randomly rough strip

This paper deals with plane wave scattering and diffraction from a randomly rough strip using a combination of three tools: the perturbation method, the Wiener-Hopf technique and a group-theoretic consideration based on the shift-invariant property of the homogeneous random surface. The D^a-Fourier transformation associated with the shift invariance is defined instead of the conventional complex Fourier transformation. For a slightly rough case, Wiener-Hopf equations for the zero-, first- and second-order perturbed fields are derived. They are reduced to a common Wiener-Hopf equation, an exact solution of which is obtained formally by means of the Wiener-Hopf technique. Using the inverse D^a-Fourier transformation, the scattered wavefield is obtained as a stochastic field. When the strip width is large compared with the wavelength, a uniformly asymptotic representation of the scattered far field is obtained by the saddle point method. For a Gaussian roughness spectrum, several numerical results are calculated and illustrated in figures, based on which the characteristics of scattering and diffraction are discussed.     

TM plane wave scattering and diffraction from a randomly rough half-plane: (part II) An evaluation of the diffraction kernel

In a previous paper (part I), it has been shown that a random wavefield from a randomly rough half-plane for a TM plane wave incidence is written in terms of a Wiener-Hermite expansion with three types of Fourier integrals. This paper studies a concrete representation of the random wavefield by an approximate evaluation of such Fourier integrals, and statistical properties of scattering and diffraction. For a Gaussian roughness spectrum, intensities of the coherent wavefield and the first-order incoherent wavefield are calculated and shown in figures. It is then found that the coherent scattering intensity decreases in the illumination side, but is almost invariant in the shadow side. The incoherent scattering intensity spreads widely in the illumination side, and have ripples at near the grazing angle. Moreover, a major peak at near the antispecular direction, and associated ripples appear in the shadow side. The incoherent scattering intensity increases rapidly at near the random half-plane. These new phenomena for the incoherent scattering are caused by couplings between TM guided waves supported by a slightly random surface and edge diffracted waves excited by a plane wave incidence or by free guided waves on a flat plane without any roughness.     

Scattering of a scalar wave from a two-dimensional randomly rough Neumann surface

We present a reciprocity and unitarity preserving formulation of the scattering of a scalar plane wave from a two-dimensional, randomly rough surface on which the Neumann boundary condition is satisfied. The theory is formulated on the basis of the Rayleigh hypothesis in terms of a single-particle Green's function G(q_‖|k_‖) for the surface electromagnetic waves that exist at the surface due to its roughness, where k_‖ and q_‖ are the projections on the mean scattering plane of the wave vectors of the incident and scattered waves, respectively. The specular scattering is expressed in terms of the average of this Green's function over the ensemble of realizations of the surface profile function (G(q_‖|k_‖)). The Dyson equation satisfied by (G(q_‖|k_‖)) is presented, and the properties of the solution are discussed, with particular attention to the proper self-energy in terms of which the averaged Green's function is expressed. The diffuse scattering is expressed in terms of the ensemble average of a two-particle Green's function, which is the product of two single-particle Green's functions. The Bethe-Salpeter equation satisfied by the averaged two-particle Green's function is presented, and properties of its solution are discussed. In the small roughness limit, and with the irreducible vertex function approximated by the sum of the contribution from the maximally-crossed diagrams, which represent the coherent interference between all time-reversed scattering sequences, the solution of the Bethe-Salpeter equation predicts the presence of enhanced backscattering in the angular dependence of the intensity of the waves scattered diffusely.     

Scattering of a scalar wave from a two-dimensional randomly rough Neumann surface

Abstract

We present a reciprocity and unitarity preserving formulation of the scattering of a scalar plane wave from a two-dimensional, randomly rough surface on which the Neumann boundary condition is satisfied. The theory is formulated on the basis of the Rayleigh hypothesis in terms of a single-particle Green's function G(q_‖|k_‖) for the surface electromagnetic waves that exist at the surface due to its roughness, where k_‖ and q_‖ are the projections on the mean scattering plane of the wave vectors of the incident and scattered waves, respectively. The specular scattering is expressed in terms of the average of this Green's function over the ensemble of realizations of the surface profile function (G(q_‖|k_‖)). The Dyson equation satisfied by (G(q_‖|k_‖)) is presented, and the properties of the solution are discussed, with particular attention to the proper self-energy in terms of which the averaged Green's function is expressed. The diffuse scattering is expressed in terms of the ensemble average of a two-particle Green's function, which is the product of two single-particle Green's functions. The Bethe-Salpeter equation satisfied by the averaged two-particle Green's function is presented, and properties of its solution are discussed. In the small roughness limit, and with the irreducible vertex function approximated by the sum of the contribution from the maximally-crossed diagrams, which represent the coherent interference between all time-reversed scattering sequences, the solution of the Bethe-Salpeter equation predicts the presence of enhanced backscattering in the angular dependence of the intensity of the waves scattered diffusely.     

Scattering of a narrow wave beam by a randomly rough locally diffuse surface subject to pulse illumination

We consider the scattering of a narrow pulse wave beam by a randomly rough surface with a complex local scattering indicatrix. Analytical expressions are found for the mean received power for a normal distribution of heights and slopes of the surface in two cases: where the direction to the receiver is close to the direction of mirror reflection and where the direction to the receiver is very different from the direction of mirror reflection. It is shown that in these two cases the echo pulse is very different in shape and is controlled by the parameters of the source and receiver, the sounding scheme, and the variance of heights of a rough surface. The received power is strongly dependent on the width of the local scattering indicatrix, and the form of this dependence is determined by the angles of illumination and reception. The analytical expressions for the mean received power are in good agreement with the results of numerical calculations. Institute for Radioelectronics and Laser Engineering of the N. é. Bauman State Technical University of Moscow, Russia. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol.42, No.4, pp. 333–339, April 1999.     

Cylindrical wave diffraction at a half-plane in an anisotropic plasma

The problem of cylindrical wave diffraction at a half-plane located in a cold anisotropic plasma is considered. The exact solution is shown to be expressible in terms of Fresnel integrals.The author thanks M. S. Bobrovnikov for suggesting the problem and his interest.     

Scatter of a plane elastic wave by a rough crack edge

The aim of this paper is to investigate the effect of roughness of the crack edge on the reliability of ultrasonic NDE (nondestructive evaluation). The rough crack face has been modeled by earlier authors as a mosaic of large triangular facets and the effect of this roughness has been simulated using the Kirchhoff approximation. We now augment this model by the rough crack edge that is a polygonal line. We then model the scattered field using the Isakovich approach, originally developed for modeling scatter from rough surfaces, also with the help of the Kirchhoff approximation.     

Scattering of a plane inhomogeneous electromagnetic wave by a spherical particle

We extend an analytical solution for the problem of diffraction of a plane wave by a spherical particle to the case of an inhomogeneous wave. Numerical examples showing a significant change in the scattered-wave structure compared with the case of diffraction of a homogeneous wave are presented. __________ Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 49, No. 1, pp. 72–81, January 2006.     

Electromagnetic wave diffraction by a rough interface of homogeneous isotropic media

Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 32, No. 4, pp. 451–460, April, 1989.     

Scattering of a plane wave by one-dimensional dielectric random rough surfaces—study with the curvilinear coordinate method

We present a method giving the bi-static scattering coefficient of a one-dimensional dielectric random rough surface illuminated by a plane wave. The theory is based on Maxwell's equations written in a nonorthogonal coordinate system. For each medium, this method leads to an eigenvalue system. The scattered field is expanded as a linear combination of eigensolutions satisfying the outgoing wave condition. The boundary conditions allow the diffraction amplitudes to be determined. The Monte Carlo technique is applied and the bi-static scattering coefficient is estimated by averaging the scattering amplitudes over several realizations. The results of a Gaussian random process with a Gaussian roughness spectrum are compared to published experimental and numerical data. Comparisons are conclusive.     

Solution of the three-dimensional problem of plane wave diffraction by a two-period plane grating

Using the discrete source method, we develop an algorithm for solving the three-dimensional problem of wave scattering by a plane grating consisting of acoustically soft or acoustically stiff bodies. An efficient algorithm is proposed for determining the periodic Green’s function of the grating. Numerical results are obtained for different geometries of the grating elements. The fulfillment of the energy conservation law is verified along with the fulfillment of the boundary condition at the surface of the central grating element.     

Scattering of a plane electromagnetic wave by bodies of conical shape

Radiophysics and Quantum Electronics -