Ali Alkumru

Relativistic Scattering of a Plane-Wave by a Uniformly Moving Half-Plane

We discuss the effect of motion on the scattering by an edge. To this end, one considers the simplest canonical structure formed by a uniformly moving perfectly conducting half-plane illuminated by a time-harmonic plane wave and investigates the effect of the motion on the reflection and shadow zones, aberration, Doppler shift, edge-diffracted wave, etc. The cases where the velocity is parallel and normal to the half-plane are considered separately. Some of the interesting results which were obtained, in addition to the classical Doppler shift and aberration phenomena, are that (i) the edge-excited wave is never time-harmonic while the waves excited by the plane (both in the shadow and in the reflection zones) are always time-harmonic, (ii) the shadow and reflection boundaries are not parallel to the incident and reflected rays, (iii) at certain values of the velocity and incidence angle, a shadow region appears in the apparent illuminated region while a lit region appears in the apparent shadow region, (iv) the moving half-plane provides, sometimes, energy to the reflected wave. The cases of upsiLtc and upsi~c are examined in detail

Multiple diffraction of plane waves by a soft/hard strip

A uniform asymptotic high-frequency solution is developed for the problem of diffraction of plane waves by a strip which is soft at one side and hard on the other. The related three-part boundary value problem is formulated into a “modified matrix Wiener-Hopf equation”. By using the known factorization of the kernel matrix through the Daniele-Khrapkov method, the modified matrix Wiener-Hopf equation is first reduced to a pair of coupled Fredholm integral equations of the second kind and then solved by iterations. An interesting feature of the present solution is that the classical Wiener-Hopf arguments yield unknown constants which can be determined by means of the edge conditions.

A generalized ART algorithm for inverse scattering problems related to buried cylindrical bodies

An inverse scattering problem whose aim is to recover the electromagnetic properties of buried cylindrical bodies is addressed. The problem is first reduced to a system of operator equations and then its solution is obtained through an iterative method which is a generalization of the algebraic reconstruction technique in diffraction tomography to the present problem. The use of such an iterative method enables us to find a unique solution with a small number of measurements. Some illustrative examples show the accuracy and the applicability of the method.

Plane Wave Diffraction By Three Parallel Thick Impedance Half-Planes

The diffraction of plane electromagnetic waves by three parallel thick impedance half-planes is investigated rigorously by using the Fourier transform technique in conjunction with the mode matching method. This mixed method of formulation gives rise to two scalar modified Wiener-Hopf equations of the second kind for odd and even excitations respectively. The solution of each Wiener-Hopf equation contains a set of infinitely many constants satisfying an infinite system of linear algebraic equations. A numerical solution of this system is obtained for various values of the plate impedances, plate thickness and the distance between the plates, wherefrom the effect of these parameters on the diffraction phenomenon is studied.

INFLUENCE OF THE VELOCITY ON THE ENERGY PATTERNS OF MOVING SCATTERERS

Parallel to the developments in the communication through space vehicles achieved during the last two decades, the scattering problems connected with moving objects became more and more important from both theoretical and practical points of view. Same problems are also arisen in point of space science, radio astronomy, radar techniques and particle physics. The earlier investigations available in the open literature concern the analysis of the scattered field pattern and, hence, treat the polarization, frequency shift (Doppler effect), aberration, etc, which are all important from both pure scientific and technological points of view. But, another issue which is also important in regard to the communication, antennas and particle physics is the influence of the motion on the scattered energy patterns which involves the radar cross-section and scattering coefficient. This paper is devoted to this purpose and aims to study the influence of the velocity on the received and scattered energies. Notice that the scattered wave is not time-harmonic even though the incident wave is so because the Lorentz transformation formulas interrelate the space coordinates and time, which makes impossible to extend the notion of radar cross-section to moving bodies. For the sake of simplicity of the mathematical manipulations, only two-dimensional case is taken into account but the method can be adapted by straightforward extensions to other types of scatterer.

One-dimensional profile inversion of a half-space bounded by a three-part impedance ground

A method which permits one to reveal the one-dimensional electromagnetic profile of a half-space over a three-part impedance ground is established. The method reduces the problem to the solution of two functional equations. By using a special representation of functions from the space , one of these equations is first reduced to a modified Riemann - Hilbert problem and then solved asymptotically. The asymptotic solution is valid when the central part of the boundary is sufficiently large as compared to the wavelength of the wave used for measurements. The second functional equation is reduced under the Born approximation to a Fredholm equation of the first kind whose kernel involves the solution to the first equation. Since this latter constitutes an ill-posed problem, its regularized solution in the sense of Tikhonov is given. The accuracy of the asymptotic solution to the first equation requires the use of waves of high frequencies while the Born approximation in the second equation is accurate for lower frequencies. A criterion to fix appropriate frequencies meeting these contradictory requirements is also given. An illustrative application shows the applicability and the accuracy of the theory. The results may have applications in profiling the atmosphere over non-homogeneous terrains.

Multiple diffraction of plane waves by an acoustically penetrable strip located between two soft/hard half-planes

Abstract A uniform asymptotic high-frequency solution is developed for the diffraction of plane waves ? by an acoustically transmissive strip located between two half-planes which are soft at the top and ?hard at the bottom. After simulating the partially transmissive strip by a set of approximate boundary ?conditions used recently by Rawlins et al. , the three-part boundary value problem is formulated into ?a “modified matrix Wiener-Hopf equation”. By performing the factorization of the kernel matrix ?through the Daniele-Khrapkov method, the modified matrix Wiener-Hopf equation is first reduced ?to a pair of coupled Fredholm integral equations of the second kind and then solved by iterations. An ?interesting feature of the present solution is that the classical Wiener-Hopf arguments yield unknown ?constants that can be determined by means of the edge conditions.

High Frequency Diffraction of Cylindrical Waves by Perfectly Conducting Successive Step Discontinuities

The diffraction of high frequency cylindrical electromagnetic waves by step discontinuities is investigated rigorously by using the Fourier transform technique in conjunction with the mode matching method. The hybrid method of formulation gives rise to a scalar Wiener-Hopf equation of the third kind, the solution of which contains infinitely many constants satisfying infinite systems of linear algebraic equations

Wiener-Hopf Analysis of the Dominant Mode Propagation in a Dual-Ridged Parallel Plate Waveguide with Impedance Loading

The dominant mode propagation in a parallel-plate waveguide with impedance-loaded interacting step discontinuities is analyzed rigorously through the Wiener-Hopf technique. Introducing the Fourier transform of the scattered field and applying the boundary conditions in the transform domain, the problem is reduced to a modified Wiener-Hopf equation of the third kind and solved approximately. Some numerical results displaying the effects of the surface impedance of the steps as well as their thicknesses and lengths on the reflection and radiation phenomenon are presented.

Multiple diffraction of a line source field by a three-part thin transmissive slab

A uniform asymptotic high-frequency solution is presented for the problem of diffraction of a line source field by a three-part thin transmissive slab. After simulating the slab by a material plane with a set of approximate boundary conditions used recently by RAWLINS et al., the three-part boundary-value problem is transformed into a modified matriz Wiener-Hopf equation. By performing the factorization of the kernel matrix through the DANIELE-KHRAPKOV method, the modified matriz Wiener-Hopf equation is first reduced to a pair of coupled Fredholm integral equations of the second kind and then solved approximately by iterations. An interesting feature of the present solution is that the classical Wiener-Hopf arguments yield unknown constants which may be determined by means of the edge conditions.