Anisotropic Impedance Half-plane Research Articles

Method of integral equations for systems of difference equations in diffraction theory

A system of difference equations of the first order with meromorphic coefficients (not necessary periodic ones) subject to certain conditions of symmetry is analysed. These conditions arise in model problems of diffraction theory. A method for the constructive solution of the system of difference equations is proposed. It consists of three steps. First, it requires factorization of a certain function. Then, scalar integral equations with the same kernel and different right-hand sides should be solved. The kernel of the equations has a fixed singularity, and the solution belongs to a class of functions with a power singularity. Finally, arbitrary constants are fixed from some conditions which guarantee the equivalence of the original system of difference equations and the integral equations. The method is illustrated by solving a model electromagnetic problem of a plane wave diffracted from an anisotropic impedance half-plane at oblique incidence.

Electromagnetic scattering from an anisotropic impedance half-plane at oblique incidence: the exact solution

Scattering of a plane electromagnetic wave from an anisotropic impedance half-plane at skew incidence is considered. The two matrix surface impedances involved are assumed to be complex and different. The problem is solved in closed form. The boundary-value problem reduces to a system of two first-order difference equations with periodic coefficients subject to a symmetry condition. The main idea of the method developed is to convert the system of difference equations into a scalar Riemann-Hilbert problem on a finite contour of a hyperelliptic surface of genus 3. A constructive procedure for its solution and the solution of the associated Jacobi inversion problem is proposed and described in detail. Numerical results for the edge diffraction coefficients are reported.

Skew Incidence Diffraction by an Anisotropic Impedance Half Plane With a PEC Face and Arbitrarily Oriented Anisotropy Axes

High-frequency expressions for the field scattered by a half-plane with a perfectly conducting and an anisotropic impedance face are provided in the format of the uniform geometrical theory of diffraction (UTD), when the half-plane is illuminated by an arbitrarily polarized plane wave obliquely incident on its edge. The loaded face is characterized by a tensor surface impedance with principal anisotropy axes arbitrarily oriented with respect to the edge; a vanishing surface impedance is exhibited in one of the principal directions. This kind of tensor surface impedance can be suitably applied for analyzing the effects on the scattered field of corrugated surfaces or grounded dielectric slabs periodically loaded by metallic strips. This solution extends previous high-frequency formulations valid in those cases in which the direction of corrugations or strips is either parallel or perpendicular to the edge. The analysis is performed by resorting to the Sommerfeld-Maliuzhinets method. To determine the spectral solution, a special function is needed that differs from the standard Maliuzhinets one and was originally introduced to study the electromagnetic scattering by a wedge embedded in a gyroelectric medium.

Vector functional-difference equation in electromagnetic scattering

A vector functional-difference equation of the first order with a special matrix coefficient is analysed. It is shown how it can be converted into a Riemann-Hilbert boundary-value problem on a union of two segments on a hyper-elliptic surface. The genus of the surface is defined by the number of zeros and poles of odd order of a characteristic function in a strip. An even solution of a symmetric Riemann-Hilbert problem is also constructed. This is a key step in the procedure for diffraction problems. The proposed technique is applied for solving in closed form a new model problem of electromagnetic scattering of a plane wave obliquely incident on an anisotropic impedance half-plane (all the four impedances are assumed to be arbitrary).

Time Domain Version of the Uapo Solution for the Field Diffracted by an Anisotropic Impedance Half-Plane

This work deals with the time domain version of the Uniform Asymptotic Physical Optics solution for the field diffracted by the edge of a nonpenetrable half-plane characterized by an anisotropic impedance boundary condition. A transient plane wave is assumed obliquely incident on the scatterer in the more general case of principal axes of anisotropy not coincident with the edge. The time domain solution is obtained from the knowledge of the corresponding frequency domain expression in the hypothesis that the impedance tensor components along the principal axes of anisotropy do not depend on the frequency. An inverse Laplace's transform is used to this end. The response to an incident unit step function plane wave is explicitly considered.

Diffraction By an Anisotropic Impedance Half Plane

For a plane wave incident at an oblique (skew) angle on an anisotropic impedance half plane, the second order difference equation for the angular spectra is converted to a pair of inhomogeneous non-singular integral equations and then solved. The exact expression for the scattered field is determined and compared with a previous approximate solution.

EM scattering from anisotropic impedance half-plane

A rigorous spectral solution for three-dimensional (3D) electromagnetic scattering by the edge of an anisotropic impedance half-plane with a perfect electric conducting (PEC) face is presented. The surface impedance tensor of the loaded face is characterised by: (i) principal anisotropy axes arbitrarily oriented with respect to the diffracting edge; (ii) a vanishing surface impedance along a principal anisotropy axis and an arbitrary impedance in the orthogonal direction.

EM scattering by metallic half plane loaded by anisotropic face with arbitrarily oriented anisotropy axes

Electromagnetic scattering by the edge of an anisotropic impedance half plane with a perfect electric conducting (PEC) face is analysed. Although only valid at normal incidence, the solution has some interesting features with respect to previous analyses presented for anisotropic impedance canonical configurations. Indeed, it allows the investigation of the case in which the principal anisotropy axes on the loaded face are arbitrarily oriented with respect to the diffracting edge. The specific tensor surface impedance considered exhibits a vanishing surface impedance along a principal anisotropy axis and an arbitrary one in the orthogonal direction.

Diffraction by an Anisotropic Impedance Half-Plane at Skew Incidence

ABSTRACT The problem of scattering from an anisotropic impedance half-plane at skew incidence is considered. Application of Maliuzhinets’ technique in combination with an approximation leads to a solution for the scattered field expressed in terms of Maliuzhinets functions. Even though the approximation is not based on the assumption that the obliquity of the incident wave is small, the exact solution is identically recovered in the cases of perpendicular incidence and skew incidence on an isotropic half-plane.

Diffraction by an anisotropic impedance half plane

We solve a new canonical problem: that of a plane wave obliquely incident on an anisotropic imperfectly conducting half plane. An exact closed-form solution is obtained by factorizing a 2 × 2 Wiener–Hopf matrix. The problem had earlier been considered insoluble, but yields to a combination of new and old matrix-factorization techniques.