Scattering of a Plane Wave by a Homogeneous Anisotropic Elliptic Cylinder

Abstract

A formal series solution to the problem of scattering of a normally incident plane wave from an infinite homogeneous anisotropic elliptic cylinder is presented. The formulation of the problem is accomplished by assuming that the permittivity and the permeability tensors of the anisotropic material referred to the elliptic cylindrical coordinate axes are mainly biaxial and diagonal, and expanding each field associated with the problem in terms of a series of suitable Mathieu functions and expansion coefficients. The incident field expansion coefficients are known, but those associated with the scattered and transmitted fields are unknown. The unknown expansion coefficients are obtained by imposing appropriate boundary conditions at the surface of the anisotropic cylinder. Numerical results are presented as normalized bistatic and backscattering widths for elliptic cylinders of different sizes and permeabilities to show the effects of the material anisotropy on scattering.

Dielectric Coated Slotted Elliptic Antenna Embedded Partly in Infinite Ground Plane

“…The even and odd angular Mathieu functions are written in terms of Fourier series as (19) (20) Substituting equations (16) to (20) into equation (14), and can finally be written in terms of the slot field as…”

“…The extension of the solution to the radiation by N slotted elliptical antenna coated with lossy dielectric material was investigated by showing the effect of lossy dielectrics material on its characteristics [7]. Solutions to materials having lossy or lossless metamaterials as well as chiral material gained considerable attention of several researchers [8][9][10], while solutions having anisotropic materials have been presented by [11][12][13][14][15][16]. It was shown that the metamaterial coating enhances the gain of the antenna while the anisotropic and chiral materials produce co and cross polarized fields.…”

Two-Dimensional Scattering by a Homogeneous Gyrotropic-Type Elliptic Cylinder

“…The above tensors are generally expressed relative to either a Cartesian coordinate system designated by = , = or a circular cylindrical coordinate system designated by = , = . Using (A3)-(A14) in [19], it can be shown that the elements of (3) in a Cartesian or a…”

“…In [17], 2-D scattering of a transverse electrically polarized normally incident plane electromagnetic wave from a weakly lossy homogeneous gyrotropic elliptic cylinder has been examined, by expressing the electromagnetic fields inside the cylinder using integrals involving Mathieu functions and Fourier series developed in [18], and then employing a first-order Taylor series expansion to calculate Mathieu functions having complex arguments. A formal series solution to the problem of scattering from an infinite homogeneous anisotropic elliptic cylinder excited by a normally incident transverse magnetically polarized plane wave was obtained recently in [19], but when the permittivity and permeability tensors of the anisotropic material referred to the elliptic coordinate axes are biaxial and diagonal. An exact series solution is reported here for the first time, to the problem of scattering of a plane wave by an infinitely long homogeneous G-type elliptic cylinder, for transverse electric (TE) polarization of the incident wave, when the plane wave is incident normal to its axis.…”

“…The solution corresponding to the case of an incident wave of arbitrary polarization can be obtained by exploiting the solutions for the TE and TM cases. When a plane wave illuminated elliptic cylinder is composed of an isotropic, a uniaxial anisotropic, or a biaxial anisotropic material as in [19], the electric field inside it can be expressed using only angular Mathieu functions, similar to that for the electric field of the incident plane wave. However, when the cylinder is made of a G-type material, to express the electric field inside it one needs both the angular Mathieu functions and their derivatives.…”