Scattering Properties Of A Plane Wave By An Anisotropic Elliptic Cylinder

An analytical solution to the scattering of a plane wave by an anisotropic elliptic cylinder is derived and the electromagnetic properties of an elliptic waveguide are analyzed in this thesis, the main contributions of this thesis are as follows:1. The problem of two-dimensional scattering of a plane wave by a homogeneous anisotropic and gyrotropic elliptic cylinder is obtained. The expression of internal field in a homogeneous anisotropic elliptic cylinder is derived. The internal field in the anisotropic elliptic cylinder is expressed as an integral equation based on plane waves with different wave numbers and different directions of propagation. The waves in all directions are represented as the eigenfunction expansion in elliptic coordinates in terms of Mathieu functions. The results are in agreement with that available when a homogeneous anisotropic elliptic cylinder degenerates to the circular one and that calculated by FDTD method.2. A solution to the two-dimensional scattering by a conducting elliptic cylinder coated with a homogeneous anisotropic shell is obtained. Two cases of a conducting elliptic cylinder coated with a confocal homogeneous anisotropic shell and with a homogeneous anisotropic shell with same value of eccentricity are considered. In order to solve the nonorthogonality properties of angular Mathieu functions at the interface of different media, a matrix is required for the computation of unknown expansion coefficients of the scattered and transmitted fields and the radar cross section (RCS) per unit length. The result is in agreement with that available as expected when a coated elliptic cylinder degenerates to the coated circular one.3. The scattering of a plane wave by a conducting elliptic cylinder coated with a nonconfocal homogeneous anisotropic shell is presented. The internal field in the shell is expressed in the local coordinate system, while the incident and scattered fields are expressed in the global one. In order to connect these fields with the boundary conditions, the internal field is transferred to the global coordinates by using the addition theorem of Mathieu functions.4. The three-dimensional scattering by an infinite homogeneous anisotropic elliptic cylinder for an obliquely incident plane wave of an arbitrary polarization is investigated. The transverse components of the electromagnetic fields are represented by the axial components of them, while the axial components of fields inside an anisotropic elliptic cylinder are expressed in terms of Mathieu functions in the elliptic coordinates. The depolarized component in the scattered field appears for an obliquely incident plane wave.5. The electromagnetic properties in an elliptic conducting waveguide filled with uniaxial anisotropic media are discussed. The fields in source-free region are derived. The dyadic Green's function (DGF) for an anisotropic elliptic cylinder in terms of elliptical vector wave functions is presented. The electric-type DGF due to the electric source is analyzed using the vector wave eigenfuncions expansion.