Plane wave scattering by dielectric elliptic cylinder coated with nonconfocal dielectric

Abstract

The scattering cross section of a dielectric elliptic cylinder coated with nonconfocal dielectric is investigated. An exact dual series solution based on the boundary value method and employing the addition theorem of Mathieu functions is derived. Both transverse magnetic and transverse electric cases are considered. The infinite series' of the solution are truncated after a finite number of terms to generate numerical data. A convergence check is built into the computer program, and the geometrical dimensions considered are within the low‐frequency range. It is shown that this solution is much more general than all other solutions given before because it can handle a variety of scattering geometries.

Scattering by an Infinite Circular Dielectric Cylinder Coating Eccentrically an Elliptic Dielectric Cylinder

“…The main advantage is that these expressions are valid for each small , Manuscript "free" of Mathieu functions, while all purely numerical techniques involve complicated calculations of these functions for each different . This advantage distinguishes the present work from the corresponding ones in [5]- [7], with more general geometries.…”

“…In (4) ( ) are the even (odd) radial Mathieu functions of the second kind, while there is (5) shown at the bottom of the page, and is given by (5) In order to satisfy the remaining boundary conditions at the circular boundary , we first use in (4) the expansion formulas connecting elliptical cylindrical wave functions with the coaxial circular ones ([2, eq. (16)]) and next the translational addition theorem for the latter ([2, eq.…”

Slot Antenna on a Conducting Elliptic Cylinder Coated by Nonconfocal Chiral Media

“…The unknown expansion coefficients, The boundary conditions at ξ = ξ 2 can be applied after the transformation of the field components inside the coating (region 2) in terms of the global coordinates system. This can be done using the addition theorem of Mathieu functions [23], so that components E 2 η c , E 2 z c , H 2 η c , and H 2 z c in the local coordinates system change to similar components (E 2 η , E 2 z , H 2 η , and H 2 z , respectively) in the global coordinates system, as…”

Closed-form solution to the scattering by an infinite lossless or lossy elliptic cylinder coating a circular metallic core

“…The scattering by a perfectly conducting elliptic metallic cylinder having a coaxial coating is examined in [1,2] when the shell is a lossless dielectric, and in [3] when the shell has losses. The scattering by an elliptical dielectric cylinder coating a nonconfocal elliptical cylinder is examined in [4] when the inner cylinder is metallic, in [5] when the inner cylinder is dielectric under normal incidence, and in [6] when the inner cylinder is dielectric under oblique illumination. The solution in [1][2][3][4][5][6] is retrieved numerically, by truncation of the system matrices composed by using Mathieu function expansions, after the satisfaction of the boundary conditions.…”

“…The scattering by an elliptical dielectric cylinder coating a nonconfocal elliptical cylinder is examined in [4] when the inner cylinder is metallic, in [5] when the inner cylinder is dielectric under normal incidence, and in [6] when the inner cylinder is dielectric under oblique illumination. The solution in [1][2][3][4][5][6] is retrieved numerically, by truncation of the system matrices composed by using Mathieu function expansions, after the satisfaction of the boundary conditions. Oblique scattering by multilayer lossy elliptical cylinders is presented in [7], where the authors apply a recursive procedure on Mathieu function expansions for the transmitted waves.…”