Exact 2‐D scattering from a slot in a ground plane backed by a semielliptical cavity and covered with a multilayer isorefractive diaphragm

Abstract

[1] A semielliptical channel flush-mounted under a metal plane and slotted along the interfocal distance of its cross section is separated from the half-space above by a multilayer diaphragm. The cavity, the diaphragm, and the half-space are all isorefractive to each other. Both the cavity and the multilayer diaphragm are filled with materials isorefractive to the medium in the half-space above. This is a two-dimensional geometry where the source is invariant with respect to the axial variable. The resulting electromagnetic boundary-value problem is solved exactly in terms of Mathieu functions, when the excitation source is either a plane wave or a line source. For plane wave incidence, the polarization is with either the electric or the magnetic field parallel to the axis of the structure and the direction of incidence is arbitrary in a plane perpendicular to the axis. For line source excitation, the polarization is with either the electric or the magnetic field parallel to the axis of the structure and the source is arbitrarily located. Numerical results are also provided.Citation: Canta, S. M., and D. Erricolo (2008), Exact 2-D scattering from a slot in a ground plane backed by a semielliptical cavity and covered with a multilayer isorefractive diaphragm, Radio Sci., 43, RS6006,

Isorefractivity: Teaching and research perspectives

“…The isorefractive condition led to many new exact analytical solutions for canonical geometries in many coordinate systems, including: the circular cylinder [5], the elliptic cylinder [6], [7], the oblate spheroidal [8], the prolate spheroidal [9], and the paraboloidal [10]. These new solutions provide additional benchmarks for the validation of computational electromagnetic software.…”

Exact Solution of Electromagnetic Scattering From a Dipole Antenna Located Inside a Multilayer Metamaterial Oblate Spheroidal Cavity

“…A brief literature survey finds that, in addition to the known exact solutions published in [2], the introduction of the isorefractive condition by Uslenghi [3,4] allowed for the development of many new exact solutions. In particular, new geometries involving isorefractive materials are available for scattering from infinite bodies, such as shapes involving the 2D wedge [5][6][7], the elliptical cylinder [8][9][10][11][12][13][14][15][16][17][18], the paraboloid [19][20][21], and finite bodies, such as shapes involving spheroidal geometries [22][23][24][25].…”

New method to obtain small parameter power series expansions of Mathieu radial and angular functions

“…Therefore, this article provides expressions for both radial and angular functions using the Stratton-Morse-Chu normalization. The choice of the Stratton-Morse-Chu normalization is dictated by a vast collection of analytical results that already exist, such as [5], [30], [7], [12], [13], [31], [14], [38], [39], [6].…”