Wiener-Hopf Analysis of Planar Canonical Structures Loaded With Longitudinally Magnetized Plasma Biased Normally to the Extra-Ordinary Wave Propagation

Abstract

Abstract-The canonical problem of an extra-ordinary TransverseElectromagnetic wave propagating in a parallel plane waveguide with a semi-infinite upper conductor and loaded with magnetized plasma is considered. The homogeneous biasing constant magnetic field is assumed parallel to the substrate and normal to the wave propagation, which incidents normally on the truncated edge. The Wiener-Hopf technique is employed and the corresponding equations are formulated for the open-radiating structure as well as for a closed one resulting from the placement of a metallic shield parallel to the waveguide planes. Closed form field expressions are obtained for the shielded geometry, while the open geometry Kernel factorization is left for future extensions. Important non-reciprocal wave propagation phenomena are involved, which lend non-even function properties to the involved Kernels. Hence, their factorization becomes non-trivial requiring new mathematical approaches. Finally, a review of the involved non-reciprocal and/or unidirectional surface waves is given, which is related to the involved mathematical complexities.

Wiener-Hopf Analysis of Planar Canonical Structures Loaded With Longitudinally Magnetized Plasma Biased Normally to the Extraordinary Wave Propagation: Near and Far Field

“…Compared with the isotropic case and leaving aside the obviously existing geometrical and physical similarities, the anisotropic substrate problem treated herein exhibits several unique features. Our previous effort [9], directed towards the solution of a canonical problem of a TEM wave propagating in a parallel-plane waveguide with a semi-infinite upper conductor loaded with a magnetized plasma and normally incident on the edge defined by the truncated upper conductor, as depicted in Fig. 1.…”

“…1. The Wiener-Hopf equations are already formulated in [9], but the Kernel factorization for the estimation of the scattered field at the edge and consequently the reflected TEM wave propagating back in the parallel plane region was carried out only for the closed shielded geometry shown in Fig. 1(a).…”

“…Field radiation is evaluated and plotted as a function of magnetizing dc field and the waveguide thickness for validations purposes. For the sake of brevity, we have omitted several mathematical proofs that the reader can find in [8][9][10][11][12][13][14][15][16][17][18].…”

Shift-Operator FDTD Method for Anisotropic Plasma in KDB Coordinates System

“…One is ordinary wave (O-wave), and the other is extraordinary wave (X-wave) [1][2][3][4]. Both of them are linearly polarized waves.…”

“…When cold plasma is placed in bias magnetic field, the plasma becomes dielectric anisotropy, and the equivalent permittivity of it is a tensor [1][2][3][4]. Therefore, the solutions of plane electromagnetic (EM) wave in anisotropic plasma could not be obtained easily in xyz Cartesian coordinates system.…”