Wiener-hopf Analysis of Planar Canonical Structures Loaded with Longitudinally Magnetized Plasma Biased Normally to the Extraordinary Wave Propagation

The canonical problem of an extra-ordinary Transverse Electromagnetic 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.