Numerical Analysis of the Azimuthally Magnetized Ferrite-Dielectric Circular Waveguide

An original numerical approach for investigation of a circular waveguide, containing a co-axially positioned ferrite cylinder of azimuthal magnetization and a dielectric toroid and that propagates normal
$TE_{01}$
mode, is developed. It utilizes certain positive purely imaginary roots in the independent variable of the characteristic equation of the structure, derived in terms of the complex Kummer confluent hypergeometric and real zeroth and first order Bessel and Neumann functions and specific real numbers (
$\bar{L}_{3\pm}$
numbers). The latter are linked with the same roots of the equation mentioned, computed at other assumptions and have been defined and discussed by the authors in earlier studies. Tables of the roots in question and of the
$\bar{L}_{3\pm}$
numbers for selected values of parameters of the configuration are given. Using them the lower and upper cut-off frequencies which specify the boundaries of the area of phase shifter operation of the transmission line are determined. The width of this area is also calculated. The discussion is confined to the case of a thick ferrite and a thin dielectric layers. It is assumed, as well that the relative permittivities of the two layers are equal.