Azimuthally Magnetized Circular Ferrite-Dielectric Waveguide: Impact of the Material and Geometry Parameters on the Cut-off Frequencies for the Normal $TE_{0\mathrm{n}}$ Modes

A method for computation of the cut-off frequencies (the critical radius) of the circular waveguide, containing a co-axial dielectric cylinder and a ferrite toroid of azimuthal magnetization that supports normal $\boldsymbol{TE}_{0\boldsymbol{n}}$ modes, is elaborated. It uses certain roots of the characteristic equation of transmission line, derived before in terms of complex Kummer and Tricomi confluent hypergeometric, and real ordinary or modified zeroth and first order Bessel functions. Their values are counted up, employing specially developed iterative technique. The dependence of cut-off frequencies on the dimension of dielectric filling and the magnitude of its relative permittivity is studied in detail, provided the latter is less than that of the ferrite one. The results are presented numerically in normalized form for the $\boldsymbol{TE}_{01}$ mode in case the off-diagonal element of the permeability tensor, describing the anisotropic medium, is small.