Numerical study of the differential phase shift in a circular ferrite-dielectric waveguide

An iterative method is elaborated and applied to reckon in normalized form the differential phase shift, afforded by the circular waveguide, containing an azimuthally magnetized ferrite toroid in contact with the wall of the latter whose hollow is filled with a dielectric cylinder of relative permittivity, equal to that of the ferrite. The case of normal TE₀₁ mode transmission is considered. The idea of the approach is to solve the structure´s characteristic equation, derived in terms of certain complex confluent hypergeometric and real Bessel functions numerically over and over again for varying purely imaginary part of the first complex parameter of the confluent functions and afterwards to figure out the normalized in a suitable way against the frequency guide radius and phase constant of the wave at fixed values of the dielectric cylinder to waveguide radius ratio and of the off-diagonal ferrite permeability tensor element. The imaginary part is changed arbitrarily, until an interval for it is found, such that the relevant one of computed numerical equivalents of the radius to contain a preliminary chosen value of the same. Then, it is divided in half and the calculations go on, till the length of the interval for the radius mentioned becomes less than the prescribed accuracy. The pertinent numerical equivalent of the phase constant is accepted as the one, sought. The difference between the constants, counted for both signs of the imaginary part (of the ferrite magnetization), gives the phase shift in question. The results are presented in a tabular form and are discussed.