Advanced iterative methods for exact computation of the differential phase shift in the circular waveguide completely filled with azimuthally magnetized ferrite: Review of recent results

A recapitulation of the up-to-date methods for accurate calculation of the differential phase shift provided by the azimuthally magnetized circular ferrite waveguide, under normal TE_0n modes excitation, is presented. The debate is focused on two groups of numerical techniques, each of which incorporates three schemes, connected with definite physical working regimes of the structure. The key point in all of them is the repeated application of an iterative procedure, yielding the positive purely imaginary zeros of the complex Kummer function Φ(a, c; x) of specially selected parameters and variable, accepted as wave function for propagation, for a fluctuating imaginary part of its complex parameter a The first set of routines allows to obtain the phase shifting diagram (the aggregate of the area of phase shifter operation and of the differential phase shift characteristics) of the configuration for the normal TE₀₁ mode in the r₀-Δβ-plane, while the second one - the same in the |α|-Δβ-plane. (r₀ and Δβ are the normalized in an appropriate way guide radius and phase shift of the wave and α is the off-diagonal ferrite permeability tensor element.) The main result of the study is that for fixed r₀, Δβ is almost proportional to α in the whole area in which it might be afforded.