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

A survey of the modern techniques for exact counting of the differential phase shift, afforded by the azimuthally magnetized coaxial ferrite waveguide which sustains normal TE_0n modes, is presented. The discussion ranges over two groups of methods, each of that includes three routines, linked with certain physical working conditions of the configuration. The backbone of all of them is the done again putting into practice of an iterative scheme, resulting in the positive purely imaginary roots of the structure´s characteristic equation, derived through complex Kummer and Tricomi confluent hypergeometric functions Φ(a, c; x) and Ψ(a, c; x), resp. of expressly chosen parameters and variable, for a varying imaginary part of their complex parameter a. The first set of procedures enables to figure up the phase shifting diagram (the combination of the domain of phase shifter operation and of the differential phase shift curves) of the geometry for the normal TE₀₁ mode in the r̅₀ -Δβ̅ - plane, while the second one - the same in the |α|-Δβ̅ plane. (r̅₀ and Δβ̅ are the normalized in an apposite way guide radius and phase shift of the wave and α is the off-diagonal ferrite permeability tensor element.) The basic outcome of the study is that for every allowable r̅₀, Δβ̅ depends almost linearly on |α| in the whole region in which it might be provided.