Abstract :
A waveguide is considered of circular cross-section and radius a. The interior is divided into two regions by a concentric cylinder of radius b. Two cases are considered; in one, the region 0<r<b contains a gyromagnetic medium, and the region b<r<a contains a dielectric, while in the other it is the region b<r<a that contains the gyromagnetic medium and the region 0<r<b that contains dielectric. In each case, by putting the phase constant equal to zero in the characteristic equation a pair of equations is obtained which are called the cut-off equations; they may be related to E- and H-modes in the empty guide. The cut-off equations may be solved for any parameter if the others are all given; the solution marks a critical value of the parameter in question, such that to one side of the critical value propagation takes place while to the other it does not. In this way it is possible to separate out the normal modes and to devise a system of nomenclature. Comparisons are made between the cut-off equations and their solutions in the ferrite-centred and dielectric-centred cases in the light of the study of the ferrite-centred case previously made by the author. Numerical results are given for the dielectric-centred case for certain of the lower modes.
