Properties of inhomogeneous cylindrical waveguides in the neighbourhood of cut-off

For suitable values of the properties of a dielectric or ferrite rod, concentrically placed in a waveguide of circular cross-section, the phase constant of the H11mode, expressed as a function of frequency, is twovalued over a range of frequencies in the neighbourhood of cut-off. In the two-valued region, one branch of the phase-constant curve has positive slope and the other negative slope, corresponding respectively to forward and backward waves. The field components and power distribution of these waves are discussed, and a method is suggested of separating the two kinds of wave by a mode filter. It is shown that at two values of the frequency where the group velocity is zero there is a high concentration of energy in the guide; this would be infinite in the lossless case, but where losses are present due to imaginary parts of the dielectric constant of the rod, and of the permeability elements in the case of a ferrite rod, they become large when the group velocity is zero, and so prevent the energy concentration from rising beyond a certain level. Over part of the waveguide cross-section the power is negative, and when the group velocity is negative the negative power exceeds the positive power. When the energy in the guide is large compared with the rate of transfer of energy, the system behaves somewhat like a cavity, and a ¿Q¿ can be defined.