Solving the cut-off wave numbers in partially filled rectangular waveguides with ferrite by the Cauchy integral method

The modal analysis of the off-centered rectangular waveguide loaded with a vertical slab of ferrite material, biased in the y-direction by a DC magnetic field, leads to the resolution of a transcendent equation whose infinite solutions are the TE_m0 cutoff wave numbers in the guide. The method based on the Cauchy integral (Delvest L.M. and Lyness, J.N., 1967) is becoming very popular for solving such equations. This powerful method is described for solving the propagation constant in a partially ferrite filled waveguide. The method is used to calculate the propagation constant of the fundamental TE mode for some configurations used in the literature about ferrites. Results obtained in these simulations are very promising, so the method overcomes some of the main drawbacks of previous approaches, and it ensures the location of all zeros of the transcendent equations derived for such structures.