Step discontinuities in waveguides

The method developed by Wiener and Hopf for solving a certain class of integral equations is applied to the problem of a discontinuity in cross section of a rectangular waveguide. We consider the problem of two waveguides of infinite width and different heights joined together with a short step when the only nonvanishing component of the magnetic field is that parallel to the edges of the step. It is assumed that the fundamental mode is incident in the larger channel traveling towards the step. For values of the channel height such that only the fundamental mode is propagated without attenuation, this problem has been treated in the "Waveguide Handbook"; our results are in very good agreement with the results given there. The present analysis is extended to cover the case where the larger channel is capable of supporting the mode above the fundamental without attenuation. Some numerical values are given for the ratio between the reflected and incident energies for various values of the channel and step heights.