The Degeneracy of the Dominant Mode in Rectangular Waveguide

We explore the exceptional point of degeneracy (EPD) at the cutoff of the dominant mode in a uniform rectangular waveguide. We show that the system matrix describing the wave propagation is similar to a Jordan matrix, and we look at the field at the degeneracy point that exhibits algebraic growth along the waveguide as a result of the Jordan matrix description. Field expressions for the dominant mode are derived at the EPD. A numerical example is used to show the degeneracy and its associated field behavior.