Mapping Between Complex Eigenmodes and Complex Propagation Constant for Uniform Rectangular Metallic Waveguides

This paper presents a rigorous mathematical map- ping between the complex eigenmodes and the complex propagation constant for a homogeneous lossy waveguide structure. We validate the results for a rectangular waveguide, comparing the analytical mapping with the results from a FEM-EM solver. It has been found that a precise mapping between Ω(β) and γ(Ω) exists, which enables predicting the driven mode solution from the eigenmode analysis. While valid for a simple canonical case of a dispersive waveguide, such mapping establishes the underlying principles of how the complex eigenmodes are formulated inside typical commercial simulators.