Frequency plane branch-point singularities in the analysis of modal interactions on guided-wave structures

Complex frequency-plane branch-point singularities are investigated in connection with mode interaction phenomena on guided-wave structures. It is found that certain types of branch points are directly associated with the leaky-wave cutoff behavior and modal interaction regimes on planar dielectric slab waveguides (including nonreciprocal waveguides) and printed-circuit transmission lines. The evolution of branch points in the complex frequency plane controls the modal behavior in the regions of interest. An important conclusion is that, in general, the discrete mode spectrum of guided-wave structures is not unique.