Applications of singular and critical point theory to the analysis and interpretation of transform and time-domain guided-wave electromagnetics

We summarize some previous progress in applying the theory of critical points to the analysis of guided-wave problems. In particular, we are interested in fold singular points and Morse critical points which occur in the spatial/temporal transform space. An important observation is that these points are associated with temporal transform-domain branch-point singularities, which ultimately govern observable modal interactions. Numerical results for a variety of guided-wave structures illustrate the role of critical and singular points in analysis and simulation, and their use in explaining observed modal phenomena.