Mode transformation and mode continuation regimes on guided-wave structures

Modal interaction phenomena on guided-wave structures are investigated using the theory of critical and singular points. It is demonstrated that two distinct regimes of modal behavior exist in the vicinity of the mode coupling region, which arise due to the presence of frequency-plane branch points of the dispersion function. These branch point singularities are intimately associated with the Morse point, which is a regular point of the dispersion function. It is further noted that which of the two regimes governs modal behavior depends on the path of frequency variation, or on the presence of loss for time-harmonic problems.