Analysis of mode coupling on printed transmission lines using Morse critical points

A new insight on mode coupling in waveguiding structures is proposed using the concept of Morse critical points from catastrophe theory. It is shown that the traditional coupled-mode formalism has clear analytical connection with functional properties of the characteristic determinant in the vicinity of the Morse critical point, which determines the minimum of coupling. Numerical results for various printed transmission line circuits demonstrate the efficiency of the proposed approach for the rapid identification of mode coupling regions, and for reconstruction of dispersion behavior in those regions via simple analytic (normal) forms.