Analysis of the mode coupling phenomena in multilayer waveguiding structures

Catastrophe theory is applied for the rigorous analysis of the mode coupling phenomena in lossy grounded slabs with anisotropic chirality and microstrip-like transmission lines. It is shown that an isolated nondegenerate critical point or a Morse critical point (MCP) exists in the vicinity of the mode coupling region. A Taylor series expansion in the neighborhood of the MCP reproduces dispersion curves with good accuracy. The type of MCP defines the structural stability of a system. The introduction of additional small perturbations changes the coordinates of the MCPs, but the type of nondegenerate critical points and their qualitative local structures remain the same.