Strongly Coupled Dielectric RIB Waveguides, use of the "Transition Function" and of Edge Discontinuities

The problem of two or more closely coupled rib waveguides, where energy is leaked from one guide to the other via the substrate and radiation mode, is of great practical and theoretical importance. Rigorous results including substrate and air modes coupling are hard to find for the general case of coupling of two or more different guides, due to the considerable complexity arising. In this contribution, we develop a method of analysis of the transverse step problems which utilize our recently developed concept of ´transition function´ and make explicit use of the edge singularity at the dielectric corners to produce a highly effective rigorous solution of the problem. We then consider multiple coupled rib guides as a cascade of interacting step discontinuities in a transverse direction. Numerical results for single rib guide, directional coupler, three guide coupler and closely spaced unequal guide in the LSE/LSM polarization are presented, and where comparison is possible, are seen to be at least as accurate as any available in the literature by much more expensive methods.