Relation Between Normal-Mode and Coupled-Mode Analyses of Parallel Waveguides

The analysis of parallel waveguides can be performed either by expressing the coupling of energy between individual, primary guides (coupled-mode approach) or by directly analyzing a structure consisting of all the guides and their surrounding media (normal-mode approach). A comparison of these two approaches, as well as the derivation of relations enabling the conversion of data, when possible, from one approach to the other, are presented in this paper. Finally, the results are used to investigate the dependence of the coupling coefficient on the spacing between the guides. Although the derivations are performed for 2-D (slab) configurations, the results pertain to 3-D guides as well, by applying an effective refractive-index method. It is also shown that normal-mode analysis predicts incomplete transfer of energy for strongly coupled guides, even for perfectly symmetric configurations.