Coupled-Mode Theory derivation of the formal equivalence between a three-mode waveguide and a set of three mutually coupled single-mode waveguides

Abstract

The formal identification between a two-mode waveguide and a system of two mutually coupled single-mode waveguides stems from the symmetries of the evolution operator. When the gap tends to zero, the super-modes of the coupled system merge continuously into the modes of the multimode waveguide. For modelling purposes, it is very tempting to extend the analogy to three-mode waveguides (and beyond). But not without some precautions…