Coupling of modes analysis of resonant channel add-drop filters

The operation principle of resonant channel add-drop filters based on degen erate symmetric and antisymmetric standing-wave modes has been described el sewhere using group theoretical arguments. In this paper, the analysis is c arried out using coupling of modes in time, A possible implementation of su ch a filter is a four-port system utilizing a pair of identical single-mode standing wave resonators. The analysis allows a simple derivation of the c onstraints imposed on the design parameters in order to establish degenerac y, Numerical simulations of wave propagation through such a filter are also shown, as idealized by a two-dimensional geometry.