Temporal coupled mode theory in ring-bus-ring configuration

We develop the temporal coupled mode theory for the ring-bus-ring device by taking account of the energy-conservation. The presence of the center waveguide in the tri-coupler section of the RBR facilitates the interaction between the two side-coupled rings. The correspondence between the coupled mode theory in time and transfer matrix formalism (TMF) is established. A very good agreement is obtained between the TMF and the 2D finite-difference time-domain simulations (FDTD). Some applications using RBR device such as channel dropping filter and selective power splitter are presented.