Field Coupling Method for the Direct Synthesis of 2-D Microring Resonator Networks

We present an analytical method for designing coupled microring resonator (CMR) networks of general 2-D coupling topologies. The method is based on the “field coupling in space” formalism of microring resonators, which gives a more rigorous and accurate description of CMRs than formulations based on “energy coupling in time,” especially under strong coupling conditions. Given the discrete-time transfer functions of the optical filter, this method enables the field coupling matrix of the CMR network to be extracted, so that an optimum coupling topology and the field coupling coefficients between the microring resonators can be determined.