Propagation in a directional coupler of parallel microring coupled-resonator optical waveguides

The fundamental concept of coupled-resonator optical waveguides (CROWs) is for the first time taken a step farther to propose the more complicated case of coupled-resonator directional couplers, by analyzing the phenomenon of propagation in two parallel chains of microring resonators. Using the method of transfer matrices it is shown that the infinite coupler supports even and odd supermodes that satisfy frequency-shifted replicas of the familiar CROW dispersion equation as well as modified periodic Floquet conditions. Depending on the relative coupling strengths between neighboring resonators in the same chain and between the two chains, the frequency bands of the supermodes can overlap or be completely separated, resulting, in the latter case, to a complete bandgap around the central resonance frequency of the microrings. Three frequency windows, corresponding to totally different properties of directional coupling, are defined through this band-overlap mechanism along the increased total bandwidth of the coupler. These predictions are fully confirmed in the response of the realistic finite-length version of the considered coupler which is also analyzed.