Quantitative modeling of coupling-induced resonance frequency shift in microring resonators.

We present a detailed study on the behavior of coupling-induced resonance frequency shift (CIFS) in dielectric microring resonators. CIFS is related to the phase responses of the coupling region of the resonator coupling structure, which are examined for various geometries through rigorous numerical simulations. Based on the simulation results, a model for the phase responses of the coupling structure is presented and verified to agree with the simulation results well, in which the first-order coupled mode theory (CMT) is extended to second order, and the important contributions from the inevitable bent part of practical resonators are included. This model helps increase the understanding of the CIFS behavior and makes the calculation of CIFS for practical applications without full numerical simulations possible.