title: Modeling quasi-dark states with temporal coupled-mode theory.
abstract: Coupled resonators are commonly used to achieve tailored spectral responses and allow novel functionalities in a broad range of applications. The Temporal Coupled-Mode Theory (TCMT) provides a simple and general tool that is widely used to model these devices. Relying on TCMT to model coupled resonators might however be misleading in some circumstances due to the lumped-element nature of the model. In this article, we report an important limitation of TCMT related to the prediction of dark states. Studying a coupled system composed of three microring resonators, we demonstrate that TCMT predicts the existence of a dark state that is in disagreement with experimental observations and with the more general results obtained with the Transfer Matrix Method (TMM) and the Finite-Difference Time-Domain (FDTD) simulations. We identify the limitation in the TCMT model to be related to the mechanism of excitation/decay of the supermodes and we propose a correction that effectively reconciles the model with expected results. Our discussion based on coupled microring resonators can be useful for other electromagnetic resonant systems due to the generality and far-reach of the TCMT formalism.
authors.forename: Mario C M M
authors.initials: MC
authors.lastname: Souza
authors.forename: Guilherme F M
authors.initials: GF
authors.lastname: Rezende
authors.forename: Luis A M
authors.initials: LA
authors.lastname: Barea
authors.forename: Gustavo S
authors.initials: GS
authors.lastname: Wiederhecker
authors.forename: Newton C
authors.initials: NC
authors.lastname: Frateschi