Extending temporal-coupled-mode theory to the antiresonant regime

The antiresonant effects, which are opposite to the resonant effects, describe the destructive interferences that occur in optical resonators. There is a growing trend in the recent development of photonic devices that explore antiresonant effects such as topology structures and photonic molecules with asymmetrical geometries. For the design of coupled optical resonators, temporal-coupled-mode theory (TCMT) has been widely applied, which provides a simple yet effective physical picture of such systems. However, TCMT is valid for optical frequencies that resonate well with the cavities. It becomes powerless to handle mode coupling at optical frequencies that resonate in part of the resonators but antiresonate in the rest. In this work, we extend TCMT to antiresonant regimes for investigating mode coupling between antiresonances and resonances in coupled-optical-cavity systems via taking the analogy of the mode splitting. Our theory agrees well with the transfer matrix method as well as the experimental results. A concrete example is given to show that our work offers an opportunity to extend the application of TCMT in the design of advanced coupled-cavity structures.