Effects of propagation phase on the coupling of plasmonic optical modes

The temporal coupled-mode theory (TCMT) has made significant progress in recent years, and is widely applied in explaining a variety of optical phenomena. In this paper, the optical characteristics of the metasurface composed of nano-bars and nano-rings are simulated. The simulation results are well explained by TCMT under the coupled basis vector. However, when the structural asymmetry is large, the fitting of results shows that the total radiation loss is not conservative, in contradiction to the requirement of traditional TCMT. We solved this inconsistency by introducing the propagation phase into the near-field coupling term of TCMT. The studies show that, unlike the local mode near the exceptional point which corresponds to the radiation loss of the bright mode, the global mode near the diabolic point is closely related to the propagation phase. Furthermore, the structure near the diabolic point shows characteristic cross-coupling with the change of period. This study proposes a new theoretical framework for comprehending the interaction of light and matter and offers some guiding implications for the application of TCMT to a variety of related domains.