Analogy to Debye model in metamaterials: Resonant frequency shifting due to coupling

In this paper, we investigate the resonant frequency shifting of metamaterials due to coupling effect. We employ the split ring resonators (SRRs) with generating magnetic dipoles by decreasing the distance between SRRs to increase the coupling. We consider two different scenarios for increasing the coupling by decreasing period of unit cell and by decreasing distance between two SRRs with maintaining period. We give the analytical analysis of the difference in resonant frequency shifting between two scenarios based on coupling mode theory and we verify our results by using simulations and experiments. Furthermore, we employ two slightly different SRRs to establish bound states in the continuum (BIC) and we find that the resonant frequency shifting of BIC follows the consistent rule of our theory based on the simulations and experimental results.