Quasinormal modes and coupled mode theory of 1D metal-dielectric photonic crystals

Metal-dielectric photonic crystals (MDPCs) are a class of photonic structure formed through the coupling of metallic microcavities. Interaction of the cavities results in hybridization of the underlying microcavity states to form photonic bands defined by the crystal periodicity, metal-to-dielectric ratio, and number of unit cells. In this study, we provide analytical solutions for the resonant states of discrete 1D MDPCs with an arbitrary number of cavities using quasinormal mode (QNM) theory. Our results show that the QNM solutions closely match the predictions of coupled mode theory (CMT) in the tight-binding regime and diverge as the metal thickness vanishes. We apply the QNM results to the CMT model to find analytical expressions for the inter-cavity coupling coefficients. Additionally, we analyze the quality factor, transmission, and absorption of both ideal and lossy MDPCs, revealing important trends in bulk optical properties. In this work, we derive practical analytical solutions for the resonant states of 1D metal-dielectric photonic crystals and critical device parameters, including quality factor, radiative and nonradiative losses, and density of states. We demonstrate equivalence between the quasinormal and CMT solutions and define conditions for a coupled oscillator regime. image