Resonant modes in metal/insulator/metal metamaterials: An analytical study on near-field couplings

Abstract

Metamaterials (MTMs) in a metal/insulator/metal (MIM) configuration have drawn much attention recently, but the resonances in such systems are still not fully understood. Here, we employ a rigorous mode expansion method to analytically study the resonance properties of a model MIM MTM where the top metallic layer consists of an array of metallic stripes. Our analyses, supported by full-wave simulations and microwave experiments, provide a unified platform to understand the resonances in such systems, in which two previously established models are found valid only at certain extreme conditions. In particular, the resonance in such a system undergoes a transition from a vertical Fabry-P\'erot type to a transverse type as the spacer thickness shrinks, and the resonance frequency saturates at a particular value in the thin-spacer limit. Finally, we derive a set of analytical formulas to describe how the essential properties (i.e., resonance frequency and quality factor) of the resonance depend on the structural details of the system and verify these analytical relationships by full-wave simulations in MIM systems with complex microstructures.