▎ 摘　　要

We theoretically design the plasmonic structures based on the coupling between the graphene sheets and resonators for the mid-IR region, which can be used to construct the ultra-compact fast-tunable optical filter, splitter, 1x2 digital optical switch, or Mach-Zehnder interferometer. Electrical tunability of the system by tiny change of the Fermi level (chemical potential) of the graphene is realized. In addition, the quality and sensitivity of the system can be optimized by changing the coupling distance. The finite element method results are verified by the resonance theory of the rings.