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Though adding a groove to a plasmonic end-coupled perfect ring (PR) resonator, two additional resonance modes, which can be controlled by the length of the groove, will arise in this proposed ring-groove (RG) joint metal-insulator-metal (MIM) waveguide. By further cascading, the PR resonator and the RG joint resonator, single and dual Fano resonances with asymmetric line shapes are obtained due to the interference effects between the dark modes and the bright modes. High figure of merit and high refractive-index sensitivity are achieved, and thus this structure is suitable for the biochemistry sensing area. Interestingly, normal and abnormal dispersions are also investigated for the Fano peaks and dips, respectively. The performances of the proposed structure are investigated by using the finite-difference time-domain method. [ABSTRACT FROM AUTHOR]