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We investigate the index sensing characteristics of plasmonic arrays based on square lattice slablike gold nanorings (NRs) with different ring widths. The gold NR arrays exhibit two extinction peaks in the visible and near-infrared corresponding to antibonding and bonding modes. Redshift and blueshift in antibonding and bonding modes when broadening the average ring width are observed. We experimentally demonstrate the sensitivity of bonding mode can be tuned by varying the average ring width. High sensitivity of 691 nm per refractive index unit is obtained for NRs with 199 nm average ring width.