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A plasmonic sensor based on the nano-cylinder photonic crystal slab is modeled and designed for the refractive index sensing application. Design considerations and sensor characteristics are explored in detail using the higher order accuracy spectral element method. The geometrical parameters of the designed plasmonic sensor are optimized. With the shallowly etched configuration and the small radius of the nano-cylinder, the sensor simultaneously achieves a high sensing performance of figure of merit <inline-formula> <tex-math notation="LaTeX">$\textrm{FoM}=280$</tex-math></inline-formula> and a clear registration of full-height/full-width at half-maximum <inline-formula> <tex-math notation="LaTeX">$\textrm{FH/FWHM}=0.34\ \textrm{nm}^{-1}$</tex-math></inline-formula> for the lattice period <inline-formula> <tex-math notation="LaTeX">$P=750\ \textrm{nm}$</tex-math></inline-formula>, the cylinder radius <inline-formula> <tex-math notation="LaTeX">$r=85\ \textrm{nm}$</tex-math></inline-formula>, and the cylinder thickness <inline-formula> <tex-math notation="LaTeX">$t=125\ \textrm{nm}$</tex-math></inline-formula>. The proposed plasmonic sensor can find its great potential for applications relying on detecting refractive index.