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Plasmonic crystal structures based on periodic arrays of gold nanorings were fabricated on glass substrates and studied by transmission measurements and by finite difference time domain simulations. Transmission measurement results, which closely match the simulation results, show two surface plasmon resonance peaks in the near infrared spectrum range and the peaks can be tuned by changing the lattice constants of the arrays. Using simulations, we investigated the quantitative performance of the sensor. The results show a sensitivity of 537 nm/RIU in bulk sensing applications and 1.6 nm spectral shift for 1 nm change in coating thickness on the surface of the gold nanorings in affinity sensing applications.