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We propose and simulate the characteristics of optical filters based on subwavelength gratings. In particular, we demonstrate through numerical simulations the feasibility of implementing SWG Bragg gratings in silicon-on-insulator (SOI). We also propose SWG ring resonators in SOI and verify their operation using numerical simulations and experiments. The fabricated devices exhibit an extinction ratio as large as 30 dB and a Q-factor as high as ~20,000. These fundamental SWG filters can serve as building blocks for more complex devices.