In this work, we have analyzed, fabricated and demonstrated concentric micro-ring resonators in silicon-on-insulator (SOI) structure for enhanced transmission notches. The operation principles of the concentric ring resonators are studied by time-domain coupled-mode theory. Directional coupling between concentric rings offers another freedom in designing deep notch optical filters and ultra-sensitive biosensors. The finite-difference-time-domain (FDTD) simulations have shown the improvement of the notch depth, evenly distributed mode field and the effect of the resonance shift. The device is demonstrated in silicon-on-insulator structure. Transmission notch depth improvement of ~ 15dB is demonstrated for the 21-20.02-μm-radius double-ring structure comparing with the single 21-μm-radius ring.