A resonator structure includes an input waveguide and an output waveguide. In one embodiment, the resonator structure also includes at least one resonator that couples the input waveguide to the output waveguide and a directional coupler that optically couples the input waveguide to the output waveguide. In another embodiment, the resonator structure includes a plurality of ring resonators that couple the input waveguide to the output waveguide. The plurality of ring resonators include a sequence of ring resonators that form a coupling loop. Each ring resonator in the sequence is coupled to at least two other ring resonators in the sequence and the first ring resonator in the sequence is coupled to the last ring resonator in the sequence so as to form the coupling loop.