Design Space Exploration of Microring Resonators in Silicon Photonic Interconnects: Impact of the Ring Curvature

A detailed analysis of fundamental tradeoffs between ring radius and coupling gap size is presented to draw realistic borders of the possible design space for microring resonators (MRRs). The coupling coefficient for the ring-waveguide structure is estimated based on an integration of the nonuniform gap between the ring and the waveguide. Combined with the supermode analysis of two coupled waveguides, this approach is further expanded into a closed-form equation that describes the coupling strength. This equation permits to evaluate how the distance separating a waveguide from a ring resonator, and the ring radius, affect coupling. The effect of ring radius on the bending loss of the ring is furthermore modeled based on the measurements for silicon MRRs with different radii. These compact models for coupling and loss are subsequently used to derive the main optical properties of MRRs, such as 3-dB optical bandwidth, extinction ratio of resonance, and insertion loss, hence identifying the design space. Our results indicate that the design space for add-drop filters in a wavelength division multiplexed link is currently limited to 5-10 μm in radius and gap sizes ranging from 120 to 210 nm. The good agreement between the results from the proposed compact model for coupling and the numerical FDTD and experimental measurements indicate the application of our approach in realizing fast and efficient design space exploration of MRRs in silicon photonic interconnects.