Design of heated-micro-resonator rings

To facilitate the design the heated-micro-resonator rings, we develop a numerical model. Particularly, an etching model based on a diffusion equation is implemented to distinguish the etched and non-etched regions. The simulations reveal that air trenches can significantly increase the thermal resistance and, as a result, reduce the power consumed in the heater to get the same tuning performance. It is found that the tunability of MRR is exponentially enhanced with the underetch level as RL > 0.825, whereas the tuning efficiency is almost the same, as RL <; 0.825. The tuning efficiency is ~0.1 nm/mW without air trenches, but it becomes 20× larger at the etched-through extreme.