Eigenmode decomposition method for full-wave modeling of microring resonators

We develop a theoretical predictive model for an all-pass ring resonator that enables the most complete description of linear coupling regimes. The model is based on eigenmode decomposition of Maxwell's equations with a full account of the confined and leaky modes, as opposed to the existing phenomenological methods restricted to the confined modes only. This model enables a quantitative description of all-pass ring resonators and provides insights into the physics underlying microring-waveguide coupling. We experimentally validate the model using transmission measurements in the linear regime of aluminum nitride resonators. The developed model is then used to explore the field enhancement in microrings crucial for nonlinear photonic applications.