  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 full account of
the confined and leaky modes, as opposed to the existing phenomenological
methods restricted to the confined modes only. This model enables 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 aluminium nitride
resonators. The developed model is then used to explore the field enhancement
in microrings crucial for nonlinear photonic applications.
