Modeling method for concentric ring resonators with dispersion engineering

We introduce a geometry-guided design method in concentric ring resonators for dispersion engineering. Using eigenmode simulations of a single ring, we construct a two-dimensional round-trip optical path length (OPL) map that systematically identifies phase-matched geometries without exhaustive parameter sweeps. The OPL map finds feasible ring and gap combinations for efficient coupling, also revealing the design limits. With this approach, we design a 50 nm-thick Si₃N₄ concentric ring resonator that achieves anomalous dispersion in a weakly-guided mode-a regime that typically exhibits normal dispersion in single-ring configurations. Lugiato-Lefever equation (LLE) simulations confirm that this dispersion-engineered concentric ring can support a bright soliton in a weakly guided mode, overcoming the dispersion limit due to a weak confinement. The proposed modeling method is generalized and readily extendable to a wide range of material platforms and wavelength regimes, providing a powerful tool for diverse integrated nonlinear photonic applications.