A mixed-field formulation for modeling dielectric ring resonators and its application in optical frequency comb generation

We present a novel finite-difference frequency-domain formulation for accurate and efficient modal analysis of dielectric ring resonators, a critical component in microresonator-based optical frequency comb (OFC) generation. Unlike previous methods, our approach solves for both electric and magnetic fields simultaneously in cylindrical coordinates, eliminating spurious modes and ensuring high fidelity at material boundaries. The solver enables rapid computation of resonant modes without requiring manual input for azimuthal mode numbers, significantly streamlining dispersion engineering for OFC design. We validate our method against experimental data and the results generated with commercial solvers, demonstrating excellent agreement in effective indices, integrated dispersion, and resonance linewidths for silicon nitride resonators excited with lasers operating at 1060 nm and 1550 nm. Our results highlight the solver's utility in predicting anomalous dispersion and coupling dynamics, offering a robust tool for designing high-performance OFC devices.