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arXiv · 2503.17745

Mixed Fields Formulation for Electromagnetic Waves Confined in Dielectric Rings

Ergun Simsek·Alioune Niang·Raonaqul Islam·Logan Courtright·Gary Carter·Curtis R. Menyuk
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Abstract

We present an easy-to-implement numerical method for analyzing electromagnetic wave propagation in dielectric rings. Our approach employs a finite-difference-based solver in cylindrical coordinates, solving a mixed electric-magnetic field formulation to accurately enforce boundary conditions and compute resonant modes. The method avoids geometric transformations; instead, it directly discretizes the Helmholtz wave equation in cylindrical coordinates and solves the resulting generalized eigenvalue problem. We validate our model against commercial solvers for various structures, including a Si3N4 ring embedded in SiO2, a ring on a thin-film-coated substrate, and a torus, achieving agreement in effective refractive indices within 0.3%. The formulation accurately captures field confinement, curvature effects, and dispersion, enabling precise determination of propagation constants and mode profiles. As an application, we model optical frequency comb generation in a high-Q microresonator, predicting a free spectral range of 99.6 GHz and a loaded quality factor of 1.6 million, corroborated by experimental measurements.

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Ergun Simsek, Alioune Niang, Raonaqul Islam, Logan Courtright, Gary Carter, Curtis R. Menyuk. 2025-03-22. Mixed Fields Formulation for Electromagnetic Waves Confined in Dielectric Rings. https://arxiv.org/abs/2503.17745

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