Mixed Fields Formulation for Electromagnetic Waves Confined in Dielectric Rings

Fuente: arXiv
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Main Authors: Simsek, Ergun, Niang, Alioune, Islam, Raonaqul, Courtright, Logan, Carter, Gary, Menyuk, Curtis R.
Format: Preprint
Published: 2025
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_version_ 1866917043779928064
author Simsek, Ergun
Niang, Alioune
Islam, Raonaqul
Courtright, Logan
Carter, Gary
Menyuk, Curtis R.
author_facet Simsek, Ergun
Niang, Alioune
Islam, Raonaqul
Courtright, Logan
Carter, Gary
Menyuk, Curtis R.
contents 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.
format Preprint
id arxiv_https___arxiv_org_abs_2503_17745
institution arXiv
publishDate 2025
record_format arxiv
spellingShingle Mixed Fields Formulation for Electromagnetic Waves Confined in Dielectric Rings
Simsek, Ergun
Niang, Alioune
Islam, Raonaqul
Courtright, Logan
Carter, Gary
Menyuk, Curtis R.
Optics
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.
title Mixed Fields Formulation for Electromagnetic Waves Confined in Dielectric Rings
topic Optics
url https://arxiv.org/abs/2503.17745