Mixed Fields Formulation for Electromagnetic Waves Confined in Dielectric Rings
Fuente:
arXiv
Saved in:
| Main Authors: | , , , , , |
|---|---|
| Format: | Preprint |
| Published: |
2025
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _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 |