{"about":{"site":"https://codewithpapers.app","non_affiliation":"Code with Papers and Syntology are not affiliated with, endorsed by, or sponsored by Papers with Code, Meta, or the pwc-archive mirror.","licence":"CC BY-SA 4.0","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","attribution":"https://codewithpapers.app/attribution","modified":"archive material modified by Syntology; see the attribution page"},"url":"/paper/resonant-modes-of-electromagnetic-waves","title":"Mixed Fields Formulation for Electromagnetic Waves Confined in Dielectric Rings","arxiv_id":"2503.17745","date":"2025-03-22","proceeding":null,"authors":["Ergun Simsek","Alioune Niang","Raonaqul Islam","Logan Courtright","Gary Carter","Curtis R. Menyuk"],"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.","url_abs":"https://arxiv.org/abs/2503.17745v3","url_pdf":"https://arxiv.org/pdf/2503.17745v3.pdf","source":{"archive":"pwc-archive (Hugging Face), CC BY-SA 4.0","snapshot":"2025-07-28","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","row_kind":"links_only","authors_date_abstract":"arXiv metadata, CC0 1.0 (https://info.arxiv.org/help/license), from the Kaggle arXiv metadata snapshot of 2026-09-12"},"code_links":[{"paper_slug":"resonant-modes-of-electromagnetic-waves","repo_url":"https://github.com/simsekergun/DieRingSolver","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":0,"framework":"none","reach":null}],"tasks":[],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"syntology_url":null,"atlas_url":null,"mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}