标题： 电磁波在介质环中约束的混合场公式 显示英文标题

标题： Mixed Fields Formulation for Electromagnetic Waves Confined in Dielectric Rings

摘要： 我们提出了一种易于实现的数值方法，用于分析电磁波在介质环中的传播。 我们的方法采用基于有限差分的求解器，在圆柱坐标系中求解混合电场和磁场公式，以准确施加边界条件并计算共振模式。 该方法避免了几何变换；相反，它直接在圆柱坐标系中离散化亥姆霍兹波动方程，并求解得到的广义特征值问题。 我们将模型与商业求解器进行验证，针对多种结构，包括嵌入在SiO2中的Si3N4环、涂有薄膜的基板上的环以及环面，有效折射率的吻合度在0.3%以内。 该公式准确捕捉了场限制、曲率效应和色散，能够精确确定传播常数和模式轮廓。 作为应用，我们对高Q微谐振器中的光学频率梳生成进行了建模，预测了99.6 GHz的自由光谱范围和160万的负载品质因数，这得到了实验测量结果的证实。 显示英文摘要

摘要： 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.