有限元方法计算介质腔谐振频率和品质因子

Computation of resonant frequencies and quality factors of dielectric cavities with finite-element method

采用有限元方法计算了二维方形介质腔和二维微盘的谐振频率和品质因子,并给出了两种腔中磁场、电场振幅分布图,介质腔中的谐振问题对应亥姆霍兹波动方程的本征值问题,本征值的实部和虚部与谐振腔Q值关联;比较了近似解析解、FDTD解、FEM解的结果,对于谐振频率比较,FEM和解析解更接近,对于品质因子比较,低Q值结果FDTD和FEM结果相近,高Q值结果两者相差较大。通过比较知道,FEM方法比时域有限差分方法计算更准确,求解速度更快。

The frequency domain finite- element method is adopted to calculate the resonant frequency and quality factors of two- dimension square dielectric cavity resonator and two - dimension micro - disk cavity. The resonant field mode patterns are also given in the paper, resonant problem in dielectric cavity corresponds to eigenvalue problem of Helmholz wave equation. The real part and imaginary part of the eigenvalue are related with Q - factor of the cavity. Among FEM, finite difference time domain method and analytical solution for the resonant frequency comparison, FEM is more close to analytical solution. For the Q- factor comparison, FEM and FDTD are closer in low Q- factor than in high Q- factor, and FEM is more precise and faster than FDTD.