论文标题
频率依赖材料的光子带结构的有限元计算
Finite Element Calculation of Photonic Band Structures for Frequency Dependent Materials
论文作者
论文摘要
我们考虑频率依赖光子晶体的频带结构的计算。相关的特征值问题是非线性的，开发有效的收敛数值方法是一项挑战。在本文中，谱带结构问题被提出为索引零的全体形态弗雷姆操作员函数的特征值问题。 Lagrange有限元素用于离散操作员功能。然后，使用抽象近似理论证明了特征值的收敛性。开发了一种光谱指标方法来实际计算特征值。提出了数值示例以验证理论并显示了所提出方法的有效性。
We consider the calculation of the band structure of frequency dependent photonic crystals. The associated eigenvalue problem is nonlinear and it is challenging to develop effective convergent numerical methods. In this paper, the band structure problem is formulated as the eigenvalue problem of a holomorphic Fredholm operator function of index zero. Lagrange finite elements are used to discretize the operator function. Then the convergence of the eigenvalues is proved using the abstract approximation theory for holomorphic operator functions. A spectral indicator method is developed to practically compute the eigenvalues. Numerical examples are presented to validate the theory and show the effectiveness of the proposed method.
