Finite Element Calculation of Photonic Band Structures for Frequency Dependent Materials

Band structure calculation of frequency dependent photonic crystals has important applications. The associated eigenvalue problem is nonlinear and the development of convergent numerical methods is challenging. In this paper, we formulate the band structure problem as the eigenvalue problem of a holomorphic Fredholm operator function of index zero. Lagrange finite elements are used to discretize the operators. The convergence of the eigenvalues is proved using the abstract approximation theory for holomorphic operator functions. Then 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.