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 convergent numerical methods challenging. In this paper, we formulate band as a holomorphic Fredholm operator function index zero. Lagrange finite elements are used to discretize operators. convergence eigenvalues proved using abstract approximation theory for functions. Then spectral indicator method developed practically compute eigenvalues. Numerical examples presented validate show effectiveness proposed method.