Band structure calculation of photonic crystals with frequency-dependent permittivities.

Abstract

We propose a new method for band structure calculation of photonic crystals. It can treat arbitrarily frequency-dependent, lossy or lossless materials. The band structure problem is first formulated as the eigenvalue problem of an operator function. Finite elements are then used for discretization. Finally, the spectral indicator method is employed to compute the eigenvalues. Numerical examples in both TE and TM cases are presented to show the effectiveness. There exist very few examples in literature for the TM case, and the examples in this paper can serve as benchmarks.