A multilevel method for the computation of eigenmodes in 3D photonic crystals

We present a multi-level finite-element-eigenmode-solver for the computation of Bloch-type modes in three-dimensional photonic crystals. We adapt the Dohler iteration method to cope with Maxwell-type eigenvalue problems of self-adjoint as well as non-selfadjoint type. Combined with an efficient multigrid method for preconditioning, we can experimentally verify linear complexity in terms of unknowns.