Modeling photonic crystals with complex unit cells by Dirichlet-to-Neumann maps

For a photonic crystal (PhC) of finite size, it is important to calculate its transmission and reflection spectra. For two-dimensional (2-D) PhCs composed of a square lattice of circular cylinders, the problem can be solved by an efficient method based on the Dirichlet-to-Neumann (DtN) map of the unit cell and a marching scheme using a pair of operators. In this paper, the DtN operator marching method is extended to handle 2-D PhCs with complex unit cells and arbitrary lattice structures.