Modeling Photonic Crystals with Complex Unit Cells by Dirichlet-to-Neumann Maps

Abstract

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.