Analyzing photonic crystal waveguides by Dirichlet-to-Neumann maps

Abstract

An efficient numerical method is developed for the modal analysis of two-dimensional photonic crystal waveguides (PCWs). Using the Dirichlet-to-Neumann (DtN) map of the supercell, the waveguide modes are solved from an eigenvalue problem formulated on two boundaries of the supercell, leading to significantly smaller matrices when it is discretized. The eigenvalue problem is linear even when the medium is dispersive. The DtN map of a domain is an operator that maps the wave field on the boundary of the domain to the normal derivative of the field. The DtN map of the supercell can be efficiently calculated by merging the DtN maps of the ordinary and defect unit cells.