Modeling photonic crystals by boundary integral equations and Dirichlet-to-Neumann maps (Q924465)

The main purpose of this paper is to extend the Dirichlet-to-Neumann map method to \(2D\) photonic crystals composed of identical and parallel cylinders with arbitrary cross sections. This study is done by means of the boundary integral equation method for unit cells containing cylinders. The approach is mainly based on the calculation of the special solutions which are needed for constructing the Dirichlet-to-Neumann map by solving scattering problems of the cylinder with different plane incident waves. The different solutions corresponding to different incident waves can be efficiently solved together, as they are related to linear systems with an identical coefficient matrix and different right-hand sides. The abstract properties established in this paper are illustrated with some numerical results.