Dirichlet-to-Neumann map method for analyzing periodic arrays of cylinders with oblique incident waves

For finite two-dimensional (2D) photonic crystals given as periodic arrays of circular cylinders in a square or triangular lattice, we develop an efficient method to compute the transmission and reflection spectra for oblique incident plane waves. The method relies on vector cylindrical wave expansions to approximate the Dirichlet-to-Neumann (DtN) map for each distinct unit cell, and uses the DtN maps to derive an efficient method that works on the edges of the unit cells only. The DtN operator maps the two longitudinal field components to their derivatives on the boundary of the unit cell. c © 2009 Optical Society of America