title: Photonic bandgap calculations with Dirichlet-to-Neumann maps.
abstract: A simple and efficient method for computing bandgap structures of two-dimensional photonic crystals is presented. Using the Dirichlet-to-Neumann (DtN) map of the unit cell, the bandgaps are calculated as an eigenvalue problem for each given frequency, where the eigenvalue is related to the Bloch wave vector. A linear matrix eigenvalue problem is obtained even when the medium is dispersive. For photonic crystals composed of a square lattice of parallel cylinders, the DtN map is obtained by a cylindrical wave expansion. This leads to eigenvalue problems for relatively small matrices. Unlike other methods based on cylindrical wave expansions, sophisticated lattice sums techniques are not needed.
authors.affiliation: Department of Mathematics, Beijing University of Posts and Telecommunications, China.
authors.forename: Jianhua
authors.initials: J
authors.lastname: Yuan
authors.forename: Ya Yan
authors.initials: YY
authors.lastname: Lu