TY - GEN A1 - Dirk, Klindworth A1 - Schmidt, Kersten T1 - Dirichlet-to-Neumann transparent boundary conditions for photonic crystal wave-guides N2 - In this work we present a complete algorithm for the exact computation of the guided mode band structure in photonic crystal (PhC) wave-guides. In contrast to the supercell method, the used approach does not introduce any modelling error and is hence independent of the confinement of the modes. The approach is based on Dirichlet-to-Neumann (DtN) transparent boundary conditions that yield a nonlinear eigenvalue problem. For the solution of this nonlinear eigenvalue problem we present a direct technique using Chebyshev interpolation that requires a band gap calculation of the PhC in advance. For this band gap calculation –- we introduce as a very efficient tool –- a Taylor expansion of the PhC band structure. We show that our algorithm –- like the supercell method –- converges exponentially, however, its computational costs –- in comparison to the supercell method –- only increase moderately since the size of the matrix to be inverted remains constant. Y1 - 2013 UR - https://opus4.kobv.de/opus4-matheon/frontdoor/index/index/docId/1252 UR - https://nbn-resolving.org/urn:nbn:de:0296-matheon-12525 ER -