TY - GEN A1 - Klindworth, Dirk A1 - Schmidt, Kersten A1 - Fliss, Sonia T1 - Numerical realization of Dirichlet-to-Neumann transparent boundary conditions for photonic crystal wave-guides N2 - The computation of guided modes in photonic crystal wave-guides is a key issue in the process of designing devices in photonic communications. Existing methods, such as the super-cell method, provide an efficient computation of well-confined modes. However, if the modes are not well-confined, the modelling error of the super-cell method becomes prohibitive and advanced methods applying transparent boundary conditions for periodic media are needed. In this work we demonstrate the numerical realization of a recently proposed Dirichlet-to-Neumann approach and compare the results with those of the super-cell method. For the resulting non-linear eigenvalue problem we propose an iterative solution based on Newton's method and a direct solution using Chebyshev interpolation of the non-linear operator. Based on the Dirichlet-to-Neumann approach, we present a formula for the group velocity of guided modes that can serve as an objective function in the optimization of photonic crystal wave-guides. KW - Dirichlet-to-Neumann map KW - photonic crystal wave-guide KW - super-cell method KW - high-order FEM KW - non-linear eigenvalue problem KW - Newton method KW - Chebyshev interpolation KW - group velocity Y1 - 2013 UR - https://opus4.kobv.de/opus4-matheon/frontdoor/index/index/docId/1200 UR - https://nbn-resolving.org/urn:nbn:de:0296-matheon-12007 ER -