caa a22 4500 605496757 CHVBK 20210128100537.0 cr unu---uuuuu 210128e20150301xx s 000 0 eng 10.1007/s10543-014-0521-1 doi (NATIONALLICENCE)springer-10.1007/s10543-014-0521-1 Robin-to-Robin transparent boundary conditions for the computation of guided modes in photonic crystal wave-guides [Elektronische Daten] [Sonia Fliss, Dirk Klindworth, Kersten Schmidt] The efficient and reliable computation of guided modes in photonic crystal wave-guides is of great importance for designing optical devices. Transparent boundary conditions based on Dirichlet-to-Neumann operators allow for an exact computation of well-confined modes and modes close to the band edge in the sense that no modelling error is introduced. The well-known super-cell method, on the other hand, introduces a modelling error which may become prohibitively large for guided modes that are not well-confined. The Dirichlet-to-Neumann transparent boundary conditions are, however, not applicable for all frequencies as they are not uniquely defined and their computation is unstable for a countable set of frequencies that correspond to so called Dirichlet eigenvalues. In this work we describe how to overcome this theoretical difficulty introducing Robin-to-Robin transparent boundary conditions whose construction do not exhibit those forbidden frequencies. They seem, hence, well suited for an exact and reliable computation of guided modes in photonic crystal wave-guides. Springer Science+Business Media Dordrecht, 2014 Robin-to-Robin map nationallicence Photonic crystal wave-guide nationallicence Surface modes nationallicence High-order FEM nationallicence Non-linear eigenvalue problem nationallicence Fliss Sonia Laboratoire POEMS, UMR 7231 CNRS/ENSTA/INRIA, ENSTA ParisTech, Paris, France aut Klindworth Dirk Department of Mathematics, Research Center MATHEON, TU Berlin, Berlin, Germany aut Schmidt Kersten Department of Mathematics, Research Center MATHEON, TU Berlin, Berlin, Germany aut BIT Numerical Mathematics Springer Netherlands 55/1(2015-03-01), 81-115 0006-3835 55:1<81 2015 55 10543 https://doi.org/10.1007/s10543-014-0521-1 text/html Onlinezugriff via DOI BK010053 XK010053 XK010000 Metadata rights reserved Springer special CC-BY-NC licence nationallicence 1 research-article jats NATIONALLICENCE NATIONALLICENCE NL-springer NATIONALLICENCE 856 40 https://doi.org/10.1007/s10543-014-0521-1 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Fliss Sonia Laboratoire POEMS, UMR 7231 CNRS/ENSTA/INRIA, ENSTA ParisTech, Paris, France aut NATIONALLICENCE 700 1- Klindworth Dirk Department of Mathematics, Research Center MATHEON, TU Berlin, Berlin, Germany aut NATIONALLICENCE 700 1- Schmidt Kersten Department of Mathematics, Research Center MATHEON, TU Berlin, Berlin, Germany aut NATIONALLICENCE 773 0- BIT Numerical Mathematics Springer Netherlands 55/1(2015-03-01), 81-115 0006-3835 55:1<81 2015 55 10543