TY - GEN A1 - Fliss, Sonia A1 - Klindworth, Dirk A1 - Schmidt, Kersten T1 - Robin-to-Robin transparent boundary conditions for the computation of guided modes in photonic crystal wave-guides T2 - BIT Numerical Mathematics N2 - 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. KW - Robin-to-Robin map KW - Photonic crystal wave-guide KW - Surface modes KW - High-order FEM KW - Non-linear eigenvalue problem Y1 - 2015 UR - http://link.springer.com/article/10.1007/s10543-014-0521-1/fulltext.html?view=classic U6 - https://doi.org/10.1007/s10543-014-0521-1 SN - 0006-3835 SN - 1572-9125 VL - 55 IS - 1 SP - 81 EP - 115 ER -