@misc{FlissKlindworthSchmidt, author = {Fliss, Sonia and Klindworth, Dirk and Schmidt, Kersten}, title = {Robin-to-Robin transparent boundary conditions for the computation of guided modes in photonic crystal wave-guides}, series = {BIT Numerical Mathematics}, volume = {55}, journal = {BIT Numerical Mathematics}, number = {1}, issn = {0006-3835}, doi = {10.1007/s10543-014-0521-1}, pages = {81 -- 115}, abstract = {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.}, language = {en} }