Robin-to-Robin transparent boundary conditions for the computation of guided modes in photonic crystal wave-guides

  • 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 modesThe 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.show moreshow less

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Author: Sonia Fliss, Dirk Klindworth, Kersten Schmidt
URL:http://link.springer.com/article/10.1007/s10543-014-0521-1/fulltext.html?view=classic
DOI:https://doi.org/10.1007/s10543-014-0521-1
ISSN:0006-3835
ISSN:1572-9125
Title of the source (English):BIT Numerical Mathematics
Document Type:Scientific journal article peer-reviewed
Language:English
Year of publication:2015
Tag:High-order FEM; Non-linear eigenvalue problem; Photonic crystal wave-guide; Robin-to-Robin map; Surface modes
Volume/Year:55
Issue number:1
First Page:81
Last Page:115
Faculty/Chair:Fakultät 1 MINT - Mathematik, Informatik, Physik, Elektro- und Informationstechnik / FG Numerische Mathematik und Wissenschaftliches Rechnen
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