Robin-to-Robin transparent boundary conditions for the computation of guided modes in photonic crystal wave-guides
Please always quote using this URN:urn:nbn:de:0296-matheon-13270
- 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.
Author: | Sonia Fliss, Dirk Klindworth, Kersten Schmidt |
---|---|
URN: | urn:nbn:de:0296-matheon-13270 |
Referee: | Frank Schmidt |
Document Type: | Preprint, Research Center Matheon |
Language: | English |
Date of first Publication: | 2014/09/08 |
Release Date: | 2014/09/08 |
Tag: | Robin-to-Robin map; high-order FEM; non-linear eigenvalue problem; photonic crystal wave-guide; surface modes |
Institute: | Research Center Matheon |
Technische Universität Berlin | |
Project: | D Optics and Electronics (Electronic and photonic devices) / D26 Asymptotic analysis of the wave-propagation in realistic photonic crystal wave-guides |
MSC-Classification: | 65-XX NUMERICAL ANALYSIS / 65Nxx Partial differential equations, boundary value problems / 65N30 Finite elements, Rayleigh-Ritz and Galerkin methods, finite methods |
65-XX NUMERICAL ANALYSIS / 65Zxx Applications to physics / 65Z05 Applications to physics | |
78-XX OPTICS, ELECTROMAGNETIC THEORY (For quantum optics, see 81V80) / 78Mxx Basic methods / 78M10 Finite element methods | |
Preprint Number: | 1073 |