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

Please wait, while we are loading the content...

An efficient $$\mathcal {O}(N)$$ algorithm for computing $$\mathcal {O}(N^2)$$ acoustic wave interactions in large $$N$$ -obstacle three dimensional configurations

A spectrally accurate direct solution technique for frequency-domain scattering problems with variable media

When is the error in the $$h$$ -BEM for solving the Helmholtz equation bounded independently of $$k$$ ?

Convergence of infinite element methods for scalar waveguide problems

Adaptive edge element approximation of H(curl)-elliptic optimal control problems with control constraints

Bounding acoustic layer potentials via oscillatory integral techniques

BIT Numerical Mathematics : Volume 54

BIT Numerical Mathematics : Volume 53

BIT Numerical Mathematics : Volume 52

BIT Numerical Mathematics : Volume 51

BIT Numerical Mathematics : Volume 50

BIT Numerical Mathematics : Volume 49

BIT Numerical Mathematics : Volume 48

BIT Numerical Mathematics : Volume 47

BIT Numerical Mathematics : Volume 46

BIT Numerical Mathematics : Volume 45

BIT Numerical Mathematics : Volume 44

BIT Numerical Mathematics : Volume 43

BIT Numerical Mathematics : Volume 42

BIT Numerical Mathematics : Volume 41

BIT Numerical Mathematics : Volume 40

BIT Numerical Mathematics : Volume 39

BIT Numerical Mathematics : Volume 38

BIT Numerical Mathematics : Volume 37

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

Content Provider	Springer Nature Link
Author	Fliss, Sonia Klindworth, Dirk Schmidt, Kersten
Copyright Year	2014
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.
Ending Page	115
Page Count	35
Starting Page	81
File Format	PDF
ISSN	00063835
e-ISSN	15729125
Journal	BIT Numerical Mathematics
Issue Number	1
Volume Number	55
Language	English
Publisher	Springer Netherlands
Publisher Date	2014-09-12
Publisher Place	Dordrecht
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	Computational Mathematics and Numerical Analysis Photonic crystal wave-guide Numeric Computing Mathematics High-order FEM Finite element methods Maxwell equations Robin-to-Robin map Applications to physics Surface modes Non-linear eigenvalue problem Explicit machine computation and programs (not the theory of computation or programming) Nonlinear eigenvalue problems, nonlinear spectral theory Finite elements, Rayleigh-Ritz and Galerkin methods, finite methods
Content Type	Text
Resource Type	Article
Subject	Applied Mathematics Computer Networks and Communications Computational Mathematics Software

Sl.	Authority	Responsibilities	Communication Details
1	Ministry of Education (GoI), Department of Higher Education	Sanctioning Authority	https://www.education.gov.in/ict-initiatives
2	Indian Institute of Technology Kharagpur	Host Institute of the Project: The host institute of the project is responsible for providing infrastructure support and hosting the project	https://www.iitkgp.ac.in
3	National Digital Library of India Office, Indian Institute of Technology Kharagpur	The administrative and infrastructural headquarters of the project	Dr. B. Sutradhar bsutra@ndl.gov.in
4	Project PI / Joint PI	Principal Investigator and Joint Principal Investigators of the project	Dr. B. Sutradhar bsutra@ndl.gov.in Prof. Saswat Chakrabarti will be added soon
5	Website/Portal (Helpdesk)	Queries regarding NDLI and its services	support@ndl.gov.in
6	Contents and Copyright Issues	Queries related to content curation and copyright issues	content@ndl.gov.in
7	National Digital Library of India Club (NDLI Club)	Queries related to NDLI Club formation, support, user awareness program, seminar/symposium, collaboration, social media, promotion, and outreach	clubsupport@ndl.gov.in
8	Digital Preservation Centre (DPC)	Assistance with digitizing and archiving copyright-free printed books	dpc@ndl.gov.in
9	IDR Setup or Support	Queries related to establishment and support of Institutional Digital Repository (IDR) and IDR workshops	idr@ndl.gov.in

Robust Eigenvalue Computation for Smoothing Operators

Spectral Approximation of a Boundary Condition for an Eigenvalue Problem

A New Nonconforming Finite Element Method for the Computation of Electromagnetic Guided Waves. I: Mathematical Analysis

Discontinuous Galerkin Approximation of the Maxwell Eigenproblem

Finite Element Eigenvalue Enclosures for the Maxwell Operator

Two-Grid Methods for Maxwell Eigenvalue Problems

Non-linear eigenvalue problems and applications to photonic crystals

Eigenvalue approximations from below using Morley elements

Mixed Discontinuous Galerkin Approximation of the Maxwell Operator

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

Similar Documents

Robust Eigenvalue Computation for Smoothing Operators

Spectral Approximation of a Boundary Condition for an Eigenvalue Problem

A New Nonconforming Finite Element Method for the Computation of Electromagnetic Guided Waves. I: Mathematical Analysis

Discontinuous Galerkin Approximation of the Maxwell Eigenproblem

Finite Element Eigenvalue Enclosures for the Maxwell Operator

Two-Grid Methods for Maxwell Eigenvalue Problems

Non-linear eigenvalue problems and applications to photonic crystals

Eigenvalue approximations from below using Morley elements

Mixed Discontinuous Galerkin Approximation of the Maxwell Operator

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