Variational modelling for integrated optical devices

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Abstract

Variational modelling is the use of a variational structure of a problem to simplify the model or to find approximations of the solutions in a consistent way. In both cases the consistent use of the variational structure consists in restricting the relevant functionals to smaller sets and consider the Euler-Lagrange equation on the restricted set instead of on the original set. One type of restriction may be to specialise the set of phenomena. To find approximate solutions, parameterized manifolds of functions are used to restrict the functional; either low-dimensional manifolds of appropriate 'trial'-functions, or high-dimensional linear subspaces for numerical discretizations. In these notes another type of restriction will be discussed. We describe how typical problems for all-optical devices in integrated optics have to be considered on unbounded domains. The variational structure is then exploited to confine the problem to a finite domain by restriction to functions that satisfy, or approximate, the equations on the exterior domain. For a typical reflection problem this leads to boundary conditions that are 'transparent' for a-priorily unknown radiation and transmittance, but allow a prescribed influx of light into the structure.
Original languageEnglish
Title of host publicationProceedings 4th IMACS-symposium on Mathematical Modelling
Place of PublicationVienna
PublisherVienna University of Technology
Pages76-82
ISBN (Print)3-91608-24-9
Publication statusPublished - 5 Feb 2003
Event4th IMCAS Symposium on Mathematical Modelling, MATHMOD 2003 - Vienna University of Technology, Vienna, Austria
Duration: 5 Feb 20037 Feb 2003
Conference number: 4

Publication series

Name
PublisherTU Vienna

Conference

Conference4th IMCAS Symposium on Mathematical Modelling, MATHMOD 2003
Abbreviated titleMATHMOD
CountryAustria
CityVienna
Period5/02/037/02/03

Fingerprint

Optical Devices
Restriction
Modeling
Integrated Optics
Exterior Domain
Euler-Lagrange Equations
Transmittance
Unbounded Domain
Simplify
Approximate Solution
High-dimensional
Discretization
Radiation
Subspace
Boundary conditions
Unknown
Approximation
Model

Keywords

  • METIS-213145
  • IR-45735

Cite this

van Groesen, E. W. C. (2003). Variational modelling for integrated optical devices. In Proceedings 4th IMACS-symposium on Mathematical Modelling (pp. 76-82). Vienna: Vienna University of Technology.
van Groesen, Embrecht W.C. / Variational modelling for integrated optical devices. Proceedings 4th IMACS-symposium on Mathematical Modelling. Vienna : Vienna University of Technology, 2003. pp. 76-82
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van Groesen, EWC 2003, Variational modelling for integrated optical devices. in Proceedings 4th IMACS-symposium on Mathematical Modelling. Vienna University of Technology, Vienna, pp. 76-82, 4th IMCAS Symposium on Mathematical Modelling, MATHMOD 2003, Vienna, Austria, 5/02/03.

Variational modelling for integrated optical devices. / van Groesen, Embrecht W.C.

Proceedings 4th IMACS-symposium on Mathematical Modelling. Vienna : Vienna University of Technology, 2003. p. 76-82.

Research output: Chapter in Book/Report/Conference proceedingConference contributionProfessional

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AB - Variational modelling is the use of a variational structure of a problem to simplify the model or to find approximations of the solutions in a consistent way. In both cases the consistent use of the variational structure consists in restricting the relevant functionals to smaller sets and consider the Euler-Lagrange equation on the restricted set instead of on the original set. One type of restriction may be to specialise the set of phenomena. To find approximate solutions, parameterized manifolds of functions are used to restrict the functional; either low-dimensional manifolds of appropriate 'trial'-functions, or high-dimensional linear subspaces for numerical discretizations. In these notes another type of restriction will be discussed. We describe how typical problems for all-optical devices in integrated optics have to be considered on unbounded domains. The variational structure is then exploited to confine the problem to a finite domain by restriction to functions that satisfy, or approximate, the equations on the exterior domain. For a typical reflection problem this leads to boundary conditions that are 'transparent' for a-priorily unknown radiation and transmittance, but allow a prescribed influx of light into the structure.

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van Groesen EWC. Variational modelling for integrated optical devices. In Proceedings 4th IMACS-symposium on Mathematical Modelling. Vienna: Vienna University of Technology. 2003. p. 76-82