Variational modelling for integrated optical devices

Embrecht W.C. van Groesen

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    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
    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

    PublisherTU Vienna


    Conference4th IMCAS Symposium on Mathematical Modelling, MATHMOD 2003
    Abbreviated titleMATHMOD


    • METIS-213145
    • IR-45735


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