A dimensionality reduction technique for scattering problems in photonics

Alyona Ivanova, Remco Stoffer, Manfred Hammer

    Research output: Chapter in Book/Report/Conference proceedingConference contributionAcademicpeer-review

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    Abstract

    Optical scattering problems in guided wave photonics are addressed. We represent the unknown optical fields as superpositions of 1D slab modes bounded by PMLs. By applying a variational principle, the problems are reduced to lower dimensional systems of differential equations for the unknown coefficient functions, which are solved using the finite elements method. Dirichlet to Neumann maps allow influx to be prescribed and radiation to freely pass the computational window boundaries. Expansions with one or a few modes give a quick, effective index-like approximation; more modes provide more accurate solutions. We give examples for a series of 2-D configurations, where reliable reference data is available.
    Original languageUndefined
    Title of host publicationFirst International Workshop on Theoretical and Computational Nano-Photonics TaCoNa-Photonics, Conference Proceedings
    Place of PublicationKarlsruhe, Germany
    PublisherUniversity of Karlsruhe
    Pages47
    Number of pages1
    ISBN (Print)not assigned
    Publication statusPublished - 3 Dec 2008

    Publication series

    Name
    PublisherUniversität Karlsruhe
    NumberWP 08-02

    Keywords

    • EWI-14885
    • METIS-255122
    • IR-65302

    Cite this

    Ivanova, A., Stoffer, R., & Hammer, M. (2008). A dimensionality reduction technique for scattering problems in photonics. In First International Workshop on Theoretical and Computational Nano-Photonics TaCoNa-Photonics, Conference Proceedings (pp. 47). Karlsruhe, Germany: University of Karlsruhe.
    Ivanova, Alyona ; Stoffer, Remco ; Hammer, Manfred. / A dimensionality reduction technique for scattering problems in photonics. First International Workshop on Theoretical and Computational Nano-Photonics TaCoNa-Photonics, Conference Proceedings. Karlsruhe, Germany : University of Karlsruhe, 2008. pp. 47
    @inproceedings{0011b5271b3e4244aba50fa5d56d2ebe,
    title = "A dimensionality reduction technique for scattering problems in photonics",
    abstract = "Optical scattering problems in guided wave photonics are addressed. We represent the unknown optical fields as superpositions of 1D slab modes bounded by PMLs. By applying a variational principle, the problems are reduced to lower dimensional systems of differential equations for the unknown coefficient functions, which are solved using the finite elements method. Dirichlet to Neumann maps allow influx to be prescribed and radiation to freely pass the computational window boundaries. Expansions with one or a few modes give a quick, effective index-like approximation; more modes provide more accurate solutions. We give examples for a series of 2-D configurations, where reliable reference data is available.",
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    author = "Alyona Ivanova and Remco Stoffer and Manfred Hammer",
    year = "2008",
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    language = "Undefined",
    isbn = "not assigned",
    publisher = "University of Karlsruhe",
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    Ivanova, A, Stoffer, R & Hammer, M 2008, A dimensionality reduction technique for scattering problems in photonics. in First International Workshop on Theoretical and Computational Nano-Photonics TaCoNa-Photonics, Conference Proceedings. University of Karlsruhe, Karlsruhe, Germany, pp. 47.

    A dimensionality reduction technique for scattering problems in photonics. / Ivanova, Alyona; Stoffer, Remco; Hammer, Manfred.

    First International Workshop on Theoretical and Computational Nano-Photonics TaCoNa-Photonics, Conference Proceedings. Karlsruhe, Germany : University of Karlsruhe, 2008. p. 47.

    Research output: Chapter in Book/Report/Conference proceedingConference contributionAcademicpeer-review

    TY - GEN

    T1 - A dimensionality reduction technique for scattering problems in photonics

    AU - Ivanova, Alyona

    AU - Stoffer, Remco

    AU - Hammer, Manfred

    PY - 2008/12/3

    Y1 - 2008/12/3

    N2 - Optical scattering problems in guided wave photonics are addressed. We represent the unknown optical fields as superpositions of 1D slab modes bounded by PMLs. By applying a variational principle, the problems are reduced to lower dimensional systems of differential equations for the unknown coefficient functions, which are solved using the finite elements method. Dirichlet to Neumann maps allow influx to be prescribed and radiation to freely pass the computational window boundaries. Expansions with one or a few modes give a quick, effective index-like approximation; more modes provide more accurate solutions. We give examples for a series of 2-D configurations, where reliable reference data is available.

    AB - Optical scattering problems in guided wave photonics are addressed. We represent the unknown optical fields as superpositions of 1D slab modes bounded by PMLs. By applying a variational principle, the problems are reduced to lower dimensional systems of differential equations for the unknown coefficient functions, which are solved using the finite elements method. Dirichlet to Neumann maps allow influx to be prescribed and radiation to freely pass the computational window boundaries. Expansions with one or a few modes give a quick, effective index-like approximation; more modes provide more accurate solutions. We give examples for a series of 2-D configurations, where reliable reference data is available.

    KW - EWI-14885

    KW - METIS-255122

    KW - IR-65302

    M3 - Conference contribution

    SN - not assigned

    SP - 47

    BT - First International Workshop on Theoretical and Computational Nano-Photonics TaCoNa-Photonics, Conference Proceedings

    PB - University of Karlsruhe

    CY - Karlsruhe, Germany

    ER -

    Ivanova A, Stoffer R, Hammer M. A dimensionality reduction technique for scattering problems in photonics. In First International Workshop on Theoretical and Computational Nano-Photonics TaCoNa-Photonics, Conference Proceedings. Karlsruhe, Germany: University of Karlsruhe. 2008. p. 47