Spectral problem on 3-D photonic crystals

Kaori Nagatou, Malcolm Brown, Myoungnyoun Kim, Yoshitaka Watanabe, Ian Wood

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

    Abstract

    In this research we will study some fundamental mathematical properties of photonic crystals which have many applications in optics and nanotechnology. A good model for these crystals is described by the Maxwell's equations with periodic electric permittivity. The spectral problem for Maxwell's equations possesses bands of essential spectrum which may be separated by gaps. Waves of a frequency in such a gap cannot propagate in the crystal, while other frequencies can. This makes photonic crystals very interesting for applications in nanotechnology and other areas. It is important not just to have quantitative numerical evidence for the location of these gaps, but to be able to prove the existence of spectral gaps with mathematical certainty. We propose to use computer assisted methods to achieve this.

    Original languageEnglish
    Title of host publicationNumerical Analysis and Applied Mathematics - International Conference on Numerical Analysis and Applied Mathematics 2009, ICNAAM-2009
    Pages922-925
    Number of pages4
    DOIs
    Publication statusPublished - Nov 26 2009
    EventInternational Conference on Numerical Analysis and Applied Mathematics 2009, ICNAAM-2009 - Rethymno, Crete, Greece
    Duration: Sep 18 2009Sep 22 2009

    Publication series

    NameAIP Conference Proceedings
    Volume1168
    ISSN (Print)0094-243X
    ISSN (Electronic)1551-7616

    Other

    OtherInternational Conference on Numerical Analysis and Applied Mathematics 2009, ICNAAM-2009
    CountryGreece
    CityRethymno, Crete
    Period9/18/099/22/09

    All Science Journal Classification (ASJC) codes

    • Physics and Astronomy(all)

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