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On Spectral Bounds for Photonic Crystal Waveguides

  • B. Malcolm Brown
  • Vu Hoang
  • Michael Plum
  • Ian G. Wood
Part of the International Series of Numerical Mathematics book series (ISNM, volume 157)

Abstract

For a (d + 1)-dimensional photonic crystal with a linear defect strip (waveguide), we calculate real intervals containing spectrum of the associated spectral problem. If such an interval falls completely into a spectral gap of the unperturbed problem (without defect), this will prove the existence of additional spectrum induced by the waveguide.

Keywords

Spectral Problem Real Interval Spectral Point Plate Problem Photonic Crystal Waveguide 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. [1]
    P. Kuchment, B. Ong, On guided waves in photonic crystal waveguides, Waves in periodic and random media, South Hadley, MA (2002), 105–115, Contemp. Math. 339, Amer. Math. Soc., Providence, RI, 2003.Google Scholar
  2. [2]
    P.D. Hislop, I.M. Sigal, Introduction to spectral theory with applications to Schrödinger operators, Springer, New York, Berlin, Heidelberg, 1996.MATHGoogle Scholar

Copyright information

© Birkhäuser Verlag Basel/Switzerland 2008

Authors and Affiliations

  • B. Malcolm Brown
    • 1
  • Vu Hoang
    • 2
  • Michael Plum
    • 2
  • Ian G. Wood
    • 3
  1. 1.Cardiff School of Computer ScienceCardiff UniversityCardiffUK
  2. 2.Institut für AnalysisUniversität KarlsruheKarlsruheGermany
  3. 3.Institute of Mathematical and Physical SciencesAberystwyth UniversityCeredigionUK

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