Localized Green’s Functions for a Two-Dimensional Periodic Material

  • C. G. Poulton
  • R. C. McPhedran
  • N. A. Nicorovici
  • L. C. Botten
Part of the Solid Mechanics and Its Applications book series (SMIA, volume 113)


We describe a method for the calculation of Green’s functions for an array of dielectric cylinders. The method is to first construct quasi-periodic Green’s functions, with Bloch vector kB. This function also obeys the appropriate electromagnetic boundary conditions on the surface of each cylinder. The Green’s function for a single source in the array can then be calculated by averaging the quasi-periodic result over the Brillouin zone.


Green’s functions photonic crystals defects Bloch functions 


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  1. [1]
    J. Dowling, H. Everitt, and E. Yablonovitch, 2002. Photonic & Acoustic Band-Gap Bibliography (
  2. [2]
    J. D. Joannopoulos, R. D. Meade, and J. N. Winn. Photonic Crystals: Molding the Flow of Light. Princeton University, New Jersey, 1995.Google Scholar
  3. [3]
    M. Agio and C.M. Soukoulis. Ministop bands in single-defect photonic crystal waveguides. Phys. Rev. E, 64:056603:056603:4, 2001.CrossRefGoogle Scholar
  4. [4]
    D. Cassagne, A. Barra, and C. Jouanin. Defects and diffraction in photonic crystals. Superlattices and microstructures, 25:343–346, 1999.CrossRefGoogle Scholar
  5. [5]
    S. S. M. Cheng, L.M. Li, C.T. Chan, and Z.Q. Zhang. Defect and transmission properties of two-dimensional quasiperiodic photonic band-gap sytems. Phys. Rev. B, 59:4091–4099, 1999.CrossRefGoogle Scholar
  6. [6]
    A. Figotin and V. Goren. Resolvent method for computation of localized defect modes of h-polarization in two-dimensional photonic crystals. Phys. Rev. E, 64:056623:1–056623:16, 2001.CrossRefMathSciNetGoogle Scholar
  7. [7]
    R. C. McPhedran, N. A. Nicorovici, L. C. Botten, and Ke-Da Bao. Green’s function, lattice sum and Rayleigh’s identity for a dynamic scattering problem, volume 96 of IMA Volumes in Mathematics and its Applications, pages 155–186. Springer-Verlag, New York, 1997.Google Scholar
  8. [8]
    M. Abramowitz and I. A. Stegun, editors. Handbook of Mathematical Functions, pages 355–433. Dover, New York, 1972.Google Scholar
  9. [9]
    R. C. McPhedran and D. H. Dawes. Lattice sums for an electromagnetic scattering problem. J. Electromagn. Waves Appl., 6:1327–1340, 1992.Google Scholar
  10. [10]
    V.V. V.V. Zalipaev, N.A. Movchan, C.G. Poulton, and R.C. McPhedran. Elastic waves and homogenization in oblique periodic structures. Proc. Roy. Soc. A, 458:1887–1912, 2002.CrossRefMathSciNetGoogle Scholar

Copyright information

© Kluwer Academic Publishers 2003

Authors and Affiliations

  • C. G. Poulton
    • 1
  • R. C. McPhedran
    • 2
  • N. A. Nicorovici
    • 2
  • L. C. Botten
    • 3
  1. 1.High Frequency and Quantum Electronics LaboratoryUniversity of KarlsruheKarlsruheGermany
  2. 2.School of PhysicsUniversity of SydneyAustralia
  3. 3.School of Mathematical SciencesUniversity of TechnologySydneyAustralia

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