Advertisement

Asymptotics of Photonic Band Structures for Doubly-periodic Arrays

  • C. G. Poulton
  • R. C. McPhedran
  • N. A. Nicorovici
  • L. C. Botten
  • A. B. Movchan
Part of the Solid Mechanics and Its Applications book series (SMIA, volume 91)

Abstract

We examine the allowed modes of polarized electromagnetic waves moving through a doubly periodic material with a cermet topology. We present analytical results for the dispersion relations in two cases; firstly when the inclusions have arbitrary shape but the wavelength of the waves is long compared to the scale size of the material; secondly when the inclusions are circular yet are considered to be very small.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Chin, S. K., Nicorovici, N. A., and McPhedran, R. C. (1994). Green’s function and lattice sums for electromagnetic scattering by a square array of cylinders. Phys. Rev. E, 49:4590–4602.CrossRefADSGoogle Scholar
  2. Guida, G., Maystre, D., Tayeb, G., and Vincent, P. (1998). Mean-field theory of two-dimensional metallic photonic crystals. J. Opt. Soc. Am. B, 15:2308–2315.ADSCrossRefGoogle Scholar
  3. McPhedran, R. C. and Dawes, D. H. (1992). Lattice sums for an electromagnetic scattering problem. J. Electromagn. Waves Appl., 6:1327–1340.Google Scholar
  4. McPhedran, R. C., Nicorovici, N. A., Botten, L. C., and Bao, K.-D. (1997). 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.Google Scholar
  5. Movchan, A. B., Nicorovici, N. A., and McPhedran, R. C. (1997). Green’s tensors and lattice sums for elastostatics and elastodynamics. Proc. R. Soc. Lond. A, 453:643–662.ADSMathSciNetzbMATHCrossRefGoogle Scholar
  6. Nicorovici, N. A., McPhedran, R. C., and Botten, L. C. (1995). Photonic band gaps for arrays of perfectly conducting cylinders. Phys. Rev. E, 52:1135–1145.CrossRefADSGoogle Scholar
  7. Nicorovici, N. A., Poulton, C. G., and McPhedran, R. C. (1996). Analytical results for a class of sums involving Bessel functions and square arrays. J. Math. Phys., 37:2043–2052.CrossRefADSMathSciNetzbMATHGoogle Scholar
  8. Perrins, W. T., McKenzie, D. R., and McPhedran, R. C. (1979). Transport properties of regular arrays of cylinders. Proc. R. Soc. Lond. A, 369:207–225.ADSMathSciNetCrossRefGoogle Scholar
  9. Strutt, J. W. (1892). On the influence of obstacles arranged in rectangular order upon the properties of a medium. Phil. Mag., 34:481–502.Google Scholar
  10. Ward, M. J. and Keller, J. B. (1993). Strong localized perturbations of eigenvalue problems. SIAM J. Appl. Math., 53:770–798.MathSciNetzbMATHCrossRefGoogle Scholar

Copyright information

© Kluwer Academic Publishers 2001

Authors and Affiliations

  • C. G. Poulton
    • 1
  • R. C. McPhedran
    • 1
  • N. A. Nicorovici
    • 1
  • L. C. Botten
    • 2
  • A. B. Movchan
    • 3
  1. 1.School of PhysicsUniversity of SydneyAustralia
  2. 2.School of Mathematical SciencesUniversity of TechnologySydneyAustralia
  3. 3.School of Mathematical SciencesUniversity of BathBathUK

Personalised recommendations