Advertisement

Electromagnetic Modelling of Dielectric and Metallic Photonic Crystals

  • D. Maystre
  • G. Tayeb
  • P. Vincent
  • S. Enoch
  • G. Guida
Part of the Solid Mechanics and Its Applications book series (SMIA, volume 91)

Conclusion

In a first part of this paper, it has been shown from numerical results based on a theory of scattering from thin metallic wires that the formulae coming from mathematical studies of homogenization provides a precise estimate of the properties of metallic photonic crystals, even when the wavelength has the same order of magnitude as the period of the crystal. This property which could simplify considerably the numerical calculations is all the more interesting since it extends to doped crystals.

In a second part we have confirmed from numerical calculations the phenomenon of ultrarefraction generated by photonic crystals at the edges of a gap.

Keywords

Photonic Crystal Incident Field Optical Index Electric Field Parallel Transmitted Field 
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.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. [1]
    J.B. Pendry, A.J. Holden, W.J. Stewart, and I. Youngs, “Extremely low frequency plasmons in metallic mesostructures”, Phys. Rev. Lett. 76, 4773–4776 (1996).CrossRefADSGoogle Scholar
  2. [2]
    D. Felbacq and G. Bouchitté, “Homogenization of a set of parallel fibers”, Waves in random media 7, 245–256 (1997).CrossRefADSMathSciNetzbMATHGoogle Scholar
  3. [3]
    R.C. McPhedran, C.G. Poulton, N.A. Nicorovici and A.B. Movchan, “Low frequency corrections to the static effective dielectric constant of a two-dimensional composite material”, Proc. R. Soc. Lond. A 452, 2231–2245 (1996).ADSGoogle Scholar
  4. [4]
    R.C. McPhedran, N.A. Nicorovici and L.C Botten, “The TEM mode and homogenization of doubly periodic structures”, J. Electrom. Waves and Appl. 11, 981–1012 (1997).zbMATHCrossRefGoogle Scholar
  5. [5]
    D. Maystre, “Electromagnetic study of photonic band gaps”, Pure Appl. Opt. 8, 875–993 (1994).Google Scholar
  6. [6]
    D. Felbacq, G. Tayeb and D. Maystre, “Scattering by a random set of parallel cylinders”, J. Opt. Soc. Am. A 11, 2526–2538 (1994).ADSMathSciNetCrossRefGoogle Scholar
  7. [7]
    G. Guida, D. Maystre, G. Tayeb, and P. Vincent, “Electromagnetic modelling of three-dimensional metallic photonic crystals”, J. Electr. Waves and Appl. 12, 1153–1179 (1998).zbMATHCrossRefGoogle Scholar
  8. [8]
    S. Enoch, G. Tayeb and D. Maystre, “Numerical evidence of ultrarefractive optics in photonic crystals”, Optics Comm. 161, 171–176 (1999).ADSCrossRefGoogle Scholar
  9. [9]
    R. Harrington, “Matrix methods for field problems”, Proc. IEEE, Vol. 55, No. 2, 136–149 (1967).CrossRefGoogle Scholar
  10. [11]
    G. Guida, “Numerical study of band gaps generated by randomly perturbed bidimensional metallic cubic photonic crystals”, Optics Comm. 156, 294–296 (1998).CrossRefADSGoogle Scholar
  11. [12]
    G. Guida, D. Maystre, G. Tayeb and P. Vincent, “Mean-field theory of two-dimensional metallic photonic crystals”, J. Opt. Soc. Am. B 15, 2308–2315 (1998).ADSGoogle Scholar
  12. [13]
    J.P. Dowling and C.M. Bowden, “Anomalous index of refraction in photonic bandgap materials”, Journal of Modern Optics 41, 345–351 (1994).ADSCrossRefGoogle Scholar
  13. [14]
    P. M. Wisser, G. Nienhuis, “Band gaps and group velocity in optical lattices”, Optics Comm. 136, 470–479 (1997).ADSCrossRefGoogle Scholar
  14. [15]
    R. Zengerle, “Light propagation in singly and doubly periodic planar waveguides”, J. Mod. Optics 34, 1589–1617 (1987).ADSCrossRefGoogle Scholar
  15. [16]
    D.R. Smith, S. Schultz, S.L. McCall, P.M. Platzmann, “Defect studies in a twodimensional periodic photonic lattice”, Journal of Modern Optics 41, 395–404 (1994).ADSCrossRefGoogle Scholar
  16. [17]
    M. Plihal and A.A. Maradudin, “Photonic band structure of two-dimensional systems: the triangular lattice”, Phys. Rev. B44, 8565–8571 (1991).ADSGoogle Scholar

Copyright information

© Kluwer Academic Publishers 2001

Authors and Affiliations

  • D. Maystre
    • 1
  • G. Tayeb
    • 1
  • P. Vincent
    • 1
  • S. Enoch
    • 1
  • G. Guida
    • 1
  1. 1.Faculté des Sciences et Techniques de St Jérôme, case 262Institut FresnelMarseille Cedex 20France

Personalised recommendations