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Optical and Quantum Electronics

, Volume 45, Issue 4, pp 317–327 | Cite as

Full vectorial band structure computation of photonic crystals with hexagonal lattice and a staircase approximation of the slanted unit cells

  • Stefan F. HelfertEmail author
  • Markus Daubenschüz
Article

Abstract

This paper describes band structure computations of photonic crystals with a hexagonal lattice. Particularly, the full vectorial three-dimensional case is considered. The unit cells are approximated with a staircase approximation. Due to their periodicity, fields inside the computational window can be related to those outside of this area. Numerical results are compared with those from the literature and show a very good agreement.

Keywords

Photonic crystals Band structures Method of Lines Staircase approximation of the unit cell 

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References

  1. Bienstman P., Baets R.: Optical modelling of photonic crystals and VCSELs using eigenmode expansion and perfectly matched layers. Opt Quantum Electron 33, 327–341 (2001)CrossRefGoogle Scholar
  2. Bogaerts W., Bienstman P., Taillaert D., Baets R., De-Zutter D.: Out-of-plane scattering in 1-D photonic crystal slabs. Opt Quantum Electron 34, 195–203 (2002)CrossRefGoogle Scholar
  3. Cao Q., Lalanne P., Hugonin J.P.: Stable and efficient bloch–mode computational method for one–dimensional grating waveguides. J Opt Soc Am A Opt Image Sci 19(2), 335–338 (2002)ADSCrossRefGoogle Scholar
  4. Cryan M.J., Wong D.C.L., Craddock I.J., Yu S., Rorison J., Railton C.J.: Electromagnetic analysis of photonic crystals waveguide operating above the light cone. IEEE Photonics Technol Lett 17, 58–60 (2005)ADSCrossRefGoogle Scholar
  5. Edelmann A.G., Helfert S.F.: Three-dimensional analysis of hexagonal structured photonic crystals using oblique coordinates. Opt Quantum Electron 41, 243–254 (2009)CrossRefGoogle Scholar
  6. Guo S., Albin S.: Numerical technique for excitation and analysis of defect modes in photonic crystals. Opt Expr 11(9), 1080–1089 (2003)ADSCrossRefGoogle Scholar
  7. Helfert S.F.: Numerical stable determination of Floquet–modes and the application to the computation of band structures. Opt Quantum Electron 36, 87–107 (2004)CrossRefGoogle Scholar
  8. Helfert S.F.: Determination of Floquet–modes in asymmetric periodic structures. Opt Quantum Electron 37, 185–197 (2005)CrossRefGoogle Scholar
  9. Helfert S.F.: Applying oblique coordinates to the method of lines. Prog Electrom Res 61, 271–278 (2006)ADSCrossRefGoogle Scholar
  10. Helfert S.F.: Staircase approximation of oblique boundaries to compute band structures of photonic crystals. Opt Quantum Electron 42, 447–461 (2010)CrossRefGoogle Scholar
  11. Helfert S.F., Pregla R.: The method of lines: a versatile tool for the analysis of waveguide structures. Electromagnetics 22:615–637, invited paper for the special issue on “Optical wave propagation in guiding structures” (2002)Google Scholar
  12. Helfert S.F., Barcz A., Pregla R.: Three–dimensional vectorial analysis of waveguide structures with the method of lines. Opt Quantum Electron 35, 381–394 (2003)CrossRefGoogle Scholar
  13. Joannopoulus J.D., Meade R.D., Winn J.N.: Photonic Crystals—Molding the Flow of Light. Princeton University Press, Princeton (1995)Google Scholar
  14. John S.: Strong localisation of photons in certain disordered dielectric superlattices. Phys Rev Lett 58, 2486–2489 (1987)ADSCrossRefGoogle Scholar
  15. Johnson S.G., Joannopoulos J.D.: Photonic Crystals—the Road from Theory to Practice. Kluwer, Boston (2002)Google Scholar
  16. Pregla R.: Methods for modeling and simulation of Guided-Wave optoelectronic devices (PIER 11), MoL-BPM method of lines based beam propagation method. In: Huang, W.P. (ed) Progress in Electromagnetic Research, pp. 51–102. EMW Publishing, Cambridge (1995)Google Scholar
  17. Pregla R.: Efficient modeling of periodic structures. AEÜ 57, 185–189 (2003)Google Scholar
  18. Pregla R.: Analysis of Electromagnetic Fields and Waves—the Method of Lines. Wiley, Chichester (2008)CrossRefGoogle Scholar
  19. Pregla R., Pascher W.: The method of lines. In: Itoh, T. (eds) Numerical Techniques for Microwave and Millimeter Wave Passive Structures, pp. 381–446. Wiley, New York (1989)Google Scholar
  20. Soukoulis C.M.: Bending back light: the science of negative index materials. Opt Phot News 17, 16–21 (2006)ADSCrossRefGoogle Scholar
  21. Villeneuve P.R., Fan S., Johnson S.G., Joannopoulos J.D.: Three–dimensional photon confinement in photonic crystals of low–dimensional periodicity. IEE Proc Optoelectron 145(6), 384–390 (1998)CrossRefGoogle Scholar
  22. Wu N., Javanmard M., Momeni B., Soltani M., Adibi A., Xu Y., Lee R.K.: General methods for designing single-mode planar photonic crystal waveguides in hexagonal lattice structures. Opt Expr 11(12), 1371–1377 (2003)ADSCrossRefGoogle Scholar
  23. Yablonovitch E.: Inhibited spontaneous emission in solid-state physics and electronics. Phys Rev Lett 58, 2059–2062 (1987)ADSCrossRefGoogle Scholar
  24. Ziolkowski R.W., Tanaka M.: FDTD analysis of PBG waveguides, power splitters and switches. Opt Quantum Electron 31, 843–855 (1999)CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media New York 2012

Authors and Affiliations

  1. 1.FernUniversität in HagenHagenGermany

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