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4. A Solid-State Theoretical Approach to the Optical Properties of Photonic Crystals

  • K. Busch
  • F. Hagmann
  • D. Hermann
  • S.F. Mingaleev
  • M. Schillinger
Part I Basic Description of Electrons and Photons in Crystals
  • 2.1k Downloads
Part of the Lecture Notes in Physics book series (LNP, volume 642)

Abstract

In this chapter, we outline an efficient approach to the calculation of the optical properties of Photonic Crystals. It is based on solid state theoretical concepts and exploits the conceptual similarity between electron waves propagation in electronic crystals and electromagnetic waves propagation in Photonic Crystals. Based on photonic bandstructure calculations for infinitely extended and perfectly periodic systems, we show how defect structures can be described through an expansion of the electromagnetic field into optimally localized photonic Wannier functions which have encoded in themselves all the information of the underlying Photonic Crystals. This Wannier function approach is supplemented by a multipole expansion method which is well-suited for finite-sized and disordered structures. To illustrate the workings and efficiency of both approaches, we consider several defect structures for TM-polarized radiation in two-dimensional Photonic Crystals.

Keywords

Photonic Crystal Cavity Mode Wannier Function Plane Wave Method Fabricational Tolerance 
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. G.P. Agrawal: Nonlinear Fiber Optics, 3rd edn (Academic Press, San Diego Dan Francisco New York Boston London Sydney Tokyo 2001)Google Scholar
  2. 2. R. März: Integrated Optics: Design and Modeling, (Artech House, 1995)Google Scholar
  3. 3. E. Yablonovitch, Phys. Rev. Lett. 58, 2059 (1987)Google Scholar
  4. 4. Phys. Rev. Lett. 58, 2486 (1987)Google Scholar
  5. 5. A. Birner, R.B. Wehrspohn, U.M. Gösele, and K. Busch, Adv. Mater. 13, 377 (2001)Google Scholar
  6. 6. T.F. Krauss and R.M. de la Rue, Prog. Quantum Electron. 23, 51 (1999)Google Scholar
  7. 7. A. Forchel et al., Microelectron. Eng. 53, 21 (2000)Google Scholar
  8. 8. M. Loncar, T. Doll, J. Vuckovic, and A. Scherer, J. Lightwave Technol. 18, 1402 (2000)Google Scholar
  9. 9. H. Benisty et al., IEEE J. Quantum Electron. 38, 770 (2002)Google Scholar
  10. 10. S. Noda, M. Imada, A. Chutinan, and N. Yamamoto, Opt. Quantum Electron. 34, 723 (2002)Google Scholar
  11. 11. C. Liguda et al., Appl. Phys. Lett. 78, 2434 (2001)Google Scholar
  12. 12. A.C. Edrington et al., Adv. Mater. 13, 421 (2001)Google Scholar
  13. 13. A. Rosenberg, R.J. Tonucci, H.B. Lin, and E.L. Shirley, Phys. Rev. B 54, R5195 (1996)Google Scholar
  14. 14. O.J.A. Schueller et al., Appl. Opt. 38, 5799 (1999)Google Scholar
  15. 15. S.-Y. Lin et al., Nature 394, 251 (1998)Google Scholar
  16. 16. S. Noda, K. Tomoda, N. Yamamoto, and A. Chutinan, Science 289, 604 (2000)Google Scholar
  17. 17. J.E.G.J. Wijnhoven and W.L. Vos, Science 281, 802 (1998)Google Scholar
  18. 18. A. Blanco et al., Nature 405, 437 (2000)Google Scholar
  19. 19. Y.A. Vlasov, X.Z. Bo, J.C. Sturm, and D.J. Norris, Nature 414, 289 (2001)Google Scholar
  20. 20. M. Campbell et al., Nature 404, 53 (2000)Google Scholar
  21. 21. Y.V. Miklyaev et al., Appl. Phys. Lett. 82, 1284 (2003)Google Scholar
  22. 22. H.B. Sun, S. Matsuo, and H. Misawa, Appl. Phys. Lett. 74, 786 (1999)Google Scholar
  23. 23. H.B. Sun et al., Appl. Phys. Lett. 79, 1 (2001)Google Scholar
  24. 24. M. Straub and M. Gu, Opt. Lett. 27, 1824 (2002)Google Scholar
  25. 25. N. Vats, S. john, and K. Busch, Phys. Rev. A 65, 043808 (2002)Google Scholar
  26. 26. K. Busch and S. John, Phys. Rev. E 58, 3896 (1998)Google Scholar
  27. 27. D. Hermann, M. Frank, K. Busch, and P. Wölfle, Optics Express 8, 167 (2001)Google Scholar
  28. 28. K.-M. Ho, C.T. Chan, and C.M. Soukoulis Phys. Rev. Lett. 65, 3152 (1990)Google Scholar
  29. 29. K. Busch and S. John, Phys. Rev. Lett. 83, 967 (1999)Google Scholar
  30. 30. A. Brandt, S. McCormick, and J. Ruge, SIAM J. Sci. Stat. Comput. 4, 244 (1983)Google Scholar
  31. 31. K. Busch, S.F. Mingaleev, A. Garcia-Martin, M. Schillinger, D. Hermann, J. Phys.: Condens. Matter 15, R1233 (2003)Google Scholar
  32. 32. N. Marzari and D. Vanderbilt, Phys. Rev. B 56, 12847 (1997)Google Scholar
  33. 33. A. Garcia-Martin, D. Hermann, K. Busch, and P. Wölfle, Mater. Res. Soc. Symp. Proc. 722, L 1.1 (2002)Google Scholar
  34. 34. D.M. Whittaker and M.P. Croucher, Phys. Rev. B 67, 085204 (2003)Google Scholar
  35. 35. A. Mekis et al., Phys. Rev. Lett. 77, 3787 (1996)Google Scholar
  36. 36. J.D. Joannopoulos, P.R. Villeneuve, and S.H. Fan, Nature 386, 143 (1997)Google Scholar
  37. 37. S.F. Mingaleev and Y.S. Kivshar, Opt. Lett. 27, 231 (2002)Google Scholar
  38. 38. S.F. Mingaleev and K. Busch, Opt. Lett. 28, 619 (2003)Google Scholar
  39. 39. H. Brand: Schaltungslehre linearer Mikrowellennetze, (Hirzel, Stuttgart 1995)Google Scholar
  40. 40. D. Hermann, A. Garcia-Martin, J.J. Saenz, S.F. Mingaleev, M. Schillinger, and K. Busch, in preparationGoogle Scholar
  41. 41. A.A. Asatryan et al., Phys. Rev. E 63, 046612 (2001)Google Scholar
  42. 42. A.A. Asatryan et al., Waves in Random Media 13, 9 (2003)Google Scholar
  43. 43. F. Hagmann and K. Busch, unpublishedGoogle Scholar

Authors and Affiliations

  • K. Busch
    • 1
  • F. Hagmann
    • 1
  • D. Hermann
    • 1
  • S.F. Mingaleev
    • 1
    • 2
  • M. Schillinger
    • 2
  1. 1.Institut für Theorie der Kondensierten Materie, Universität Karlsruhe, 76128 KarlsruheGermany
  2. 2.Bogolyubov Institute for Theoretical Physics, 03143 KievUkraine

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