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Journal of the Optical Society of America A

Journal of the Optical Society of America A

| OPTICS, IMAGE SCIENCE, AND VISION

  • Vol. 15, Iss. 5 — May. 1, 1998
  • pp: 1423–1435

Localization of light in lossless inhomogeneous dielectrics

Alexander Figotin and Abel Klein  »View Author Affiliations


JOSA A, Vol. 15, Issue 5, pp. 1423-1435 (1998)
http://dx.doi.org/10.1364/JOSAA.15.001423


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Abstract

The localization of electromagnetic waves in lossless inhomogeneous dielectric media is studied. We consider a three-dimensional lossless periodic medium (photonic crystal) having a gap in the frequency spectrum (photonic bandgap). If such a medium is perturbed by either a single defect or a random array of defects, exponentially localized electromagnetic waves arise with frequencies in the gap. For a single defect, we derive equations for these midgap frequencies and estimate their number. For a random medium, we show the occurrence of Anderson localization for electromagnetic waves.

© 1998 Optical Society of America

OCIS Codes
(260.2110) Physical optics : Electromagnetic optics
(350.7420) Other areas of optics : Waves

Citation
Alexander Figotin and Abel Klein, "Localization of light in lossless inhomogeneous dielectrics," J. Opt. Soc. Am. A 15, 1423-1435 (1998)
http://www.opticsinfobase.org/josaa/abstract.cfm?URI=josaa-15-5-1423


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References

  1. P. W. Anderson, “A question of classical localization. A theory of white paint,” Philos. Mag. B 53, 505–509 (1985).
  2. P. Sheng, ed., Scattering and Localization of Classical Waves (World Scientific, Singapore, 1990).
  3. S. John, “Localization of light,” Phys. Today 44 (5), 32–40 (1991).
  4. S. John, “The localization of light,” in Photonic Band Gaps and Localization, C. M. Soukoulis, ed., Vol. 308 of NATO ASI Ser. B. (Plenum, New York, 1993), pp. 1–22.
  5. R. Meade, D. Brommer, A. Rappe, and J. Joannopoulos, “Photonic bound states in periodic materials,” Phys. Rev. Lett. 67, 3380–3384 (1991).
  6. J. Rarity and C. Weisbuch, eds., Microcavities and Photonic Bandgaps: Physics and Applications (Kluwer Academic, Dordrecht, The Netherlands, 1995).
  7. C. Soukoulis, ed., Photonic Band Gap Materials (Kluwer Academic, Dordrecht, The Netherlands, 1996).
  8. A. Figotin and A. Klein, “Localization of electromagnetic and acoustic waves in random media. Lattice model,” J. Stat. Phys. 76, 985–1003 (1994).
  9. A. Figotin and A. Klein, “Localization of classical waves II: Electromagnetic waves,” Commun. Math. Phys. 184, 411–441 (1997).
  10. A. Figotin and A. Klein, “Localized classical waves created by defects,” J. Stat. Phys. 86, 165–177 (1997).
  11. A. Figotin and A. Klein, “Midgap defect modes in dielectric and acoustic media,” SIAM (Soc. Ind. Appl. Math.) J. Appl. Math. (to be published).
  12. Special issue on development and applications of materials exhibiting photonic bandgaps, J. Opt. Soc. Am. B 10, 279–413 (1993).
  13. P. R. Villeneuve and M. Piché, “Photonic band gaps in periodic dielectric structures,” Prog. Quantum Electron. 18, 153–200 (1994).
  14. P. M. Hui and N. F. Johnson, “Photonic band-gap materials,” in Solid State Physics, H. Ehrenreich and F. Spaepen, eds. (Academic, New York, 1995), Vol. 49, pp. 151–203.
  15. P. R. Villeneuve and J. Joannopoulos, “Working at the speed of light,” Sci. Spectra 9, 18–24 (1997).
  16. J. Joannopoulos, R. Meade, and J. Winn, Photonic Crystals (Princeton U. Press, Princeton, N.J., 1995).
  17. C. Soukoulis, ed., Photonic Band Gaps and Localization (Plenum, New York, 1993).
  18. E. Yablonovitch, T. Gmitter, R. Meade, D. Brommer, A. Rappe, and J. Joannopoulos, “Donor and acceptor modes in photonic periodic structure,” Phys. Rev. B 44, 13772–13774 (1991).
  19. A. Figotin and P. Kuchment, “Band-gap structure of spectra of periodic dielectric and acoustic media. I. Scalar model,” SIAM (Soc. Ind. Appl. Math.) J. Appl. Math. 56, 68–88 (1996).
  20. A. Figotin and P. Kuchment, “Band-gap structure of spectra of periodic dielectric and acoustic media. II. 2D photonic crystals,” SIAM (Soc. Ind. Appl. Math.) J. Appl. Math. 56, 1561–1620 (1996).
  21. P. W. Anderson, “Absence of diffusion in certain random lattice,” Phys. Rev. 109, 1492–1505 (1958).
  22. B. Shklovskii and A. Efros, Electronic Properties of Doped Semiconductors (Springer-Verlag, Heidelberg, 1984).
  23. I. M. Lifshits, S. A. Greduskul, and L. A. Pastur, Introduction to the Theory of Disordered Systems (Wiley, New York, 1988).
  24. J. Fröhlich and T. Spencer, “Absence of diffusion in the Anderson tight binding model for large disorder or low energy,” Commun. Math. Phys. 88, 151–184 (1983).
  25. J. Fröhlich, F. Martinelli, E. Scoppola, and T. Spencer, “Constructive proof of localization in the Anderson tight binding model,” Commun. Math. Phys. 101, 21–46 (1985).
  26. H. Holden and F. Martinelli, “On absence of diffusion near the bottom of the spectrum for a random Schrödinger operator on L2(Rν),” Commun. Math. Phys. 93, 197–217 (1984).
  27. H. Cycon, R. Froese, W. Kirsch, and B. Simon, Schrödinger Operators (Springer-Verlag, Heidelberg, 1987).
  28. H. Dreifus and A. Klein, “A new proof of localization in the Anderson tight binding model,” Commun. Math. Phys. 124, 285–299 (1989).
  29. R. Carmona and J. Lacroix, Spectral Theory of Random Schrödinger Operators (Birkhäuser, Boston, Mass., 1990).
  30. L. Pastur and A. Figotin, Spectra of Random and Almost-Periodic Operators (Springer-Verlag, Heidelberg, 1991).
  31. J. Combes and P. Hislop, “Localization for some continuous, random Hamiltonians in d-dimensions,” J. Funct. Anal. 124, 149–180 (1994).
  32. A. Figotin and A. Klein, “Localization phenomenon in gaps of the spectrum of random lattice operators,” J. Stat. Phys. 75, 997–1021 (1994).
  33. A. Figotin and A. Klein, “Localization of classical waves I: Acoustic waves,” Commun. Math. Phys. 180, 439–482 (1996).
  34. J. Maynard, “Acoustic Anderson localization,” in Random Media and Composites, B. V. Kohn and G. W. Milton, eds., (Society for Industrial and Applied Mathematics, Philadel-phia, Pa., 1988), pp. 206–207.
  35. W. Kohler, G. Papanicolaou, and B. White, “Localization and mode conversion for elastic waves in randomly layered media,” Wave Motion 23, 1–22 and 181–201 (1996).
  36. A. Maradudin, E. Montroll, and G. Weiss, Theory of Lattice Dynamics in the Harmonic Approximation (Academic, New York, 1963).
  37. L. Deych and A. Lisyansky, “Impurity localization of electromagnetic waves in polariton region,” Phys. Rev. Lett. (to be published).
  38. Research done by F. Klopp on Internal Lifshits tails for random perturbations of periodic Schrödinger operators.
  39. L. Schiff, Quantum Mechanics (McGraw-Hill, New York, 1968).
  40. M. Reed and B. Simon, Analysis of Operators, Vol. 4 of Methods of Modern Mathematical Physics (Academic, New York, 1978).
  41. M. Klaus, “Some applications of the Birman–Schwinger principle,” Helv. Phys. Acta 55, 49–68 (1982).

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