OSA's Digital Library

Journal of the Optical Society of America B

Journal of the Optical Society of America B


  • Vol. 21, Iss. 1 — Jan. 1, 2004
  • pp: 132–140

Almost localized photon modes in continuous and discrete models of disordered media

V. M. Apalkov, M. E. Raikh, and B. Shapiro  »View Author Affiliations

JOSA B, Vol. 21, Issue 1, pp. 132-140 (2004)

View Full Text Article

Enhanced HTML    Acrobat PDF (201 KB)

Browse Journals / Lookup Meetings

Browse by Journal and Year


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools



In a weakly disordered sample, light waves (or electrons) propagate, on average, by diffusion. However, with some small probability, random high-quality cavities can be formed within the sample. Such cavities are due to rare events, i.e., to some rare disorder configurations which can support “almost localized” eigenstates and thus can trap the wave for a long time in a small region of space of sub-mean-free-path size. The almost localized states are nonuniversal in the sense that their character and likelihood are determined not only by the average strength of the disorder (the dimensionless conductance) but also by microscopic details of the system. In particular, they are extremely sensitive to the correlation radius Rc of the disordered potential. Moreover, on a lattice, a new type of almost localized state becomes possible that has no analog in the continuum. The likelihood of these lattice-specific states decreases with the increase of Rc, in sharp contrast to the situation in the continuum. We review the earlier work on the almost localized states in the continuum and develop a theory of those states on a lattice. We emphasize that extreme care must be taken in trying to simulate on a lattice the rare events in a continuous, random medium.

© 2004 Optical Society of America

OCIS Codes
(000.6800) General : Theoretical physics
(140.7010) Lasers and laser optics : Laser trapping
(290.4210) Scattering : Multiple scattering

V. M. Apalkov, M. E. Raikh, and B. Shapiro, "Almost localized photon modes in continuous and discrete models of disordered media," J. Opt. Soc. Am. B 21, 132-140 (2004)

Sort:  Author  |  Year  |  Journal  |  Reset  


  1. H. Cao, Y. G. Zhao, S. T. Ho, E. W. Seelig, Q. H. Wang, and R. P. H. Chang, “Random laser action in semiconductor powder,” Phys. Rev. Lett. 82, 2278–2281 (1999). [CrossRef]
  2. S. V. Frolov, Z. V. Vardeny, K. Yoshino, A. Zakhidov, and R. H. Baughman, “Stimulated emission in high-gain organic media,” Phys. Rev. B 59, R5284–R5287 (1999). [CrossRef]
  3. A. A. Chabanov, Z. Q. Zhang, and A. Z. Genack, “Breakdown of diffusion in dynamics of extended waves in mesoscopic media,” http://arxiv.org/abs/cond-mat/0211651.
  4. B. L. Altshuler, V. E. Kravtsov, and I. V. Lerner, “Distribution of mesoscopic fluctuations and relaxation processes in disordered conductors,” in Mesoscopic Phenomena in Solids, B. L. Altshuler, P. A. Lee, and R. A. Webb, eds. (North-Holland, Amsterdam, 1991).
  5. B. A. Muzykantskii and D. E. Khmelnitskii, “Nearly localized states in weakly disordered conductors,” Phys. Rev. B 51, 5480–5483 (1995). [CrossRef]
  6. V. I. Fal’ko and K. B. Efetov, “Statistics of prelocalized states in disordered conductors,” Phys. Rev. B 52, 17413–17429 (1995). [CrossRef]
  7. A. D. Mirlin, “Statistics of energy levels and eigenfunctions in disordered systems,” Phys. Rep. 326, 259–382 (2000). [CrossRef]
  8. V. G. Karpov, “Resonant electronic states in disordered systems,” Phys. Rev. B 48, 4325–4328 (1993). [CrossRef]
  9. V. G. Karpov, “Quasilocalized sound excitations in disordered systems,” Phys. Rev. B 48, 12539–12549 (1993). [CrossRef]
  10. V. M. Apalkov, M. E. Raikh, and B. Shapiro, “Random resonators and prelocalized modes in disordered dielectric films,” Phys. Rev. Lett. 89, 016802–016805 (2002). [CrossRef] [PubMed]
  11. V. M. Apalkov, M. E. Raikh, and B. Shapiro, “Crossover between universality classes in the statistics of rare events in disordered conductors,” Phys. Rev. Lett. 89, 126601–126604 (2002). [CrossRef] [PubMed]
  12. V. M. Apalkov, M. E. Raikh, and B. Shapiro, “Coherent random lasing and ‘almost localized’ photon modes,” http://arxiv.org/abs/cond-mat/0212231.
  13. V. Uski, B. Mehlig, R. A. Römer, and M. Schreiber, “Exact diagonalization study of rare events in disordered conductors,” Phys. Rev. B 62, R7699–R7702 (2000). [CrossRef]
  14. V. Uski, B. Mehlig, and M. Schreiber, “Signature of ballistic effects in disordered conductors,” Phys. Rev. B 63, R241101–241104 (2001). [CrossRef]
  15. V. Uski, B. Mehlig, and M. Schreiber, “Spatial structure of anomalously localized states in disordered conductors,” Phys. Rev. B 66, 233104–233107 (2002). [CrossRef]
  16. B. K. Nikolic and P. B. Allen, “Resistivity of a metal between the Boltzmann transport regime and the Anderson transition,” Phys. Rev. B 63, 020201–020204 (2001). [CrossRef]
  17. B. K. Nikolic, “Statistical properties of eigenstates in three-dimensional mesoscopic systems with off-diagonal or diagonal disorder,” Phys. Rev. B 64, 014203–014210 (2001). [CrossRef]
  18. B. K. Nikolic, “Quest for rare events in mesoscopic disordered metals,” Phys. Rev. B 65, 012201–012204 (2002). [CrossRef]
  19. B. K. Nikolic and V. Z. Cerovski, “Structure of quantum disordered wave functions: weak localization, far tails, and mesoscopic transport,” Eur. Phys. J. B 30, 227–238 (2002). [CrossRef]
  20. A. Ossipov, T. Kottos, and T. Geisel, “Signatures of prelocalized states in classically chaotic systems,” Phys. Rev. E 65, 055209–055212 (2002). [CrossRef]
  21. M. Patra, “Influence of spatial correlations on the lasing threshold of random lasers,” http://arxiv.org/abs/cond-mat/0302506.
  22. M. L. Mehta, Random Matrices and the Statistical Theory of Energy Levels (Academic, New York, 1991).
  23. The opposite case of light trapping by strongly non-Gaussian disorder was addressed numerically in C. Vanneste and P. Sebbah, “Selective excitation of localized modes in active random media,” Phys. Rev. Lett. 87, 183903–183906 (2001). [CrossRef]
  24. B. I. Halperin and M. Lax, “Impurity-band tails in the high-density limit. I. Minimum counting methods,” Phys. Rev. 148, 722–740 (1966). [CrossRef]
  25. J. Zittartz and J. S. Langer, “Theory of bound states in a random potential,” Phys. Rev. 148, 741–747 (1966). [CrossRef]
  26. G. R. Williams, S. B. Bayram, S. C. Rand, T. Hinklin, and R. M. Laine, “Laser action in strongly scattering rare-earth-metal-doped dielectric nanophosphors,” Phys. Rev. A 65, 013807–013812 (2002). [CrossRef]
  27. X. Jiang and C. M. Soukoulis, “Time dependent theory for random lasers,” Phys. Rev. Lett. 85, 70–73 (2000). [CrossRef] [PubMed]
  28. D. S. Wiersma, P. Bartolini, A. Lagendijk, and R. Righini, “Localization of light in a disordered medium,” Nature 390, 671–673 (1997). [CrossRef]

Cited By

Alert me when this paper is cited

OSA is able to provide readers links to articles that cite this paper by participating in CrossRef's Cited-By Linking service. CrossRef includes content from more than 3000 publishers and societies. In addition to listing OSA journal articles that cite this paper, citing articles from other participating publishers will also be listed.


Fig. 1 Fig. 2 Fig. 3

« Previous Article  |  Next Article »

OSA is a member of CrossRef.

CrossCheck Deposited