OSA's Digital Library

Optics Express

Optics Express

  • Editor: Andrew M. Weiner
  • Vol. 21, Iss. 1 — Jan. 14, 2013
  • pp: 927–934

Enhanced distribution of a wave-packet in lattices with disorder and nonlinearity

Uta Naether, Santiago Rojas-Rojas, Alejandro J. Martínez, Simon Stützer, Andreas Tünnermann, Stefan Nolte, Mario I. Molina, Rodrigo A. Vicencio, and Alexander Szameit  »View Author Affiliations

Optics Express, Vol. 21, Issue 1, pp. 927-934 (2013)

View Full Text Article

Enhanced HTML    Acrobat PDF (1432 KB)

Browse Journals / Lookup Meetings

Browse by Journal and Year


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools



We show, numerically and experimentally, that the presence of weak disorder results in an enhanced energy distribution of an initially localized wave-packet, in one- and two-dimensional finite lattices. The addition of a focusing nonlinearity facilitates the spreading effect even further by increasing the wave-packet effective size. We find a clear transition between the regions of enhanced spreading (weak disorder) and localization (strong disorder).

© 2013 OSA

OCIS Codes
(130.2790) Integrated optics : Guided waves
(190.0190) Nonlinear optics : Nonlinear optics
(070.7345) Fourier optics and signal processing : Wave propagation

ToC Category:
Nonlinear Optics

Original Manuscript: October 11, 2012
Revised Manuscript: November 27, 2012
Manuscript Accepted: November 28, 2012
Published: January 9, 2013

Uta Naether, Santiago Rojas-Rojas, Alejandro J. Martínez, Simon Stützer, Andreas Tünnermann, Stefan Nolte, Mario I. Molina, Rodrigo A. Vicencio, and Alexander Szameit, "Enhanced distribution of a wave-packet in lattices with disorder and nonlinearity," Opt. Express 21, 927-934 (2013)

Sort:  Author  |  Year  |  Journal  |  Reset  


  1. S. Flach and A. Gorbach, “Discrete breathers: Advances in theory and applications,” Phys. Reps.467, 1–116 (2008). [CrossRef]
  2. P. W. Anderson, “Absence of diffusion in certain random lattices,” Phys. Rev.109, 1492–1505 (1958). [CrossRef]
  3. B. Deissler, M. Zaccantu, G. Roati, C. D’Errico, M. Fattori, M. Modugno, G. Modugno, and M. Inguscio, “Delocalization of a disordered bosonic system by repulsive interactions,” Nature Phys.6, 354–358 (2010). [CrossRef]
  4. Y. S. Kivshar, S. A. Gredeskul, A. Sánchez, and L. Vázquez, “Localization decay induced by strong nonlinearity in disordered systems,” Phys. Rev. Lett.64, 1693–1696 (1990). [CrossRef] [PubMed]
  5. M. I. Molina, “Transport of localized and extended excitations in a nonlinear Anderson model,” Phys. Rev. B58, 12547–12550 (1998). [CrossRef]
  6. G. Kopidakis, S. Komineas, S. Flach, and S. Aubry, “Absence of wave packet diffusion in disordered nonlinear systems,” Phys. Rev. Lett.100, 084103 (2008). [CrossRef] [PubMed]
  7. A. S. Pikovsky and D. L. Shepelyansky, “Destruction of Anderson localization by a weak nonlinearity,” Phys. Rev. Lett.100, 094101 (2008). [CrossRef] [PubMed]
  8. S. Flach, D. O. Krimer, and Ch. Skokos, “Universal spreading of wave packets in disordered nonlinear systems,” Phys. Rev. Lett.102, 024101 (2009). [CrossRef] [PubMed]
  9. S. Fishman, Y. Krivolapov, and A. Soffer, “The nonlinear Schrödinger equation with a random potential: Results and puzzles,” eprint: arXiv 1108.2956v1 [math-ph].
  10. P. Sheng, Introduction to Wave Scattering, Localization, and Mesoscopic Phenomena (Springer, 2006).
  11. R. L. Weaver, “Anderson localization of ultrasound,” Wave Motion12, 129–142 (1990). [CrossRef]
  12. R. Dalichaouch, J. P. Armstrong, S. Schulz, P. M. Platzman, and S. L. McCal, “Microwave localization by two-dimensional random scattering,” Nature354, 53–55 (1991). [CrossRef]
  13. R. Bruinsma and S. N. Coppersmith, “Anderson localization and breakdown of hydrodynamics in random ferromagnets,” Phys. Rev. B33, 6541–6544 (1986). [CrossRef]
  14. J. Billy, V. Josse, Z. C. Zuo, A. Bernard, B. Hambrecht, P. Lugan, C. Clement, L. Sanchez-Palencia, P. Bouyer, and A. Aspect, “Direct observation of Anderson localization of matter waves in a controlled disorder,” Nature453, 891–894 (2008). [CrossRef] [PubMed]
  15. L. Sanchez-Palencia and M. Lewenstein, “Disordered quantum gases under control,” Nature Phys.6, 87–95 (2010). [CrossRef]
  16. F. Lederer, G. I. Stegeman, D. N. Christodoulides, G. Assanto, M. Segev, and Y. Silberberg, “Discrete solitons in optics,” Phys. Rep.463, 1–126 (2008). [CrossRef]
  17. T. Pertsch, U. Peschel, J. Kobelke, K. Schuster, H. Bartelt, S. Nolte, A. Tünnermann, and F. Lederer, “Nonlinearity and disorder in fiber arrays,” Phys. Rev. Lett.93, 053901 (2004). [CrossRef] [PubMed]
  18. T. Schwartz, G. Bartal, S. Fishman, and M. Segev, “Transport and Anderson localization in disordered two-dimensional photonic lattices,” Nature446, 52–55 (2007). [CrossRef] [PubMed]
  19. Y. Lahini, A. Avidan, F. Pozzi, M. Sorel, R. Morandotti, D. N. Christodoulides, and Y. Silberberg, “Anderson localization and nonlinearity in one-dimensional disordered photonic lattices,” Phys. Rev. Lett.100, 013906 (2008). [CrossRef] [PubMed]
  20. S. Flach, “Wave propagation in nonlinear disordered media,” Phys. Part. Nucl.41, 1020 (2010). [CrossRef]
  21. M. V. Ivanchenko, T. V. Laptyeva, and S. Flach, “Anderson localization or nonlinear waves? A matter of probability,” Phys. Rev. Lett.107, 240602 (2011). [CrossRef]
  22. L. Levi, M. Rechtsman, B. Freedman, T. Schwartz, O. Manela, and M. Segev, “Disorder-enhanced transport in photonic quasicrystals,” Science332, 1541–1544 (2011). [CrossRef] [PubMed]
  23. D. Weaire and A. R. Williams, “The Anderson localization problem. I. A new numerical approach,” J. Phys. C: Solid State Phys.10, 1239 (1977). [CrossRef]
  24. R. A. Vicencio and S. Flach, “Control of wave packet spreading in nonlinear finite disordered lattices,” Phys. Rev. E79, 016217 (2009). [CrossRef]
  25. D. N. Christodoulides and R. I. Joseph, “Discrete self-focusing in nonlinear arrays of coupled waveguides,” Opt. Lett.13, 794–796 (1988). [CrossRef] [PubMed]
  26. M. I. Molina and G. P. Tsironis, “Dynamics of self-trapping in the discrete nonlinear Schrödinger equation,” Phys. D65, 267–273 (1993). [CrossRef]
  27. P. G. Kevrekidis, J. A. Espinola-Rocha, Y. Drossino, and A. Stefanov, “Dynamical barrier for the formation of solitary waves in discrete lattices,” Phys. Lett. A372, 2247–2253 (2008). [CrossRef]
  28. U. Naether, A. J. Martínez, D. Guzmán-Silva, M. I. Molina, and R. A. Vicencio, “Self-trapping transition in nonlinear cubic lattices,” in preparation (2012).
  29. A. Szameit and S. Nolte, “Discrete optics in femtosecond-laser-written photonic structures,” J. Phys. B43, 163001 (2010). [CrossRef]
  30. S. Stützer, Y. Kartashov, V. Vysloukh, A. Tünnermann, S. Nolte, M. Lewenstein, L. Torner, and A. Szameit, “Anderson cross-localization,” Opt. Lett.37, 1715–1717 (2012). [CrossRef] [PubMed]
  31. B. Kramer and A. MacKinnon, “Localization: theory and experiment,” Rep. Prog. Phys.56, 1469 (1993). [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
Fig. 4

« Previous Article  |  Next Article »

OSA is a member of CrossRef.

CrossCheck Deposited