Skip to main content

Thank you for visiting nature.com. You are using a browser version with limited support for CSS. To obtain the best experience, we recommend you use a more up to date browser (or turn off compatibility mode in Internet Explorer). In the meantime, to ensure continued support, we are displaying the site without styles and JavaScript.

  • Review Article
  • Published:

Anderson localization of light

Nature Photonics volume 7, pages 197–204 (2013)Cite this article

Subjects

Abstract

Over the past decade, the Anderson localization of light and a wide variety of associated phenomena have come to the forefront of research. Numerous investigations have been made into the underlying physics of how disorder affects transport in a crystalline lattice incorporating disorder. The physics involved relies on the analogy between the paraxial equation for electromagnetic waves and the Schrödinger equation describing quantum phenomena. Experiments have revealed how wavefunctions evolve during the localization process, and have led to discoveries of new physics that are universal to wave systems incorporating disorder. This Review summarizes the phenomena associated with the transverse localization of light, with an emphasis on the history, new ideas and future exploration of the field.

This is a preview of subscription content, access via your institution

Access options

Buy this article

  • Purchase on Springer Link
  • Instant access to full article PDF
Buy now

Prices may be subject to local taxes which are calculated during checkout

Figure 1: Transition from ballistic transport to diffusive transport, and eventually to Anderson localization.
Figure 2: Hyper-transport of a light beam propagating through fluctuating spatial disorder.
Figure 3: Simulations of the correlations between the positions of two particles co-localizing in a disordered lattice.
Figure 4: Experimental measurements of quantum correlations in a 1D photonic lattice.

Similar content being viewed by others

Article 30 March 2021

Andrew Forbes, Michael de Oliveira & Mark R. Dennis

References

  1. Anderson, P. W. Absence of diffusion in certain random lattices. Phys. Rev. 109, 1492–1505 (1958).

    Article  ADS  Google Scholar 

  2. John, S. Electromagnetic absorption in a disordered medium near a photon mobility edge. Phys. Rev. Lett. 53, 2169–2172 (1984).

    Article  ADS  Google Scholar 

  3. Anderson, P. W. The question of classical localization: A theory of white paint. Phil. Mag. B 52, 505–509 (1985).

    Article  ADS  Google Scholar 

  4. John, S. Strong localization of photons near in certain disordered dielectric superlattices. Phys. Rev. Lett. 58, 2486–2489 (1987).

    Article  ADS  Google Scholar 

  5. Dalichaouch, R. et al. Microwave localization by 2-dimensional random scattering. Nature 354, 53–55 (1991).

    Article  ADS  Google Scholar 

  6. Wiersma, D. S., Bartolini, P., Lagendijk, A. & Righini, R. Localization of light in a disordered medium. Nature 390, 671–673 (1997).

    Article  ADS  Google Scholar 

  7. Chabanov, A. A., Stoytchev, M. & Genack, A. Z. Statistical signatures of photon localization. Nature 404, 850–853 (2000).

    Article  ADS  Google Scholar 

  8. Störzer, M., Gross, P., Aegerter, C. M. & Maret, G. Observation of the critical regime near Anderson localization of light. Phys. Rev. Lett. 96, 063904 (2006).

    Article  ADS  Google Scholar 

  9. De Raedt, H., Lagendijk, A. & de Vries, P. Transverse localization of light. Phys. Rev. Lett. 62, 47–50 (1989).

    Article  ADS  Google Scholar 

  10. Abdullaev, S. S. & Abdullaev, F. K. On light propagation in a system of tunnel-coupled waveguides. Izv. Vuz. Radiofiz. 23, 766 (1980).

    Google Scholar 

  11. Christodoulides, D. N. & Joseph, R. I. Discrete self-focusing in a nonlinear array of coupled waveguides. Opt. Lett. 13, 794–796 (1988).

    Article  ADS  Google Scholar 

  12. Eisenberg, H. et al. Discrete spatial optical solitons in waveguide arrays. Phys. Rev. Lett. 81, 3383–3386 (1998).

    Article  ADS  Google Scholar 

  13. Fleischer, J. W., Segev, M., Efremidis, N. K. & Christodoulides, D. N. Observation of two-dimensional discrete solitons in optically induced nonlinear photonic lattices. Nature 422, 147–150 (2003).

    Article  ADS  Google Scholar 

  14. Christodoulides, D. N., Lederer, F. & Silberberg, Y. Discretizing light behavior in linear and nonlinear waveguide lattices. Nature 424, 817–823 (2003).

    Article  ADS  Google Scholar 

  15. Lederer, F. et al. Discrete solitons in optics. Phys. Rep. 463, 1–126 (2008).

    Article  ADS  Google Scholar 

  16. Eisenberg, H. Nonlinear Effects in Waveguide Arrays PhD dissertation, Weizmann Institute of Science (2002).

    Google Scholar 

  17. Pertsch, T. et al. Nonlinearity and disorder in fiber arrays. Phys. Rev. Lett. 93, 053901 (2004).

    Article  ADS  Google Scholar 

  18. Schwartz, T., Bartal, G., Fishman, S. & Segev, M. Transport and Anderson localization in disordered two-dimensional photonic lattices. Nature 446, 52–55 (2007).

    Article  ADS  Google Scholar 

  19. Lahini, Y. et al. Anderson localization and nonlinearity in one-dimensional disordered photonic lattices. Phys. Rev. Lett. 100, 013906 (2008).

    Article  ADS  Google Scholar 

  20. Lahini, Y. et al. Observation of a localization transition in quasiperiodic photonic lattices. Phys. Rev. Lett. 103, 013901 (2009).

    Article  ADS  Google Scholar 

  21. Szameit, A. et al. Wave localization at the boundary of disordered photonic lattices. Opt. Lett. 35, 1172–1174 (2010).

    Article  ADS  Google Scholar 

  22. Levi, L. et al. Disorder-enhanced transport in photonic quasicrystals. Science 332, 1541–1544 (2011).

    Article  ADS  Google Scholar 

  23. Billy, J. et al. Direct observation of Anderson localization of matter waves in a controlled disorder. Nature 453, 891–894 (2008).

    Article  ADS  Google Scholar 

  24. Roati, G. et al. Anderson localization of a non-interacting Bose–Einstein condensate. Nature 453, 895–898 (2008).

    Article  ADS  Google Scholar 

  25. Sperling, T., Buhrer, W., Aegerter, C. M. & Maret, G. Direct determination of the transition to localization in three dimensions. Nature Photon. 7, 48–52 (2013).

    Article  ADS  Google Scholar 

  26. Kondov, S. S., McGehee, W. R., Zirbel, J. J. & DeMarco, B. Three-dimensional Anderson localization of ultracold matter. Science 334, 66–68 (2011).

    Article  ADS  Google Scholar 

  27. Jendrzejewski, F. et al. Three dimensional localization of ultracold atoms in an optical trap. Nature Phys. 8, 398–403 (2012).

    Article  ADS  Google Scholar 

  28. Belitz, D. & Kirkpatrick, T. R. The Anderson–Mott transition. Rev. Mod. Phys. 66, 261–380 (1994).

    Article  ADS  Google Scholar 

  29. Basko, D. M., Aleiner, I. L. & Altshuler, B. L. Metal–insulator transition in a weakly interacting many-electron system with localized single-electron states. Ann. Physics. 321, 1126–1205 (2006).

    Article  ADS  Google Scholar 

  30. Frohlich, J., Spencer, T. & Wayne, C. E. Localization in disordered nonlinear dynamical systems. J. Stat. Phys. 42, 247–274 (1986).

    Article  ADS  MathSciNet  Google Scholar 

  31. Pikovsky, A. S. & Shepelyansky, D. L. Destruction of Anderson localization by weak nonlinearity. Phys. Rev. Lett. 100, 094101 (2008).

    Article  ADS  Google Scholar 

  32. Flach, S., Krimer, D. O. & Skokos, C. Universal spreading of wave packets in disordered nonlinear systems. Phys. Rev. Lett. 102, 024101 (2009).

    Article  ADS  Google Scholar 

  33. Fishman, S., Krivolapov, Y. & Soffer, A. Perturbation theory for nonlinear Schrödinger equation with random potential. Nonlinearity 22, 2862–2887 (2009).

    Article  ADS  Google Scholar 

  34. Fishman, S., Krivolapov, Y. & Soffer, A. The nonlinear Schrödinger equation with a random potential: results and puzzles. Nonlinearity 25, R53–R72 (2012).

    Article  ADS  Google Scholar 

  35. Shechtman, D., Blech, I., Gratias, D. & Cahn, J. W. Metallic phase with long-range orientational order and no translational symmetry. Phys. Rev. Lett. 53, 1951–1953 (1984).

    Article  ADS  Google Scholar 

  36. Levine, D. & Steinhardt, P. J. Quasicrystals: A new class of ordered structures. Phys. Rev. Lett. 53, 2477–2480 (1984).

    Article  ADS  Google Scholar 

  37. Vardeny, Z. V., Nahata, A. & Agrawal, A. Optics of photonic quasicrystals. Nature Photon. 7, 177–187.

  38. Rieth, T. & Schreiber, M. The Anderson transition in three-dimensional quasiperiodic lattices: Finite-size scaling and critical exponent. Z. Phys. B 104, 99–102 (1997).

    Article  ADS  Google Scholar 

  39. Fujiwara, T., Yamamoto, S. & Trambly de Laissardière, G. Band structure effects of transport properties in icosahedral quasicrystals. Phys. Rev. Lett. 71, 4166–4169 (1993).

    Article  ADS  Google Scholar 

  40. Mayou, D. et al. Evidence for unconventional electronic transport in quasicrystals. Phys. Rev. Lett. 70, 3915–3918 (1993).

    Article  ADS  Google Scholar 

  41. Man, W., Megens, M., Steinhardt, P. J. & Chaikin, P. M. Experimental measurement of the photonic properties of icosahedral quasicrystals. Nature 436, 993–996 (2005).

    Article  ADS  Google Scholar 

  42. Bratfalean, R. et al. Harmonic generation in a two-dimensional photonic quasicrystal. Opt. Lett. 30, 424–426 (2005).

    Article  ADS  Google Scholar 

  43. Lifshitz, R., Arie, A. & Bahabad, A. Photonic quasicrystals for nonlinear optical frequency conversion. Phys. Rev. Lett. 95, 133901 (2005).

    Article  ADS  Google Scholar 

  44. Freedman, B. et al. Wave and defect dynamics in nonlinear photonic quasicrystals. Nature 440, 1166–1169 (2006).

    Article  ADS  Google Scholar 

  45. Freedman, B., Lifshitz, R., Fleischer, J. W. & Segev, M. Phason dynamics in nonlinear photonic quasicrystals. Nature Mater. 6, 776–781 (2007).

    Article  ADS  Google Scholar 

  46. Aubry, S. & André, G. Analyticity breaking and Anderson localization in incommensurate lattices. Ann. Israel Phys. Soc. 3, 133–140 (1980).

    MathSciNet  MATH  Google Scholar 

  47. Kraus, Y. E. et al. Topological states and adiabatic pumping in quasicrystals. Phys. Rev. Lett. 109, 106402 (2012).

    Article  ADS  Google Scholar 

  48. Levi, L., Krivolapov, Y., Fishman, S. & Segev, M. Hyper-transport of light and stochastic acceleration by evolving disorder. Nature Phys. 8, 912–917 (2012).

    Article  ADS  Google Scholar 

  49. Krivolapov, Y. et al. Super-diffusion in optical realizations of Anderson localization. New J. Phys. 14, 043047 (2012).

    Article  ADS  Google Scholar 

  50. Lee, P. A. & Ramakrishnan, T. V. Disordered electronic systems. Rev. Mod. Phys. 57, 287–337 (1985).

    Article  ADS  Google Scholar 

  51. Hu, H., Strybulevych, A., Page, J. H., Skipetrov, S. E. & van Tiggelen, B. A. Localization of ultrasound in a three dimensional elastic network. Nature Phys. 4, 945–948 (2008).

    Article  ADS  Google Scholar 

  52. Zaslavskii, G. M. & Chirikov, B. V. Stochastic instability of nonlinear oscillation. Sov. Phys. Usp. 14, 549–567 (1972).

    Article  ADS  Google Scholar 

  53. Jayannavar, A. M. & Kumar, N. Nondiffusive quantum transport in a dynamically disordered medium. Phys. Rev. Lett. 48, 553–556 (1982).

    Article  ADS  Google Scholar 

  54. Golubovic, L., Feng, S. & Zeng, F. Classical and quantum superdiffusion in a time-dependent random potential. Phys. Rev. Lett. 67, 2115–2118 (1991).

    Article  ADS  MathSciNet  Google Scholar 

  55. Rosenbluth, M. N. Comment on “Classical and quantum superdiffusion in a time-dependent random potential”. Phys. Rev. Lett. 69, 1831 (1992).

    Article  ADS  MathSciNet  Google Scholar 

  56. Arvedson, E., Wilkinson, M., Mehlig, B. & Nakamura, K. Staggered ladder spectra. Phys. Rev. Lett. 96, 030601 (2006).

    Article  ADS  Google Scholar 

  57. Perets, H. B. et al. Realization of quantum walks with negligible decoherence in waveguide lattices. Phys. Rev. Lett. 100, 170506 (2008).

    Article  ADS  Google Scholar 

  58. Bromberg, Y., Lahini, Y., Morandotti, R. & Silberberg, Y. Classical and quantum correlations in waveguide lattices. Phys. Rev. Lett. 102, 253904 (2009).

    Article  ADS  Google Scholar 

  59. Peruzzo, A. et al. Quantum walks of correlated photons. Science 329, 1500–1503 (2010).

    Article  ADS  Google Scholar 

  60. Lahini, Y., Bromberg, Y., Christodoulides, D. N. & Silberberg, Y. Quantum correlations in two-particle Anderson localization. Phys. Rev. Lett. 105, 163905 (2010).

    Article  ADS  Google Scholar 

  61. Sansoni, L. et al. Two-particle bosonic-fermionic quantum walk via integrated photonics. Phys. Rev. Lett. 108, 010502 (2012).

    Article  ADS  Google Scholar 

  62. Lahini, Y. et al. Hanbury Brown and Twiss correlations of Anderson localized waves. Phys. Rev. A 84, 041806(R) (2011).

    Article  ADS  Google Scholar 

  63. Cao, H. et al. Random laser action in semiconductor powder. Phys. Rev. Lett. 82, 2278–2281 (1999).

    Article  ADS  Google Scholar 

  64. Rechtsman, M. C. et al. Amorphous photonic lattices: band gaps, effective mass and suppressed transport. Phys. Rev. Lett. 106, 193904 (2011).

    Article  ADS  Google Scholar 

  65. Butenko, A. V., Shalaev, V. M. & Stockman, M. I. Giant optical nonlinearities of impurities of fractal clusters. Sov. Phys. JETP 67, 60–69 (1988).

    Google Scholar 

  66. Oganesyan, V. & Huse, D. A. Localization of interacting fermions at high temperature. Phys. Rev. B 75, 155111 (2007).

    Article  ADS  Google Scholar 

  67. Radic, J. et al. Anderson localization of a Tonks–Girardeau gas in potentials with controlled disorder. Phys. Rev. A 81, 063639 (2010).

    Article  ADS  Google Scholar 

Download references

Acknowledgements

M.S. and Y.S. acknowledge the support of their Advanced Grants from the European Research Council. D.N.C and M.S. acknowledge support from the Binational USA–Israel Science Foundation. The authors are grateful to their current and former students from the Technion and the Weizmann Institute: Tal Schwartz, Yoav Lahini, Liad Levi, and Yaron Bromberg, for years of high-quality research. M.S. gratefully acknowledges the fruitful collaboration with Prof. Shmuel Fishman and Dr. Yevgeny Krivolapov (Bar Lev) of the Technion, and the highly professional technical support of Tony Yasinger.

Author information

Authors and Affiliations

  1. Physics Department, Technion – Israel Institute of Technology, Haifa, 32000, Israel

    Mordechai Segev

  2. Solid State Institute, Technion – Israel Institute of Technology, Haifa, 32000, Israel

    Mordechai Segev

  3. Department of Physics of Complex Systems, Weizmann Institute of Science, Rehovot, 76100, Israel

    Yaron Silberberg

  4. CREOL/College of Optics, University of Central Florida, Orlando, 32816, Florida, USA

    Demetrios N. Christodoulides

Authors
  1. Mordechai Segev
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Yaron Silberberg
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Demetrios N. Christodoulides
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Mordechai Segev.

Ethics declarations

Competing interests

The authors declare no competing financial interests.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Segev, M., Silberberg, Y. & Christodoulides, D. Anderson localization of light. Nature Photon 7, 197–204 (2013). https://doi.org/10.1038/nphoton.2013.30

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1038/nphoton.2013.30

Search

Advanced search

Quick links

Nature Briefing

Sign up for the Nature Briefing newsletter — what matters in science, free to your inbox daily.

Get the most important science stories of the day, free in your inbox. Sign up for Nature Briefing