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.

  • Article
  • Published:

Mesoscopic light transport by very strong collective multiple scattering in nanowire mats

Abstract

Under the extreme condition of the scattering length being much shorter than the wavelength, light transport in random media is strongly modified by mesoscopic interference, and can even be halted in an effect known as Anderson localization. Anderson localization in three dimensions has recently been realized for acoustic waves and for cold atoms. Mats of disordered, high-refractive-index semiconductor nanowires are one of the strongest three-dimensional scattering materials for light, but localization has not been shown. Here, we use statistical methods originally developed for microwave waveguides to demonstrate that transport of light through nanowire mats is strongly correlated and governed by mesoscopic interference contributions. Our results confirm the contribution of only a few open modes to the transmission.

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

Access options

Buy this article

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

Figure 1: Morphology and basic light transport parameters reveal strong multiple scattering in nanowire mats.
Figure 2: Enhanced spatial intensity fluctuations in optical transmission through nanowire mats are explained by a small number of open channels.
Figure 3: Total transmission measurements show a significant deviation from Gaussian statistics.
Figure 4: The mesoscopic regime is confirmed by observation of long-range spatial and spectral correlations.

Similar content being viewed by others

References

  1. Beenakker, C. W. J. Random-matrix theory of quantum transport. Rev. Mod. Phys. 69, 731–808 (1997).

    Article  ADS  Google Scholar 

  2. Akkermans, E. & Montambaux, G. Mesoscopic Physics of Electrons and Photons 427–464 (Cambridge Univ. Press, 2007).

    Book  Google Scholar 

  3. Popoff, S. M. et al. Measuring the transmission matrix in optics: an approach to the study and control of light propagation in disordered media. Phys. Rev. Lett. 104, 100601 (2010).

    Article  ADS  Google Scholar 

  4. Mosk, A. P., Lagendijk, A., Lerosey, G. & Fink, M. Controlling waves in space and time for imaging and focusing in complex media Nature Photon. 6, 283–292 (2012).

    Article  ADS  Google Scholar 

  5. Kim, M. et al. Maximal energy transport through disordered media with the implementation of transmission eigenchannels. Nature Photon. 6, 581–585 (2012).

    Article  ADS  Google Scholar 

  6. Lagendijk, A., van Tiggelen, B. A. & Wiersma, D. S. Fifty-years of Anderson localization. Phys. Today 62, 24–29 (2009).

    Article  Google Scholar 

  7. Strybulevych, A., Hu, H., 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 

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

    Article  ADS  Google Scholar 

  9. 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 

  10. 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 

  11. Van der Beek, T., Barthelemy, P., Johnson, P. M., Wiersma, D. S. & Lagendijk, A. Light transport through disordered layers of dense gallium arsenide submicron particles. Phys. Rev. B 85, 115401 (2012).

    Article  ADS  Google Scholar 

  12. Scheffold, F., Härtl, W., Maret, G. & Matjevic, E. Observation of long-range correlations in temporal intensity fluctuations of light. Phys. Rev. B 56, 10942–10952 (1997).

    Article  ADS  Google Scholar 

  13. De Boer, J. F., van Rossum, M. C. W., van Albada, M. P., Nieuwenhuizen, T. M. & Lagendijk, A. Probability distribution of multiple scattered light measured in total transmission. Phys. Rev. Lett. 73, 2567–2570 (1994).

    Article  ADS  Google Scholar 

  14. Yan, R., Gargas, D. & Yang, P. Nanowire photonics. Nature Photon. 3, 569–576 (2009).

    Article  ADS  Google Scholar 

  15. Garnett, E. & Yang, P. Light trapping in silicon nanowire solar cells. Nano Lett. 10, 1082–1087 (2010).

    Article  ADS  Google Scholar 

  16. Cao, L. et al. Engineering light absorption in semiconductor nanowire devices. Nature Mater. 8, 643–647 (2009).

    Article  ADS  Google Scholar 

  17. Wallentin, J. et al. InP nanowire array solar cells achieving 13.8% efficiency by exceeding the ray optics limit. Science 339, 1057–1060 (2013).

    Article  ADS  Google Scholar 

  18. Muskens, O. L. et al. Large photonic strength of highly tunable resonant nanowire materials. Nano Lett. 9, 930–934 (2009).

    Article  ADS  Google Scholar 

  19. Muskens, O. L. & Lagendijk, A . Method for broadband spectroscopy of light transport through opaque scattering media. Opt. Lett. 34, 395–397 (2009).

    Article  ADS  Google Scholar 

  20. Brönstrup, G. et al. Optical properties of individual silicon nanowires for photonic devices. ACS Nano 4, 7113–7122 (2010).

    Article  Google Scholar 

  21. Kaas, B., van Tiggelen, B. & Lagendijk, A. Anisotropy and interference in wave transport: an analytic theory. Phys. Rev. Lett. 100, 243901 (2008).

    Article  Google Scholar 

  22. Park, J., Zhang, S. & Genack, A. Z. Intensity statistics and photon localization beyond one dimension. Phys. Rev. E 82, 045101(R) (2010).

    Article  ADS  Google Scholar 

  23. 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 

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

    Article  ADS  Google Scholar 

  25. Genack, A. Z. & Chabanov, A. A . Signatures of photon localization. J. Phys. A 38, 10465–10488 (2005).

    Article  ADS  MathSciNet  Google Scholar 

  26. Pnini, R. & Shapiro, B. Fluctuations in transmission of waves through disordered slabs. Phys. Rev. B 39, 6986–6994 (1989).

    Article  ADS  Google Scholar 

  27. Nieuwenhuizen, T. M. & van Rossum, M. C. W. Intensity distributions of waves transmitted through a multiple scattering medium. Phys. Rev. Lett. 74, 2674–2677 (1995).

    Article  ADS  Google Scholar 

  28. Van Rossum, M. C. W., Nieuwenhuizen, Th. M. & Vlaming, R. Optical conductance fluctuations: diagrammatic analysis in the Landauer approach and nonuniversal effects. Phys. Rev. E 51, 6158–6176 (1995).

    Article  ADS  Google Scholar 

  29. Muttalib, K. A., Markoš, P. & Wölfe, P. Conductance distribution in strongly disordered mesoscopic systems in three dimensions. Phys. Rev. B 72, 012317 (2005).

    Article  Google Scholar 

  30. Vynck, K., Burresi, M., Riboli. F. & Wiersma, D. S. Photon management in two-dimensional disordered media. Nature Mater. 11, 1017–1022 (2012).

    Article  ADS  Google Scholar 

Download references

Acknowledgements

The authors thank A. Mosk of the University of Twente and A. Lagendijk of the FOM-Institute AMOLF for valuable discussions. The research leading to these results has received funding from the European Union Seventh Framework Programme (grant agreement no. 265073). O.L.M. acknowledges financial support from the EPSRC (grant EP/J016918/1), from the Royal Society through an International Joint Project, and from the EU Network of Excellence ‘Nanophotonics for Energy Efficiency’ (N4E).

Author information

Authors and Affiliations

Authors

Contributions

O.L.M. and T.S. conceived the idea and designed the experiments. C.B. and T.S. constructed the set-up, performed the experiments and data analysis. T.Z. fabricated and characterized the nanowire mats. O.L.M. and E.P.A.M.B. coordinated and directed the study. All authors contributed to manuscript preparation, data interpretation, and discussed the results.

Corresponding author

Correspondence to Otto L. Muskens.

Ethics declarations

Competing interests

The authors declare no competing financial interests.

Supplementary information

Supplementary information

Supplementary information (PDF 980 kb)

Rights and permissions

Reprints and permissions

About this article

Cite this article

Strudley, T., Zehender, T., Blejean, C. et al. Mesoscopic light transport by very strong collective multiple scattering in nanowire mats. Nature Photon 7, 413–418 (2013). https://doi.org/10.1038/nphoton.2013.62

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1038/nphoton.2013.62

This article is cited by

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