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.

Exploiting disorder for perfect focusing

Abstract

Optical microscopy and manipulation methods rely on the ability to focus light to a small volume. However, in inhomogeneous media such as biological tissue, light is scattered out of the focusing beam. Disordered scattering is thought to fundamentally limit the resolution and penetration depth of optical methods1,2,3. Here we demonstrate, in an optical experiment, that scattering can be used to improve, rather than deteriorate, the sharpness of the focus. The resulting focus is even sharper than that in a transparent medium. By using scattering in the medium behind a lens, light was focused to a spot ten times smaller than the diffraction limit of that lens. Our method is the optical equivalent of highly successful methods for improving the resolution and communication bandwidth of ultrasound, radio waves and microwaves4,5,6. Our results, obtained using spatial wavefront shaping, apply to all coherent methods for focusing through scattering matter, including phase conjugation7 and time-reversal4.

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

Relevant articles

Open Access articles citing this article.

Access options

Buy article

Get time limited or full article access on ReadCube.

$32.00

All prices are NET prices.

Figure 1: Schematic of the experiment.
Figure 2: Measured intensity distribution in the focal plane at 200±3 mm from the glass lens.
Figure 3: Focal width w, relative to the diffraction limit of the glass lens (w0 = 62 µm, dashed line), as a function of the distance f2 between the scattering sample and the focal plane.
Figure 4: Intensity profile of the focus at y = 0 (solid curve) and speckle correlation function (dashed curve).

References

  1. Ishimaru, A. Wave Propagation and Scattering in Random Media (Academic Press, 1978).

    MATH  Google Scholar 

  2. Sebbah, P. (ed.) Waves and Imaging through Complex Media (Kluwer Academic, 2001).

    Book  Google Scholar 

  3. Hayakawa, C. K., Venugopalan, V., Krishnamachari, V. V. & Potma, E. O. Amplitude and phase of tightly focused laser beams in turbid media. Phys. Rev. Lett. 103, 043903 (2009).

    Article  ADS  Google Scholar 

  4. Derode, A., Roux, P. & Fink, M. Robust acoustic time reversal with high-order multiple scattering. Phys. Rev. Lett. 75, 4206–4209 (1995).

    Article  ADS  Google Scholar 

  5. Foschini, G. J. Layered space–time architecture for wireless communication in a fading environment when using multi-element antennas. Bell Labs Tech. J. 1, 41–59 (1996).

    Article  Google Scholar 

  6. Simon, S. H., Moustakas, A. L., Stoytchev, M. & Safar, H. Communication in a disordered world. Phys. Today 54, 38–43 (2001).

    Article  Google Scholar 

  7. Yaqoob, Z., Psaltis, D., Feld, M. S. & Yang, C. Optical phase conjugation for turbidity suppression in biological samples. Nature Photon. 2, 110–115 (2008).

    Article  ADS  Google Scholar 

  8. Vellekoop, I. M. & Mosk, A. P. Focusing coherent light through opaque strongly scattering media. Opt. Lett. 32, 2309–2311 (2007).

    Article  ADS  Google Scholar 

  9. Popoff, S. M. et al. Measuring the transmission matrix in optics: an approach to the study and control of light propagation in disordered media. Preprint at <http://ArXiv:physics.optics/0910.5436v1> (2009).

  10. Derode, A., Tourin, A. & Fink, M. Random multiple scattering of ultrasound. II. Is time reversal a self-averaging process? Phys. Rev. E 64, 036606 (2001).

    Article  ADS  Google Scholar 

  11. Pappu, R., Recht, B., Taylor, J. & Gershenfeld, N. Physical one-way functions. Science 297, 2026–2030 (2002).

    Article  ADS  Google Scholar 

  12. Tyson, R. K. Principles of Adaptive Optics 2nd edn (Academic Press, 1998).

    Google Scholar 

  13. van Putten, E. G., Vellekoop, I. M. & Mosk, A. P. Spatial amplitude and phase modulation using commercial twisted nematic LCDs. Appl. Opt. 47, 2076–2081 (2008).

    Article  ADS  Google Scholar 

  14. Tanter, M., Thomas, J.-L. & Fink, M. Time reversal and the inverse filter. J. Acoust. Soc. Am. 108, 223–234 (2000).

    Article  ADS  Google Scholar 

  15. Vellekoop, I. M. & Mosk, A. P. Universal optimal transmission of light through disordered materials. Phys. Rev. Lett. 101, 120601 (2008).

    Article  ADS  Google Scholar 

  16. Goodman, J. W. Statistical Optics (Wiley, 2000).

    Google Scholar 

  17. Lerosey, G., de Rosny, J., Tourin, A. & Fink, M. Focusing beyond the diffraction limit with far-field time reversal. Science 315, 1120–1122 (2007).

    Article  ADS  Google Scholar 

  18. Stockman, M. I., Faleev, S. V. & Bergman, D. J. Coherent control of femtosecond energy localization in nanosystems. Phys. Rev. Lett. 88, 067402 (2002).

    Article  ADS  Google Scholar 

  19. Bartal, G., Lerosey, G. & Zhang, X. Subwavelength dynamic focusing in plasmonic nanostructures using time reversal. Phys. Rev. B 79, 201103 (2009).

    Article  ADS  Google Scholar 

Download references

Acknowledgements

The authors thank W.L. Vos and E.G. van Putten for support and discussions. This work is part of the research programme of the Stichting voor Fundamenteel Onderzoek der Materie (FOM), which is financially supported by the Nederlandse Organisatie voor Wetenschappelijk Onderzoek (NWO). A.P.M. is supported by a VIDI grant from NWO.

Author information

Authors and Affiliations

Authors

Contributions

I.M.V., A.L. and A.P.M. designed the experiments, analysed the data, developed the theory and wrote the paper. I.M.V. performed the experiments.

Corresponding author

Correspondence to A. P. Mosk.

Ethics declarations

Competing interests

The authors declare no competing financial interests.

Supplementary information

Rights and permissions

Reprints and Permissions

About this article

Cite this article

Vellekoop, I., Lagendijk, A. & Mosk, A. Exploiting disorder for perfect focusing. Nature Photon 4, 320–322 (2010). https://doi.org/10.1038/nphoton.2010.3

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1038/nphoton.2010.3

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