Skip to main content

Thank you for visiting 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.

Experimental demonstration of optical transport, sorting and self-arrangement using a ‘tractor beam’


A Corrigendum to this article was published on 27 February 2013

This article has been updated


Following the Keplerian idea of optical forces, one would intuitively expect that an object illuminated by sunlight radiation or a laser beam will be accelerated along the direction of photon flow. Recent theoretical studies1,2,3,4,5 have shown that small particles can be pulled by light beams against the photon stream, even in beams with uniform optical intensity along the propagation axis. Here, we present a geometry to generate such a ‘tractor beam’, and experimentally demonstrate its functionality using spherical microparticles of various sizes, as well as its enhancement with optically self-arranged structures of microparticles. In addition to the pulling of the particles, we also demonstrate that their two-dimensional motion and one-dimensional sorting may be controlled conveniently by rotation of the polarization of the linearly polarized incident beam. The relative simplicity of this geometry could serve to encourage its widespread application, and ongoing investigations will broaden the understanding of the light–matter interaction through studies combining more interacting micro-objects with various properties.

Access options

Rent or Buy article

Get time limited or full article access on ReadCube.


All prices are NET prices.

Figure 1: Pulling and pushing forces along a fringe (z-axis) in the geometry of two interfering plane waves.
Figure 2: Experimental arrangement and results.
Figure 3: Examples of particle sorting by polarization-switching of the ‘tractor beam’.
Figure 4: Optically self-arranged structures and their different behaviour in the ‘tractor beam’.

Change history

  • 06 February 2013

    In this version of this Letter originally published, the surname of the first author of ref. 26 should have been “Zhang” and the reference should have read: 26. Zhang, L. & Marston, P. L. Geometrical interpretation of negative radiation forces of acoustical Bessel beams on spheres. Phys. Rev. E 84, 035601 (2011). This has now been corrected in the HTML and PDF versions of the Letter.


  1. 1

    Lee, S-H., Roichman, Y. & Grier, D. Optical solenoid beams. Opt. Express 18, 6988–6993 (2010).

    ADS  Article  Google Scholar 

  2. 2

    Chen, J., Ng, J., Lin, Z. & Chan, C. T. Optical pulling force. Nature Photon. 5, 531–534 (2011).

    ADS  Article  Google Scholar 

  3. 3

    Novitsky, A., Qiu, C-W. & Wang, H. Single gradientless light beam drags particles as tractor beams. Phys. Rev. Lett. 107, 203601 (2011).

    ADS  Article  Google Scholar 

  4. 4

    Sukhov, S. & Dogariu, A. Negative nonconservative forces: optical ‘tractor beams’ for arbitrary objects. Phys. Rev. Lett. 107, 203602 (2011).

    ADS  Article  Google Scholar 

  5. 5

    Saenz, J. Laser tractor beams. Nature Photon. 5, 514–515 (2011).

    ADS  Article  Google Scholar 

  6. 6

    Sukhov, S. & Dogariu, A. On the concept of ‘tractor beams’. Opt. Lett. 35, 3847–3849 (2010).

    ADS  Article  Google Scholar 

  7. 7

    Ashkin, A., Dziedzic, J. M., Bjorkholm, J. E. & Chu, S. Observation of a single-beam gradient force optical trap for dielectric particles. Opt. Lett. 11, 288–290 (1986).

    ADS  Article  Google Scholar 

  8. 8

    Fazal, F. M. & Block, S. M. Optical tweezers study life under tension. Nature Photon. 5, 318–321 (2011).

    ADS  Article  Google Scholar 

  9. 9

    Padgett, M. & Bowman, R. Tweezers with a twist. Nature Photon. 5, 343–348 (2011).

    ADS  Article  Google Scholar 

  10. 10

    Dholakia, K. & Čižmár, T. Shaping the future of manipulation. Nature Photon. 5, 335–342 (2011).

    ADS  Article  Google Scholar 

  11. 11

    Juan, M. L., Righini, M. & Quidant, R. Plasmon nano-optical tweezers. Nature Photon. 5, 349–356 (2011).

    ADS  Article  Google Scholar 

  12. 12

    Čižmár, T., Garcés-Chávez, V., Dholakia, K. & Zemánek, P. Optical conveyor belt for delivery of submicron objects. Appl. Phys. Lett. 86, 174101 (2005).

    ADS  Article  Google Scholar 

  13. 13

    Čižmár, T., Kollárová, V., Bouchal, Z. & Zemánek, P. Sub-micron particle organization by self-imaging of non-diffracting beams. New. J. Phys. 8, 1–23 (2006).

    MathSciNet  Article  Google Scholar 

  14. 14

    Ruffner, D. B. & Grier, D. G. Optical conveyors: a class of active tractor beams. Phys. Rev. Lett. 109, 163903 (2012).

    ADS  Article  Google Scholar 

  15. 15

    Chiou, A. E., Wang, W., Sonek, G. J., Hong, J. & Berns, M. W. Interferometric optical tweezers. Opt. Commun. 133, 7–10 (1997).

    ADS  Article  Google Scholar 

  16. 16

    Mizrahi, A. & Fainman, Y. Negative radiation pressure on gain medium structures. Opt. Lett. 35, 3405–3407 (2010).

    ADS  Article  Google Scholar 

  17. 17

    Grover, A., Swartzlander, J., Peterson, T. J., Artusio-Glimpse, A. B. & Raisanen, A. D. Stable optical lift. Nature Photon. 5, 48–51 (2011).

    ADS  Article  Google Scholar 

  18. 18

    Brzobohatý, O. et al. Experimental and theoretical determination of optical binding forces. Opt. Express 18, 25389–25402 (2010).

    ADS  Article  Google Scholar 

  19. 19

    Demergis, V. & Florin, E-L. Ultrastrong optical binding of metallic nanoparticles. Nano Lett. 12, 5756–5760 (2012).

    ADS  Article  Google Scholar 

  20. 20

    MacDonald, M. P., Spalding, G. C. & Dholakia, K. Microfluidic sorting in an optical lattice. Nature 426, 421–424 (2003).

    ADS  Article  Google Scholar 

  21. 21

    Dholakia, K., MacDonald, M. P., Zemánek, P. & Čižmár, T. Cellular and colloidal separation using optical forces. Methods Cell Biol. 82, 467–495 (2007).

    Article  Google Scholar 

  22. 22

    Burns, M. M., Fournier, J-M. & Golovchenko, J. A. Optical matter: crystallization and binding in intense optical fields. Science 249, 749–754 (1990).

    ADS  Article  Google Scholar 

  23. 23

    Dholakia, K. & Zemánek, P. Gripped by light: optical binding. Rev. Mod. Phys. 82, 1767–1791 (2010).

    ADS  Article  Google Scholar 

  24. 24

    Marston, P. L. Axial radiation force of a Bessel beam on a sphere and direction reversal of the force. J. Acoust. Soc. Am. 120, 3518–3524 (2006).

    ADS  Article  Google Scholar 

  25. 25

    Mitri, F. Negative axial radiation force on a fluid and elastic spheres illuminated by a high-order Bessel beam of progressive waves. J. Phys. A 42, 245202 (2009).

    ADS  MathSciNet  Article  Google Scholar 

  26. 26

    Zhang, L. & Marston, P. L. Geometrical interpretation of negative radiation forces of acoustical Bessel beams on spheres. Phys. Rev. E 84, 035601 (2011).

    ADS  Article  Google Scholar 

  27. 27

    Barton, J. P., Alexander, D. R. & Schaub, S. A. Theoretical determination of net radiation force and torque for a spherical particle illuminated by a focused laser beam. J. Appl. Phys. 66, 4594–4602 (1989).

    ADS  Article  Google Scholar 

  28. 28

    Gouesbet, G., Lock, J. & Grehan, G. Generalized Lorenz–Mie theories and description of electromagnetic arbitrary shaped beams: localized approximations and localized beam models, a review. J. Quant. Spectr. Rad. Transf. 112, 1–27 (2011).

    ADS  Article  Google Scholar 

  29. 29

    Draine, B. The discrete-dipole approximation and its application to interstellar graphite grains. Astrophys. J. 333, 848–872 (1988).

    ADS  Article  Google Scholar 

Download references


The authors acknowledge the comments of H.I.C. Dalgarno and support from the USTAN and the following projects: CSF (GA202/09/0348, GPP205/11/P294), MEYS CR (LH12018), ISI (RVO:68081731), COST-STSM-MP0604-04235 and EC (ALISI CZ.1.05/2.1.00/01.0017).

Author information




O.B., T.Č. and P.Z. developed the presented method, supervised the project and wrote the manuscript. O.B. performed all the experiments and subsequent data analysis. O.B., V.K., M.Š. and L.C. performed computer simulations.

Corresponding author

Correspondence to P. Zemánek.

Ethics declarations

Competing interests

The authors declare no competing financial interests.

Supplementary information

Supplementary information

Supplementary information (PDF 2113 kb)

Supplementary video

Supplementary video (AVI 756 kb)

Supplementary video

Supplementary video (AVI 480 kb)

Supplementary video

Supplementary video (AVI 3583 kb)

Supplementary video

Supplementary video (AVI 627 kb)

Rights and permissions

Reprints and Permissions

About this article

Cite this article

Brzobohatý, O., Karásek, V., Šiler, M. et al. Experimental demonstration of optical transport, sorting and self-arrangement using a ‘tractor beam’. Nature Photon 7, 123–127 (2013).

Download citation

Further reading


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