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Spatiotemporal control of laser intensity

A Publisher Correction to this article was published on 22 May 2018

This article has been updated


The controlled coupling of a laser to plasma has the potential to address grand scientific challenges1,2,3,4,5,6, but many applications have limited flexibility and poor control over the laser focal volume. Here, we present an advanced focusing scheme called a ‘flying focus’, where a chromatic focusing system combined with chirped laser pulses enables a small-diameter laser focus to propagate nearly 100 times its Rayleigh length. Furthermore, the speed at which the focus moves (and hence the peak intensity) is decoupled from the group velocity of the laser. It can co- or counter-propagate along the laser axis at any velocity. Experiments validating the concept measured subluminal (−0.09c) to superluminal (39c) focal-spot velocities, generating a nearly constant peak intensity over 4.5 mm. Among possible applications, the flying focus could be applied to a photon accelerator7 to mitigate dephasing, facilitating the production of tunable XUV sources.

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Fig. 1: Schematic of the chromatic focusing system coupled to a chirped laser pulse.
Fig. 2: Evolution of the flying focus intensity.
Fig. 3: Measured and calculated \([v/c={(1\pm \frac{cT}{L})}^{-1}]\) focal-spot velocities plotted as a function of normalized laser pulse duration.
Fig. 4: Instantaneous longitudinal intensity.

Change history

  • 22 May 2018

    In the version of this Letter originally published, in the first sentence of the Methods, ref. 31 was incorrectly cited; it should have been ref. 32. This has now been corrected.


  1. Bulanov, S. S., Esirkepov, T. Z., Thomas, A. G. R., Koga, J. K. & Bulanov, S. V. Schwinger limit attainability with extreme power lasers. Phys. Rev. Lett. 105, 220407 (2010).

    Article  ADS  Google Scholar 

  2. Pellegrini, C. The history of X-ray free-electron lasers. Eur. Phys. J. H 37, 659–708 (2012).

    Article  Google Scholar 

  3. Joshi, C. et al. Ultrahigh gradient particle-acceleration by intense laser-driven plasma-density waves. Nature 311, 525–529 (1984).

    Article  ADS  Google Scholar 

  4. Corde, S. et al. Multi-gigaelectronvolt acceleration of positrons in a self-loaded plasma wakefield. Nature 524, 442–445 (2015).

    Article  ADS  Google Scholar 

  5. Yan, W. et al. High-order multiphoton Thomson scattering. Nat. Photon 11, 514–520 (2017).

    Article  Google Scholar 

  6. Malka, V. et al. Principles and applications of compact laser-plasma accelerators. Nat. Phys. 4, 447–453 (2008).

    Article  Google Scholar 

  7. Wilks, S. C., Dawson, J. M. & Mori, W. B. Frequency up-conversion of electromagnetic radiation with use of an overdense plasma. Phys. Rev. Lett. 61, 337–340 (1988).

    Article  ADS  Google Scholar 

  8. Durfee, C. G. & Milchberg, H. M. Light pipe for high intensity laser pulses. Phys. Rev. Lett. 71, 2409–2412 (1993).

    Article  ADS  Google Scholar 

  9. Jackel, S. et al. Channeling of terawatt laser-pulses by use of hollow wave-guides. Opt. Lett. 20, 1086–1088 (1995).

    Article  ADS  Google Scholar 

  10. Dorchies, F. et al. Monomode guiding of 1016 W/cm2 laser pulses over 100 Rayleigh lengths in hollow capillary dielectric tubes. Phys. Rev. Lett. 82, 4655–4658 (1999).

    Article  ADS  Google Scholar 

  11. Froula, D. H. et al. Magnetically controlled plasma waveguide for laser wakefield acceleration. Plasma Phys. Control. Fusion 51, 024009 (2009).

    Article  ADS  Google Scholar 

  12. Wattellier, B., Sauteret, C., Chanteloup, J. C. & Migus, A. Beam-focus shaping by use of programmable phase-only filters: application to an ultralong focal line. Opt. Lett. 27, 213–215 (2002).

    Article  ADS  Google Scholar 

  13. Garcia-Guerrero, E. E., Mendez, E. R. & Escamilla, H. M. Design and fabrication of random phase diffusers for extending the depth of focus. Opt. Express 15, 910–923 (2007).

    Article  ADS  Google Scholar 

  14. Vincenti, H.,& Quéré, F. Attosecond lighthouses: how to use spatiotemporally coupled light fields to generate isolated attosecond pulses. Phys. Rev. Lett 108, 113904 (2012).

    Article  ADS  Google Scholar 

  15. Malkin, V. M., Shvets, G. & Fisch, N. J. Fast compression of laser beams to highly overcritical powers. Phys. Rev. Lett. 82, 4448–4451 (1999).

    Article  ADS  Google Scholar 

  16. Ren, J., Cheng, W., Li, S. & Suckewer, S. A new method for generating ultraintense and ultrashort laser pulses. Nat. Phys. 3, 732–736 (2007).

    Article  Google Scholar 

  17. Ping, Y. et al. Amplification of ultrashort laser pulses by a resonant Raman scheme in a gas-jet plasma. Phys. Rev. Lett. 92, 175007 (2004).

    Article  ADS  Google Scholar 

  18. Vieux, G. et al. An ultra-high gain and efficient amplifier based on Raman amplification in plasma. Sci. Rep. 7, 2399 (2017).

    Article  ADS  Google Scholar 

  19. Bingham, R. Plasma physics—surfing the wake. Nature 394, 617–619 (1998).

    Article  ADS  Google Scholar 

  20. Hooker, S. M. Developments in laser-driven plasma accelerators. Nat. Photon. 7, 775–782 (2013).

    Article  ADS  Google Scholar 

  21. Butler, A. et al. Demonstration of a collisionally excited optical-field-ionization XUV laser driven in a plasma waveguide. Phys. Rev. Lett. 91, 205001 (2003).

    Article  ADS  Google Scholar 

  22. Rocca, J. J. et al. Demonstration of a discharge pumped table-top soft-X-ray laser. Phys. Rev. Lett. 73, 2192–2195 (1995).

    Article  ADS  Google Scholar 

  23. Powers, N. D. et al. Quasi-monoenergetic and tunable X-rays from a laser-driven compton light source. Nat. Photon. 8, 29–32 (2014).

    Article  ADS  Google Scholar 

  24. Phuoc, K. T. et al. All-optical compton gamma-ray source. Nat. Photon. 6, 308–311 (2012).

    Article  ADS  Google Scholar 

  25. Stuart, B. C. et al. Laser-induced damage in dielectrics with nanosecond to subpicosecond pulses. Phys. Rev. Lett. 74, 2248–2251 (1995).

    Article  ADS  Google Scholar 

  26. Palastro, J. P. et al. Ionization waves of arbitrary velocity driven by a flying focus. Phys. Rev. A (in the press).

  27. Kim, K. Y. et al. Coherent control of terahertz supercontinuum generation in ultrafast laser-gas interactions. Nat. Photon. 2, 605–609 (2008).

    Article  Google Scholar 

  28. Geddes, C. G. R. et al. High-quality electron beams from a laser wakefield accelerator using plasma-channel guiding. Nature 431, 538–541 (2004).

    Article  ADS  Google Scholar 

  29. Steinke, S. et al. Multistage coupling of independent laser-plasma accelerators. Nature 530, 190–193 (2016).

    Article  ADS  Google Scholar 

  30. Turnbull, D. et al. Raman amplification with a flying focus. Phys. Rev. Lett. 120, 024801 (2018).

    Article  ADS  Google Scholar 

  31. Sainte-Marie, A., Gobert, O. & Quere, F. Controlling the velocity of ultrashort light pulses in vacuum through spatio-temporal couplings. Optica 4, 1298–1304 (2017).

    Article  Google Scholar 

  32. Bagnoud, V., Begishev, I. A., Guardalben, M. J., Puth, J. & Zuegel, J. D. 5-Hz, >250-mJ optical parametric chirped-pulse amplifier at 1053 nm. Opt. Lett. 30, 1843–1845 (2005).

    Article  ADS  Google Scholar 

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The work published here was supported by the US Department of Energy Office of Fusion Energy Sciences under contract no. DE-SC0016253, the Department of Energy under cooperative agreement no. DE-NA0001944, the University of Rochester, and the New York State Energy Research and Development Authority. The support of the Department of Energy does not constitute an endorsement of the views expressed in this article.

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Authors and Affiliations



D.H.F. contributed the concept of flying focus to the team. D.T. carried out the experiments and performed the data analysis. T.J.K. designed, tested and delivered the diffractive optic. D.H. oversaw the experimental area and contributed to the design. J.P.P. and S.-W.B. performed electromagnetic wave calculations of the flying focus. I.A.B. designed the chirp and operated the laser system. R.B. designed the experimental set-up. S.B., J.L.S. and J.K. set up the experiment. A.S.D. helped with the analytic calculations.

Corresponding author

Correspondence to Dustin H. Froula.

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The authors declare no competing interests.

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Supplementary information

Supplementary Information

Flying focus data, flying focus spot size, photon accelerator including detailed captions for each Supplementary Video.


Supplementary Video 1

Measurement of the flying focus for a T = 65 ps positively chirped pulse.

Supplementary Video 2

Measurement of the flying focus for a T = 55 ps positively chirped pulse.

Supplementary Video 3

Calculation of the flying focus for T = 29.8 ps negatively chirped pulse.

Supplementary Video 4

Calculation of the flying focus for a T = 14.9 ps negatively chirped pulse.

Supplementary Video 5

Calculation of the flying focus for a T = 11.9 ps negatively chirped pulse.

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Froula, D.H., Turnbull, D., Davies, A.S. et al. Spatiotemporal control of laser intensity. Nature Photon 12, 262–265 (2018).

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