Abstract

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.

Access optionsAccess options

Rent or Buy article

Get time limited or full article access on ReadCube.

from$8.99

All prices are NET prices.

Additional information

Publisher’s note: Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

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.

References

  1. 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).

  2. 2.

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

  3. 3.

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

  4. 4.

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

  5. 5.

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

  6. 6.

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

  7. 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).

  8. 8.

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

  9. 9.

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

  10. 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).

  11. 11.

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

  12. 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).

  13. 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).

  14. 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).

  15. 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).

  16. 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).

  17. 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).

  18. 18.

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

  19. 19.

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

  20. 20.

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

  21. 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).

  22. 22.

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

  23. 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).

  24. 24.

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

  25. 25.

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

  26. 26.

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

  27. 27.

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

  28. 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).

  29. 29.

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

  30. 30.

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

  31. 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).

  32. 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).

Download references

Acknowledgements

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.

Author information

Affiliations

  1. Laboratory for Laser Energetics, University of Rochester, Rochester, NY, USA

    • Dustin H. Froula
    • , David Turnbull
    • , Andrew S. Davies
    • , Terrance J. Kessler
    • , Dan Haberberger
    • , John P. Palastro
    • , Seung-Whan Bahk
    • , Ildar A. Begishev
    • , Robert Boni
    • , Sara Bucht
    • , Joseph Katz
    •  & Jessica L. Shaw
  2. Physics Department, University of Rochester, Rochester, NY, USA

    • Dustin H. Froula
    • , Andrew S. Davies
    •  & Sara Bucht

Authors

  1. Search for Dustin H. Froula in:

  2. Search for David Turnbull in:

  3. Search for Andrew S. Davies in:

  4. Search for Terrance J. Kessler in:

  5. Search for Dan Haberberger in:

  6. Search for John P. Palastro in:

  7. Search for Seung-Whan Bahk in:

  8. Search for Ildar A. Begishev in:

  9. Search for Robert Boni in:

  10. Search for Sara Bucht in:

  11. Search for Joseph Katz in:

  12. Search for Jessica L. Shaw in:

Contributions

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.

Competing interests

The authors declare no competing interests.

Corresponding author

Correspondence to Dustin H. Froula.

Supplementary information

  1. Supplementary Information

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

Videos

  1. Supplementary Video 1

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

  2. Supplementary Video 2

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

  3. Supplementary Video 3

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

  4. Supplementary Video 4

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

  5. Supplementary Video 5

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

About this article

Publication history

Received

Accepted

Published

DOI

https://doi.org/10.1038/s41566-018-0121-8