Letter | Published:

Spatiotemporal control of laser intensity


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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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.


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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.

Author information

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.

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.


  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.

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Further reading

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.