Sub-femtosecond precision measurement of relative X-ray arrival time for free-electron lasers

Journal name:
Nature Photonics
Year published:
Published online

Today's brightest coherent X-ray sources, X-ray free-electron lasers, produce ultrafast X-ray pulses for which full-width at half-maximum durations as short as 3 fs have been measured1. There has been a marked increase in the popularity of such short pulses now that optical timing techniques have begun to report an X-ray/optical delay below ∼10 fs r.m.s. errors. As a result, sub-10 fs optical pulses have been implemented at the Linac Coherent Light Source (LCLS) X-ray beamlines, thus warranting a push to reduce the error in X-ray/optical delay measurements to the 1 fs level. Here, we report a unique two-dimensional spectrogram measurement of the relative X-ray/optical delay. This easily scalable relative delay measurement already surpasses previous techniques by an order of magnitude with its sub-1 fs temporal resolution and opens up the prospect of time-resolved X-ray measurements to the attosecond community.

At a glance


  1. Schematic of the single-shot geometry for measurement of the spectrogram.
    Figure 1: Schematic of the single-shot geometry for measurement of the spectrogram.

    a, The X-ray and optical beams are crossed in a silicon nitride membrane and their relative delay is encoded in the spatial beam profile of the optical probe. The crossing angle α and beam diameters define the time window in which the X-ray-induced absorption is probed. b, Measured spectrogram using an unpumped normalization spectrogram to calculate the change in transmission. The result of the two-step edge-finding algorithm to determine the X-ray arrival time is overlaid as a black dashed line.

  2. Edge finding.
    Figure 2: Edge finding.

    a, Fitting of the transmission model (blue) to a lineout of the measured spectrogram (black). b, Error (r.m.s.) of edge position t0 based on least-squares fitting of equation (3) for a single 110 µJ X-ray shot with 800 eV photon energy.

  3. Results for timing precision.
    Figure 3: Results for timing precision.

    a, Timing precision based on 1,310 shots with X-ray pulse energies greater than 40 µJ. Of the shots, 48% have an r.m.s. timing error below 1 fs. b, Scaling of transmission signals with X-ray fluence. The data points correspond to the left abscissa and the error bars are given as standard deviation. The induced transmission change increases linearly up to a fluence of 0.5 J cm−2. Black line: fit of the linear regime with the slope given in equation (8).


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Author information


  1. The Linac Coherent Light Source, SLAC National Accelerator Laboratory, 2575 Sand Hill Road, Menlo Park, California 94025, USA

    • N. Hartmann,
    • W. Helml,
    • K. R. Ferguson,
    • S. Schorb,
    • M. L. Swiggers,
    • S. Carron,
    • C. Bostedt,
    • J.-C. Castagna,
    • J. Bozek,
    • J. M. Glownia,
    • A. R. Fry,
    • W. E. White &
    • R. N. Coffee
  2. Institute of Applied Physics, University of Bern, Sidlerstrasse 5, 3012 Bern, Switzerland

    • N. Hartmann &
    • T. Feurer
  3. Technische Universität München, James-Franck-Strasse 1, 85748 Garching, Germany

    • W. Helml
  4. European XFEL GmbH, Notkestrasse 85, 22607 Hamburg, Germany

    • A. Galler,
    • J. Grünert &
    • S. L. Molodtsov
  5. LCAR-UMR 5589-Université Paul Sabatier Toulouse III-CNRS, 118 Route de Narbonne, Bat. 3R1B4, 31062 Toulouse Cedex 9, France

    • M. R. Bionta
  6. Institute of Experimental Physics, University of Technology Bergakademie Freiberg, Leipziger Strasse 23, 09599 Freiberg, Germany

    • S. L. Molodtsov
  7. Mesa Photonics, LLC, 1550 Pacheco St. Santa Fe, New Mexico 87505, USA

    • D. J. Kane
  8. Paul Scherrer Institute, 5232 Villigen, Switzerland

    • C. P. Hauri
  9. Physics Department, Ecole Polytechnique Federale de Lausanne, 1013 Lausanne, Switzerland

    • C. P. Hauri


N.H. and R.N.C conceived and coordinated the experiment. M.R.B., J.G. and R.N.C. carried out sample preparation. N.H., W.H., A.G., J.M.G., D.J.K. and R.N.C. built the optical set-up. M.R.B., K.R.F., S.S., M.L.S., S.C., C.B., J.-C.C. and J.B. carried out instrument control and integration. N.H. and D.J.K. performed data analysis. N.H., R.N.C., T.F., C.P.H. and W.H. interpreted data. R.N.C., T.F., C.P.H., A.R.F., W.E.W. and S.L.M. oversaw manuscript production. N.H. wrote the paper with extensive suggestions from R.N.C., T.F., C.P.H., W.H. and D.J.K. and contributions from all other authors.

Competing financial interests

D.J.K., head of Mesa Photonics, has referenced some of the results herein for SBIR proposals regarding the development of temporal X-ray diagnostics.

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