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Attosecond pulse shaping using a seeded free-electron laser


Attosecond pulses are central to the investigation of valence- and core-electron dynamics on their natural timescales1,2,3. The reproducible generation and characterization of attosecond waveforms has been demonstrated so far only through the process of high-order harmonic generation4,5,6,7. Several methods for shaping attosecond waveforms have been proposed, including the use of metallic filters8,9, multilayer mirrors10 and manipulation of the driving field11. However, none of these approaches allows the flexible manipulation of the temporal characteristics of the attosecond waveforms, and they suffer from the low conversion efficiency of the high-order harmonic generation process. Free-electron lasers, by contrast, deliver femtosecond, extreme-ultraviolet and X-ray pulses with energies ranging from tens of microjoules to a few millijoules12,13. Recent experiments have shown that they can generate subfemtosecond spikes, but with temporal characteristics that change shot-to-shot14,15,16. Here we report reproducible generation of high-energy (microjoule level) attosecond waveforms using a seeded free-electron laser17. We demonstrate amplitude and phase manipulation of the harmonic components of an attosecond pulse train in combination with an approach for its temporal reconstruction. The results presented here open the way to performing attosecond time-resolved experiments with free-electron lasers.

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Fig. 1: Multi-photon sideband generation and principle of the measurement.
Fig. 2: Correlation plots of the oscillating components of the sidebands and retrieval of phase difference Δφ7,8,9.
Fig. 3: Complete phase and amplitude shaping of attosecond waveforms.
Fig. 4: Synthesis of complex attosecond waveforms.

Data availability

Raw data were generated at the FERMI large-scale facility. Derived data supporting the findings of this study are available from the corresponding author on reasonable request.


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This project received funding from the European Union’s Horizon 2020 research and innovation programme under the Marie Sklodowska-Curie grant agreement no. 641789 MEDEA and the Italian Ministry of Research (Project FIRB no. RBID08CRXK). K.U. acknowledges support from the X-ray Free Electron Laser Utilization Research Project and the X-ray Free Electron Laser Priority Strategy Program of the Ministry of Education, Culture, Sports, Science and Technology of Japan (MEXT), from the Cooperative Research Program ‘Network Joint Research Center for Materials and Devices: Dynamic Alliance for Open Innovation Bridging Human, Environment and Materials’, from the bilateral project CNR-JSPS ‘Ultrafast science with extreme ultraviolet Free Electron Lasers’, and from the IMRAM project for international co-operation. R.F. and J.M. thank the Swedish Research Council (VR) and the Knut and Alice Wallenberg Foundation for financial support. E.V.G. acknowledges support from the Foundation for the Advancement of Theoretical Physics and Mathematics ‘BASIS’. M. Meyer and T.M. acknowledge support from the Deutsche Forschungsgemeinschaft (DFG) under grant no. SFB925/1. A.A.L. was supported by the US Department of Energy contract no. DE-AC02-76SF00515. Research at Louisiana State University was supported by the US Department of Energy, Office of Science, Basic Energy Sciences, under contract no. de-sc0010431. Portions of this research were conducted with high performance computing resources provided by Louisiana State University ( and by Louisiana Optical Network Infrastructure ( G.S. acknowledges useful discussions about the simulations and the data analysis with T. Pfeifer and M. Kübel. We acknowledge L. Foglia, A. Simoncig and M. Coreno for valuable discussions.

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Authors and Affiliations



P.K.M., M. Moioli, D.E., M.D.F., O.P., H.A., P.C., T.M., M. Meyer, S.B., N.I., E.R.S., J.M., T.C., M.D., S.K., H.N.G., D.Y., K.U., K.C.P., C.G. and C.C. contributed to data acquisition and to data analysis. L.G., E.A., G.D.N., C.S., G.P. and S.S. operated the machine and designed the three and four harmonic generation scheme. A.A.L. contributed to the machine operation. A.D. and M. B. D. designed the beam path for the NIR pulse. P.F. designed the mechanics for the recombination mirror. A.D. and C.G. designed the recombination mirror, and the whole set-up was installed by A.D., C.G. and M.D.F. A.D. and M.D.F. designed and installed the beam dump diagnostic system for alignment of the collinear configuration. M.D.F., O.P. and C.C. prepared the end station. R.B., G.K., C.E.S.D.R. and F.B. developed the analysis tools used during beamtime. M.R. contributed to the preliminary development of the simulation codes. M.L., J.E.B. and K.J.S. performed the TDSE calculations. R.J.S. and R.F. constructed and operated the magnetic bottle electron spectrometer. A.N.G.-G. and E.V.G. developed the perturbation-theory approach and derived the atomic phase contributions. C.C. and G.S. conceived the idea of the experiment. G.S. developed the numerical code for the SFA simulations. P.K.M. developed the numerical code for the correlation analysis. P.K.M., C.C. and G.S. analysed the experimental data and performed the simulations. G.S. supervised the work. P.K.M., A.N.G.-G., E.V.G., C.C. and G.S. wrote the manuscript, which was discussed and agreed by all coauthors.

Corresponding author

Correspondence to Giuseppe Sansone.

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The authors declare no competing interests.

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Peer review information Nature thanks Eduard Prat Costa, Makina Yabashi and the other, anonymous, reviewer(s) for their contribution to the peer review of this work.

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Extended data figures and tables

Extended Data Fig. 1 Free-electron laser configuration for the generation of multiple harmonics and experimental setup.

a, b, Configurations of the six undulators (U1–U6) for the generation of three (a) and four (b) harmonics. In the first case, two undulators per harmonic were used, while in the second case, each harmonic was generated by one undulator only. The phase-shifters (PS1–PS5) used to control the relative phase between the harmonics are indicated in yellow for the two configurations. c, d, Typical single-shot photoelectron spectra without (black lines) and with (red lines) the NIR pulse, measured for the three (c) and four (d) harmonic cases. e, Schematic, half-section view of the spectrometer, including the ion flight tube (bottom) and electron flight tube (top). f, Normalized simulated geometrical collection efficiency as a function of polar emission angle for 2–42 eV electrons, using a cylindrical magnet configuration with the pole placed 5 mm away from the interaction region. Electrons were simulated using steps of 5 eV. An emission angle of 0° (180°) corresponds to the axis of the spectrometer in (away from) the direction of the electron detector.

Extended Data Fig. 2 Simulated correlation plots.

Shown are simulated correlation plots (P8,9, P7,8) for different values of Δφ7,8,9 from 0 to 2π in steps of π/4: Δφ7,8,9 = 0 (a), π/4 (b), π/2 (c), 3π/4 (d), π (e), 5π/4 (f), 3π/2 (g), 7π/4 (h) and 2π (i). The intensities of the three harmonics are equal.

Extended Data Fig. 3 Simulated correlation parameter ρ7,8,9.

Evolution of the correlation parameter ρ7,8,9 as a function of the phase difference Δφ7,8,9 simulated using the SFA (red) and the TDSE (blue). The black curve indicates a cosine evolution.

Extended Data Fig. 4 Phase reordering of single-shot sideband intensities.

a, b, Intensity of the sidebands \({{\rm{S}}}_{8,9}^{(-)}\) (a) and \({{\rm{S}}}_{7,8}^{(-)}\) (b) (black points) as a function of the relative phase 3ωNIRτ between the attosecond pulse train and the NIR field. The red curves show sinusoidal fits of the distributions. c, Comparison of the reconstructed attosecond pulse train using the correlation parameter method ρ7,8,9 (black curve) and the ‘reconstruction of attosecond beating by interference of two-photon transitions’ method (red curve) based on the phase differences extracted from the sinusoidal fits. The second method is typically used for the characterization of attosecond pulse trains produced by HHG. The error in the reconstructions is indicated by the shaded areas.

Extended Data Fig. 5 Reconstruction of attosecond pulses for multi-NIR photon transitions.

ad, Input (black line) and reconstructed (a, red line; b, blue line; c, green line; and d, magenta line) intensity profiles of the attosecond train, corresponding to Fig. 1c–f for phase differences Δφ7,8,9 = 0 (a), π/2 (b), π (c) and 3π/2 (d). e, Reconstruction of attosecond pulses from sideband oscillations for multi-NIR photon transitions for the trace presented in Fig. 1b (input (black line) and reconstructed (blue dotted line) intensity profiles). The intensity of the NIR pulse is INIR = 1.5 × 1011 W cm−2. The relative phases between the harmonics are: φ10 − φ9 = 108°, φ9 − φ8 = 160° and φ8 − φ7 = 8°.

Extended Data Fig. 6 GENESIS 1.3 simulations.

Shown is the attosecond pulse train simulated using the GENESIS 1.3 code: a, complete temporal evolution of the train, and b, magnified view of the attosecond pulses in the train.

Extended Data Table 1 XUV experimental parameters
Extended Data Table 2 Experimental correlation coefficients
Extended Data Table 3 Amplitudes and harmonic phase differences
Extended Data Table 4 Parameters for the GENESIS 1.3 simulations

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Maroju, P.K., Grazioli, C., Di Fraia, M. et al. Attosecond pulse shaping using a seeded free-electron laser. Nature 578, 386–391 (2020).

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