Coherent soft X-ray pulses from an echo-enabled harmonic generation free-electron laser


X-ray free-electron lasers (FELs), which amplify light emitted by a relativistic electron beam, are extending nonlinear optical techniques to shorter wavelengths, adding element specificity by exciting and probing electronic transitions from core levels. These techniques would benefit tremendously from having a stable FEL source, generating spectrally pure and wavelength-tunable pulses. We show that such requirements can be met by operating the FEL in the so-called echo-enabled harmonic generation (EEHG) configuration. Here, two external conventional lasers are used to precisely tailor the longitudinal phase space of the electron beam before emission of X-rays. We demonstrate high-gain EEHG lasing producing stable, intense, nearly fully coherent pulses at wavelengths as short as 5.9 nm (~211 eV) at the FERMI FEL user facility. Low sensitivity to electron-beam imperfections and observation of stable, narrow-band, coherent emission down to 2.6 nm (~474 eV) make the technique a prime candidate for generating laser-like pulses in the X-ray spectral region, opening the door to multidimensional coherent spectroscopies at short wavelengths.

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Fig. 1: The EEHG scheme together with the electron-beam longitudinal phase space at different stages of the evolution.
Fig. 2: EEHG gain curve at 7.3 nm (~169 eV) and typical electron-beam longitudinal phase space at the FERMI FEL.
Fig. 3: Sensitivity of the FEL output to the electron-beam properties.
Fig. 4: EEHG performance at the FERMI FEL in the soft X-ray region.
Fig. 5: EEHG at high harmonics.
Fig. 6: EEHG in two-colour operation.

Data availability

The data that support the plots within this paper and other findings of this study are available from the corresponding authors upon reasonable request.

Code availability

The FEL code Genesis is available at


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The authors thank G. Stupakov, S. Bettoni, D. Ratner, G. Marcus, F. Bencivenga, E. Pedersoli, M. Sacchi, C. Callegari, Z. Huang, T. Raubenheimer and A. Zholents for useful discussions. The authors also acknowledge the continuous support of R. Godnig, R. Bracco, R. Visintini, and the FERMI – Elettra operator group during the experiment. This work was supported in part by the Director, Office of Science, Office of Basic Energy Sciences, of the US Department of Energy under contract nos DE-AC02-76SF00515 and DE-AC02-05CH11231 and award no. 2017-SLAC-100382. D.G. was supported by an Outgoing CEA fellowship from the CEA-Enhanced Eurotalents programme, co-funded by FP7 Marie-Skłodowska-Curie COFUND programme (grant agreement 600382).

Author information




E.M.A., G.D.N., D.X., L.G. and P.R.R. proposed the original idea of an EEHG experiment at FERMI. E.M.A. and P.R.R. guided the work and organized the experimental activities. E.M.A., L.B., N.B., G.D.N., S.D.M., B.D., W.M.F., E.F., G.G., D.G., L.G., N.S.M., G.M.P., P.R.R., E.R., S.S., C.Spezzani, M.T. and M.V. conducted the experiment on the accelerator and FEL. E.M.A., W.M.F., E.F., D.G., A.G., V.G., G.M.P., M.P., P.R.R. and E.R. analysed the data. E.P., E.F., E.H., G.P., P.R.R. and S.R. carried out numerical simulations and supported the experiment with theoretical analysis. A.A., E.M.A., M.B., D.C., M.Cautero, P.C., I.C., A.D., B.D., M.F., G.G., F.G., L.G., S.G., M.L., F.I., N.M., M.V., M.Manfredda, P.M., I.P.N., L.P., L.R., P.R.R., R.S., C.Scafuri, P.S., L.S., M.S., D.V., M.Zaccaria, D.Z. and M.Zangrando contributed to the experimental design and preparation. P.C., A.D., G.K., P.S., I.P.N. and M.B.D. prepared, operated and optimized the laser systems. F.C., M.Coreno, F.F., N.S.M., M.Malvestuto, M.Manfredda, P.M., L.R. and M.Zangrando optimized the photon diagnostic used during the experiment. P.R.R. wrote the manuscript draft. All authors participated in the experiment and contributed to improving the final version of the manuscript.

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Correspondence to Primož Rebernik Ribič or Enrico Massimiliano Allaria.

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Rebernik Ribič, P., Abrami, A., Badano, L. et al. Coherent soft X-ray pulses from an echo-enabled harmonic generation free-electron laser. Nat. Photonics 13, 555–561 (2019).

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