- Physical Review Journals
All JournalsPhysics Magazine

Physical Review Letters

Reuse & Permissions

It is not necessary to obtain permission to reuse this article or its components as it is available under the terms of the Creative Commons Attribution 4.0 International license. This license permits unrestricted use, distribution, and reproduction in any medium, provided attribution to the author(s) and the published article's title, journal citation, and DOI are maintained. Please note that some figures may have been included with permission from other third parties. It is your responsibility to obtain the proper permission from the rights holder directly for these figures.

Export citation

Export citation

Choose format for download:

Download Citation
  • Featured in Physics
  • Editors' Suggestion
  • Open Access

Demonstration of Mode-Locked Frequency Comb for an X-Ray Free-Electron Laser

Wenxiang Hu1,2, Gabriel Aeppli1,2,3, Christopher Arrell1, Marco Calvi1, Sergio Carbajo4,5,6,7, Andreas Dax1, Yunpei Deng1, Philipp Dijkstal8, David Dunning9,10 et al.

Simon Gerber1, Martin Huppert1, Stefan Neppl1, Sven Reiche8, Thomas Schietinger8, Neil Thompson9,10, Alexandre Trisorio1, Carlo Vicario1, Alexander Zholents11, and Eduard Prat8,*

  • *Contact author: eduard.prat@psi.ch
PDF

Phys. Rev. Lett. 135, 265001 – Published 23 December, 2025

DOI: https://doi.org/10.1103/wn8d-l7sh

Abstract

X-ray free-electron lasers (FELs) are powerful photon sources offering a wide wavelength range, subfemtosecond pulse duration, and high brightness. Most x-ray FELs are based on self-amplified spontaneous emission (SASE). SASE-FEL radiation has excellent transverse but only limited longitudinal coherence, with power and spectral profiles consisting of multiple randomly distributed spikes. In this Letter, we present the first experimental demonstration of mode-locked SASE, which generates periodic trains of phase-locked subfemtosecond pulses, thus providing an x-ray analog of the optical frequency comb. Our approach combines the mode-coupled SASE scheme, where magnetic chicanes between the undulator modules of the FEL increase the coherence of the output radiation, and an external optical laser that restricts the FEL amplification to periodic and short regions of the electron bunch. The work relies on evidence in the frequency and time domains for photons and electrons, respectively, and will benefit investigations of ultrafast dynamics as well as coherent spectroscopy, and enable new types of experiments requiring phase-correlated x-ray pulses.

View figure in article

Physics Subject Headings (PhySH)

Viewpoint

Boosting the Coherence of X-Ray Free-Electron Lasers

Published 23 December, 2025

Mode locking—a laser technique that revolutionized optical physics—has been extended to x rays, producing stable trains of attosecond pulses with unprecedented phase coherence.

See more in Physics

Article Text

References (58)

  1. C. Pellegrini, A. Marinelli, and S. Reiche, The physics of x-ray free-electron lasers, Rev. Mod. Phys. 88, 015006 (2016).
  2. E. A. Seddon, J. A. Clarke, D. J. Dunning, C. Masciovecchio, C. J. Milne, F. Parmigiani, D. Rugg, J. C. H. Spence, N. R. Thompson, K. Ueda, S. M. Vinko, J. S. Wark, and W. Wurth, Short-wavelength free-electron laser sources and science: A review, Rep. Prog. Phys. 80, 115901 (2017).
  3. T. Gruhl, T. Weinert, M. J. Rodrigues, C. J. Milne, G. Ortolani, K. Nass, E. Nango, S. Sen, P. J. M. Johnson, C. Cirelli et al., Ultrafast structural changes direct the first molecular events of vision, Nature (London) 615, 939 (2023).
  4. P. Fromme, W. S. Graves, and J. M. Martin-Garcia, Serial femtosecond crystallography: A decade at the forefront in structural biology, in eLS (John Wiley & Sons Ltd, New York, 2020), pp. 1–17.
  5. R. W. Schoenlein, S. Boutet, M. P. Minitti, and A. Dunne, The Linac Coherent Light Source: Recent developments and future plans, Appl. Sci. 7, 850 (2017).
  6. A. Round, E. Jungcheng, C. Fortmann-Grote, K. Giewekemeyer, R. Graceffa, C. Kim, H. Kirkwood, G. Mills, E. Round, T. Sato, S. Pascarelli, and A. Mancuso, Characterization of biological samples using ultra-short and ultra-bright XFEL pulses, in Advanced Technologies for Protein Complex Production and Characterization: Volume II, edited by M. C. Vega and F. J. Fernández (Springer Nature Switzerland, Cham, 2024), pp. 141–162.
  7. C. Bostedt, S. Boutet, D. M. Fritz, Z. Huang, H. J. Lee, H. T. Lemke, A. Robert, W. F. Schlotter, J. J. Turner, and G. J. Williams, Linac Coherent Light Source: The first five years, Rev. Mod. Phys. 88, 015007 (2016).
  8. J. B. Hastings, L. Rivkin, and G. Aeppli, Present and future accelerator-based x-ray sources: A perspective, Rev. Accel. Sci. Techol. 10, 33 (2019).
  9. A. M. Kondratenko and E. L. Saldin, Generation of coherent radiation by a relativistic electron beam in an ondolator, Part. Accel. 10, 207 (1980).
  10. R. Bonifacio, C. Pellegrini, and L. Narducci, Collective instabilities and high-gain regime in a free electron laser, Opt. Commun. 50, 373 (1984).
  11. S. Huang, Y. Ding, Y. Feng, E. Hemsing, Z. Huang, J. Krzywinski, A. A. Lutman, A. Marinelli, T. J. Maxwell, and D. Zhu, Generating single-spike hard x-ray pulses with nonlinear bunch compression in free-electron lasers, Phys. Rev. Lett. 119, 154801 (2017).
  12. A. Marinelli, J. MacArthur, P. Emma, M. Guetg, C. Field, D. Kharakh, A. A. Lutman, Y. Ding, and Z. Huang, Experimental demonstration of a single-spike hard-x-ray free-electron laser starting from noise, Appl. Phys. Lett. 111, 151101 (2017).
  13. Z. Zhang, J. Duris, J. P. MacArthur, A. Zholents, Z. Huang, and A. Marinelli, Experimental demonstration of enhanced self-amplified spontaneous emission by photocathode temporal shaping and self-compression in a magnetic wiggler, New J. Phys. 22, 083030 (2020).
  14. A. Malyzhenkov, Y. P. Arbelo, P. Craievich, P. Dijkstal, E. Ferrari, S. Reiche, T. Schietinger, P. Juranić, and E. Prat, Single- and two-color attosecond hard x-ray free-electron laser pulses with nonlinear compression, Phys. Rev. Res. 2, 042018 (2020).
  15. J. P. Duris, J. P. MacArthur, J. M. Glownia, S. Li, S. Vetter, A. Miahnahri, R. Coffee, P. Hering, A. Fry, M. E. Welch et al., Controllable x-ray pulse trains from enhanced self-amplified spontaneous emission, Phys. Rev. Lett. 126, 104802 (2021).
  16. E. Prat, A. Malyzhenkov, C. Arrell, P. Craievich, S. Reiche, T. Schietinger, and G. Wang, Coherent sub-femtosecond soft x-ray free-electron laser pulses with nonlinear compression, APL Photonics 8, 111302 (2023).
  17. J. Yan, W. Qin, Y. Chen, W. Decking, P. Dijkstal, M. Guetg, I. Inoue, N. Kujala, S. Liu, T. Long, N. Mirian, and G. Geloni, Terawatt-attosecond hard x-ray free-electron laser at high repetition rate, Nat. Photonics 18, 1293 (2024).
  18. J. Amann, W. Berg, V. Blank, F. J. Decker, Y. Ding, P. Emma, Y. Feng, J. Frisch, D. Fritz, J. Hastings et al., Demonstration of self-seeding in a hard-x-ray free-electron laser, Nat. Photonics 6, 693 (2012).
  19. D. Ratner, R. Abela, J. Amann, C. Behrens, D. Bohler, G. Bouchard, C. Bostedt, M. Boyes, K. Chow, D. Cocco et al., Experimental demonstration of a soft x-ray self-seeded free-electron laser, Phys. Rev. Lett. 114, 054801 (2015).
  20. I. Inoue, T. Osaka, T. Hara, T. Tanaka, T. Inagaki, T. Fukui, S. Goto, Y. Inubushi, H. Kimura, R. Kinjo et al., Generation of narrow-band x-ray free-electron laser via reflection self-seeding, Nat. Photonics 13, 319 (2019).
  21. I. Nam, C.-K. Min, B. Oh, G. Kim, D. Na, Y. J. Suh, H. Yang, M. H. Cho, C. Kim, M.-J. Kim et al., High-brightness self-seeded x-ray free-electron laser covering the 3.5 keV to 14.6 keV range, Nat. Photonics 15, 435 (2021).
  22. S. Liu, C. Grech, M. Guetg, S. Karabekyan, V. Kocharyan, N. Kujala, C. Lechner, T. Long, N. Mirian, W. Qin et al., Cascaded hard x-ray self-seeded free-electron laser at megahertz repetition rate, Nat. Photonics 17, 984 (2023).
  23. Z. Zhao, D. Wang, J. Chen, Z. Chen, H. Deng, J. Ding, C. Feng, Q. Gu, M. Huang, T. Lan et al., First lasing of an echo-enabled harmonic generation free-electron laser, Nat. Photonics 6, 360 (2012).
  24. P. R. Ribič, A. Abrami, L. Badano, M. Bossi, H. H. Braun, N. Bruchon, F. Capotondi, D. Castronovo, M. Cautero, P. Cinquegrana et al., Coherent soft x-ray pulses from an echo-enabled harmonic generation free-electron laser, Nat. Photonics 13, 555 (2019).
  25. N. R. Thompson and B. W. J. McNeil, Mode locking in a free-electron laser amplifier, Phys. Rev. Lett. 100, 203901 (2008).
  26. B. W. J. McNeil, N. R. Thompson, and D. J. Dunning, Transform-limited x-ray pulse generation from a high-brightness self-amplified spontaneous-emission free-electron laser, Phys. Rev. Lett. 110, 134802 (2013).
  27. E. Prat, W. Hu, C. Arrell, M. Calvi, P. Dijkstal, R. Follath, and S. Reiche, Experimental demonstration of mode-coupled and high-brightness self-amplified spontaneous emission in an x-ray free-electron laser, Phys. Rev. Lett. 133, 205001 (2024).
  28. R. R. Robles, K. A. Larsen, D. Cesar, T. Driver, J. Duris, P. Franz, D. Garratt, V. Guo, G. Just, R. Lemons et al., Spectrotemporal shaping of attosecond x-ray pulses with a fresh-slice free-electron laser, Phys. Rev. Lett. 134, 115001 (2025).
  29. A. Wituschek, L. Bruder, E. M. Allaria, U. Bangert, M. Binz, R. Borghes, C. Callegari, G. Cerullo, P. Cinquegrana, L. Giannessi et al., Tracking attosecond electronic coherences using phase-manipulated extreme ultraviolet pulses, Nat. Commun. 11, 883 (2020).
  30. S. Reiche, G. Knopp, B. Pedrini, E. Prat, G. Aeppli, and S. Gerber, A perfect x-ray beam splitter and its applications to time-domain interferometry and quantum optics exploiting free-electron lasers, Proc. Natl. Acad. Sci. U.S.A. 119, e2117906119 (2022).
  31. D. Xiang, Y. Ding, T. Raubenheimer, and J. Wu, Mode-locked multichromatic x rays in a seeded free-electron laser for single-shot x-ray spectroscopy, Phys. Rev. ST Accel. Beams 15, 050707 (2012).
  32. E. Kur, D. J. Dunning, B. W. J. McNeil, J. Wurtele, and A. A. Zholents, A wide bandwidth free-electron laser with mode locking using current modulation, New J. Phys. 13, 063012 (2011).
  33. B. Adams, G. Aeppli, T. Allison, A. Q. R. Baron, P. Bucksbaum, A. I. Chumakov, C. Corder, S. P. Cramer, S. DeBeer, Y. Ding et al., Scientific opportunities with an x-ray free-electron laser oscillator, arXiv:1903.09317.
  34. E. Prat, A. Alhaddad, C. Arrell, S. Augustin, M. Boll, C. Bostedt, M. Calvi, A. Cavalieri, P. Craievich, A. Dax et al., An x-ray free-electron laser with a highly configurable undulator and integrated chicanes for tailored pulse properties, Nat. Commun. 14, 5069 (2023).
  35. M. Calvi, X. Liang, E. Ferrari, A. Alarcon, E. Prat, S. Reiche, T. Schmidt, D. Voulot, K. Zhang, and R. Ganter, Versatile modulators for laser-based FEL seeding at SwissFEL, J. Synchrotron Radiat. 30, 276 (2023).
  36. A. Trisorio, S. Reiche, C. Arrell, A. L. Cavalieri, A. Dax, C. M. Deutschendorf, P. Dijkstal, E. Divall, R. Ganter, R. Ischebeck et al., Laser-based seeding of SwissFEL Athos, in Proceedings of the FEL2022, International Free Electron Laser Conference No. 40 (JACoW Publishing, Geneva, Switzerland, 2022), pp. 304–308.
  37. X. Liang, M. Calvi, M.-E. Couprie, R. Ganter, C. Kittel, N. Sammut, T. Schmidt, M. Valléau, and K. Zhang, Analysis of the first magnetic results of the PSI APPLE X undulators in elliptical polarisation, Nucl. Instrum. Methods Phys. Res., Sect. A 987, 164741 (2021).
  38. P. Craievich, M. Bopp, H.-H. Braun, A. Citterio, R. Fortunati, R. Ganter, T. Kleeb, F. Marcellini, M. Pedrozzi, E. Prat et al., Novel x-band transverse deflection structure with variable polarization, Phys. Rev. Accel. Beams 23, 112001 (2020).
  39. E. Prat, Z. Geng, C. Kittel, A. Malyzhenkov, F. Marcellini, S. Reiche, T. Schietinger, and P. Craievich, Attosecond time-resolved measurements of electron and photon beams with a variable polarization x-band radiofrequency deflector at an x-ray free-electron laser, Adv. Photonics 7, 026002 (2025).
  40. R. Ischebeck, E. Prat, V. Thominet, and C. Ozkan Loch, Transverse profile imager for ultrabright electron beams, Phys. Rev. ST Accel. Beams 18, 082802 (2015).
  41. Y. Ding, C. Behrens, P. Emma, J. Frisch, Z. Huang, H. Loos, P. Krejcik, and M.-H. Wang, Femtosecond x-ray pulse temporal characterization in free-electron lasers using a transverse deflector, Phys. Rev. ST Accel. Beams 14, 120701 (2011).
  42. C. Behrens, F.-J. Decker, Y. Ding, V. Dolgashev, J. Frisch, Z. Huang, P. Krejcik, H. Loos, A. Lutman, T. Maxwell, J. Turner, J. Wang, M.-H. Wang, J. Welch, and J. Wu, Few-femtosecond time-resolved measurements of x-ray free-electron lasers, Nat. Commun. 5, 3762 (2014).
  43. C. Arrell, V. Thominet, Y. Arbelo, U. Wagner, N. Gradwohl, E. Prat, L. Patthey, and R. Follath, High resolution soft x-ray spectrometer for FEL characterisation and optimisation, in Conference on Lasers and Electro-Optics (Optica Publishing Group, Washington, D.C., 2022), JTu3A.62.
  44. A. A. Sorokin, Y. Bican, S. Bonfigt, M. Brachmanski, M. Braune, U. F. Jastrow, A. Gottwald, H. Kaser, M. Richter, and K. Tiedtke, An x-ray gas monitor for free-electron lasers, J. Synchrotron Radiat. 26, 1092 (2019).
  45. J. W. Goodman, Statistical Optics (John Wiley & Sons, New York, 2000).
  46. P. Dijkstal, W. Qin, and S. Tomin, Longitudinal phase space diagnostics with a nonmovable corrugated passive wakefield streaker, Phys. Rev. Accel. Beams 27, 050702 (2024).
  47. D. J. Dunning, Methods for the generation of ultra-short free-electron laser pulses, Ph.D. thesis, University of Strathclyde, 2015.
  48. A. Cavalieri, N. Mueller, T. Uphues, V. Yakovlev, A. Baltuska, B. Horvath, B. Schmidt, L. Blümel, R. Holzwarth, S. Hendel et al., Attosecond spectroscopy in condensed matter, Nature (London) 449, 1029 (2007).
  49. Z. Guo, T. Driver, S. Beauvarlet, D. Cesar, J. Duris, P. Franz, O. Alexander, D. Bohler, C. Bostedt, V. Averbukh et al., Experimental demonstration of attosecond pump–probe spectroscopy with an x-ray free-electron laser, Nat. Photonics 18, 691 (2024).
  50. T. W. Hänsch, Nobel lecture: Passion for precision, Rev. Mod. Phys. 78, 1297 (2006).
  51. N. F. Ramsey, A molecular beam resonance method with separated oscillating fields, Phys. Rev. 78, 695 (1950).
  52. P. M. Paul, E. S. Toma, P. Breger, G. Mullot, F. Augé, P. Balcou, H. G. Muller, and P. Agostini, Observation of a train of attosecond pulses from high harmonic generation, Science 292, 1689 (2001).
  53. P. K. Maroju, C. Grazioli, M. Di Fraia, M. Moioli, D. Ertel, H. Ahmadi, O. Plekan, P. Finetti, E. Allaria, L. Giannessi et al., Attosecond pulse shaping using a seeded free-electron laser, Nature (London) 578, 386 (2020).
  54. P. K. Maroju, M. Di Fraia, O. Plekan, M. Bonanomi, B. Merzuk, D. Busto, I. Makos, M. Schmoll, R. Shah, P. R. Ribič et al., Attosecond coherent control of electronic wave packets in two-colour photoionization using a novel timing tool for seeded free-electron laser, Nat. Photonics 17, 200 (2023).
  55. M. Han, J.-B. Ji, K. Ueda, and H. J. Wörner, Attosecond metrology in circular polarization, Optica 10, 1044 (2023).
  56. T. Popmintchev, Design of coherent x-rays for 5D imaging at the space-time resolution extreme (conference presentation), in Ultrafast Phenomena and Nanophotonics XXI, edited by M. Betz and A. Y. Elezzabi, International Society for Optics and Photonics (SPIE, 2017), Vol. 10102, p. 1010217.
  57. W. Hu, Demonstration of mode-locked frequency comb for an x-ray free-electron laser (2025), https://zenodo.org/records/17260204.
  58. E. Prat, E. Ferrari, M. Calvi, R. Ganter, S. Reiche, and T. Schmidt, Demonstration of a compact x-ray free-electron laser using the optical Klystron effect, Appl. Phys. Lett. 119, 151102 (2021).

Outline

Information

Phys. Rev. Lett. 135, 265001– Published 23 December, 2025
  • Received 23 July 2025
  • Accepted 30 September 2025
Crossmark - Check for updates button
Creative Commons Logo

Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI.

Published by the American Physical Society

Sign In to Your Journals Account

Filter

Filter

Article Lookup

Enter a citation