- Physical Review Journals
All JournalsPhysics Magazine

Physical Review Research

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
  • Open Access

Orbit-controlled generation of two-color attosecond mode-locked free-electron lasers

Lingjun Tu1, Hao Sun1, Huaiqian Yi1, Li Zeng1, Yifan Liang1, Yong Yu1, Xiaofan Wang1,*, and Weiqing Zhang2,†

  • *Contact author: wangxf@mail.iasf.ac.cn
  • †Contact author: weiqingzhang@dicp.ac.cn
PDF

Phys. Rev. Research 7, 043296 – Published 15 December, 2025

DOI: https://doi.org/10.1103/wn3m-s5xf

Abstract

The generation of attosecond x-ray pulses has garnered significant attention within the x-ray free-electron laser (FEL) community due to their potential for ultrafast time-resolved studies. Such pulses enable the investigation of electron dynamics with unprecedented temporal resolution, opening avenues in fields such as quantum control and ultrafast spectroscopy. In an FEL, the mode-locking technique synthesizes a comb of longitudinal modes by applying spatiotemporal shifts between the co-propagating radiation and the electron bunch. Here, we propose a scheme for generating two-color attosecond mode-locked FEL pulses via orbit control in two-stage mode-locked undulators. Specifically, a chicane with a wiggler inserted in the middle generates periodic temporal-transverse modulation in the electron beam. In this configuration, the low-energy and high-energy components of the beam lase in separate undulator sections, with each producing attosecond mode-locked FEL pulses. Three-dimensional simulations with realistic parameters confirm that trains of 250-attosecond soft x-ray pulses at the gigawatt level can be independently generated in each undulator section. Furthermore, the time delay between the two pulse trains can be adjusted over a range of several hundred femtoseconds.

View figure in article

Physics Subject Headings (PhySH)

Article Text

References (48)

  1. I. Pupeza, C. Zhang, M. Högner, and J. Ye, Extreme-ultraviolet frequency combs for precision metrology and attosecond science, Nat. Photon. 15, 175 (2021).
  2. M. Hentschel, R. Kienberger, C. Spielmann, G. A. Reider, N. Milosevic, T. Brabec, P. Corkum, U. Heinzmann, M. Drescher, and F. Krausz, Attosecond metrology, Nature (London) 414, 509 (2001).
  3. S. Kühn, M. Dumergue, S. Kahaly, S. Mondal, M. Füle, T. Csizmadia, B. Farkas, B. Major, Z. Várallyay, E. Cormier et al., The ELI-ALPS facility: The next generation of attosecond sources, J. Phys. B: At. Mol. Opt. Phys. 50, 132002 (2017).
  4. B. W. McNeil and N. R. Thompson, X-ray free-electron lasers, Nat. Photon. 4, 814 (2010).
  5. P. Emma, R. Akre, J. Arthur, R. Bionta, C. Bostedt, J. Bozek, A. Brachmann, P. Bucksbaum, R. Coffee, F.-J. Decker et al., First lasing and operation of an ångstrom-wavelength free-electron laser, Nat. Photon. 4, 641 (2010).
  6. S. Huang, Y. Ding, Y. Feng, E. Hemsing, Z. Huang, J. Krzywinski, A. Lutman, A. Marinelli, T. 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).
  7. J. Yan, W. Qin, Y. Chen, W. Decking, P. Dijkstal, M. Guetg, I. Inoue, N. Kujala, S. Liu, T. Long et al., Terawatt-attosecond hard x-ray free-electron laser at high repetition rate, Nat. Photon. 18, 1293 (2024).
  8. M. Wang, L. Zeng, B. Zhang, Q. Zhu, X. Shen, X. Wang, Q. Li, and W. Zhang, High-efficiency plasma-based compressor for ultrafast soft x-ray free-electron lasers, Phys. Rev. Lett. 135, 155001 (2025).
  9. J. Duris, S. Li, T. Driver, E. G. Champenois, J. P. MacArthur, A. A. Lutman, Z. Zhang, P. Rosenberger, J. W. Aldrich, R. Coffee et al., Tunable isolated attosecond x-ray pulses with gigawatt peak power from a free-electron laser, Nat. Photon. 14, 30 (2020).
  10. P. Franz, S. Li, T. Driver, R.R. Robles, D. Cesar, E. Isele, Z. Guo, J. Wang, J.P. Duris, K. Larsen et al., Terawatt-scale attosecond x-ray pulses from a cascaded superradiant free-electron laser, Nat. Photon. 18, 698 (2024).
  11. N. R. Thompson and B. W. J. McNeil, Mode locking in a free-electron laser amplifier, Phys. Rev. Lett. 100, 203901 (2008).
  12. E. Kur, D. Dunning, B. McNeil, J. Wurtele, and A. Zholents, A wide bandwidth free-electron laser with mode locking using current modulation, New J. Phys. 13, 063012 (2011).
  13. C. Feng, J. Chen, and Z. Zhao, Generating stable attosecond x-ray pulse trains with a mode-locked seeded free-electron laser, Phys. Rev. ST Accel. Beams 15, 080703 (2012).
  14. 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).
  15. D. J. Dunning, B. W. J. McNeil, and N. R. Thompson, Few-cycle pulse generation in an x-ray free-electron laser, Phys. Rev. Lett. 110, 104801 (2013).
  16. 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).
  17. E. Prat, A. Al Haddad, C. Arrell, S. Augustin, M. Boll, C. Bostedt, M. Calvi, A.L. 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).
  18. W. Hu, C. H. Shim, G. Kim, S. Kim, S.-H. Kwon, C.-K. Min, K.-J. Moon, D. Na, Y. J. Suh, C.-K. Sung et al., Tunable, phase-locked hard x-ray pulse sequences generated by a free-electron laser, arXiv:2508.00455.
  19. J. Morgenweg, I. Barmes, and K. S. Eikema, Ramsey-comb spectroscopy with intense ultrashort laser pulses, Nat. Phys. 10, 30 (2014).
  20. D. Spangenberg, P. Neethling, E. Rohwer, M. H. Brügmann, and T. Feurer, Time-domain ptychography, Phys. Rev. A 91, 021803 (2015).
  21. 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. USA 119, e2117906119 (2022).
  22. I. Coddington, N. Newbury, and W. Swann, Dual-comb spectroscopy, Optica 3, 414 (2016).
  23. M.-G. Suh, Q.-F. Yang, K. Y. Yang, X. Yi, and K. J. Vahala, Microresonator soliton dual-comb spectroscopy, Science 354, 600 (2016).
  24. M. Yu, Y. Okawachi, A.G. Griffith, N. Picqué, M. Lipson, and A.L. Gaeta, Silicon-chip-based mid-infrared dual-comb spectroscopy, Nat. Commun. 9, 1869 (2018).
  25. A. Lutman, F.-J. Decker, J. Arthur, M. Chollet, Y. Feng, J. Hastings, Z. Huang, H. Lemke, H.-D. Nuhn, A. Marinelli et al., Demonstration of single-crystal self-seeded two-color x-ray free-electron lasers, Phys. Rev. Lett. 113, 254801 (2014).
  26. 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).
  27. E. Prat, P. Dijkstal, E. Ferrari, R. Ganter, P. Juranić, A. Malyzhenkov, S. Reiche, T. Schietinger, G. Wang, A. A. Haddad et al., Widely tunable two-color x-ray free-electron laser pulses, Phys. Rev. Res. 4, L022025 (2022).
  28. Z. Guo, T. Driver, S. Beauvarlet, D. Cesar, J. Duris, P. L. 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. Photon. 18, 691 (2024).
  29. A. A. Lutman, T. J. Maxwell, J. P. MacArthur, M. W. Guetg, N. Berrah, R. N. Coffee, Y. Ding, Z. Huang, A. Marinelli, S. Moeller et al., Fresh-slice multicolour x-ray free-electron lasers, Nat. Photon. 10, 745 (2016).
  30. M. W. Guetg, A. A. Lutman, Y. Ding, T. J. Maxwell, and Z. Huang, Dispersion-based fresh-slice scheme for free-electron lasers, Phys. Rev. Lett. 120, 264802 (2018).
  31. G. Wang, P. Dijkstal, S. Reiche, K. Schnorr, and E. Prat, Millijoule femtosecond x-ray pulses from an efficient fresh-slice multistage free-electron laser, Phys. Rev. Lett. 132, 035002 (2024).
  32. E. L. Saldin, E. A. Schneidmiller, and M. V. Yurkov, Self-amplified spontaneous emission FEL with energy-chirped electron beam and its application for generation of attosecond x-ray pulses, Phys. Rev. ST Accel. Beams 9, 050702 (2006).
  33. X. Wang, L. Zeng, J. Shao, Y. Liang, H. Yi, Y. Yu, J. Sun, X. Li, C. Feng, Z. Wang et al., Physical design for Shenzhen superconducting soft x-ray free-electron laser (S3FEL), in Proceedings of IPAC'23, Venice, Italy (TUPL043)  (JACoW Publishing, Geneva, Switzerland, 2023).
  34. V. Petrov, F. Noack, P. Tzankov, M. Ghotbi, M. Ebrahim-Zadeh, I. Nikolov, and I. Buchvarov, High-power femtosecond optical parametric amplification at 1 kHz in BiB3O6 pumped at 800 nm, Opt. Express 15, 556 (2007).
  35. M.-S. Tsai, A.-Y. Liang, C.-L. Tsai, P.-W. Lai, M.-W. Lin, and M.-C. Chen, Nonlinear compression toward high-energy single-cycle pulses by cascaded focus and compression, Sci. Adv. 8, eabo1945 (2022).
  36. 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).
  37. 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).
  38. Y.-D. Chuang, Y.-C. Shao, A. Cruz, K. Hanzel, A. Brown, A. Frano, R. Qiao, B. Smith, E. Domning, S.-W. Huang et al., Modular soft x-ray spectrometer for applications in energy sciences and quantum materials, Rev. Sci. Instrum. 88, 013110 (2017).
  39. S. Li, E. Champenois, R. Coffee, Z. Guo, K. Hegazy, A. Kamalov, A. Natan, J. O’Neal, T. Osipov, M. Owens et al., A co-axial velocity map imaging spectrometer for electrons, AIP Adv. 8, 115308 (2018).
  40. A. Sanchez-Gonzalez, P. Micaelli, C. Olivier, T. Barillot, M. Ilchen, A. Lutman, A. Marinelli, T. Maxwell, A. Achner, M. Agåker et al., Accurate prediction of x-ray pulse properties from a free-electron laser using machine learning, Nat. Commun. 8, 15461 (2017).
  41. J. Sun, X. Li, J. Yang, L. Zeng, J. Shao, Y. Yu, W. Zhang, and X. Yang, An experimental application of machine learning algorithms to optimize the FEL lasing via beam trajectory tuning at dalian coherent light source, Nucl. Instrum. Methods Phys. Res., Sect. A 1063, 169320 (2024).
  42. A.W. Chao, M. Tigner, H. Weise, and F. Zimmermann, Handbook of Accelerator Physics and Engineering (World Scientific, Singapore, 2013).
  43. M. Borland, Elegant: A Flexible SDDS-Compliant Code for Accelerator Simulation (Argonne National Lab., Lemont, IL, 2000).
  44. S. Reiche, Genesis 1.3: A fully 3D time-dependent FEL simulation code, Nucl. Instrum. Methods Phys. Res., Sect. A 429, 243 (1999).
  45. P. Cinquegrana, A. Demidovich, G. Kurdi, I. Nikolov, P. Sigalotti, P. Susnjar, and M. Danailov, The seed laser system of the FERMI free-electron laser: Design, performance and near future upgrades, High Power Laser Sci. Eng. 9, e61 (2021).
  46. R. Bonifacio, B. McNeil, and P. Pierini, Superradiance in the high-gain free-electron laser, Phys. Rev. A 40, 4467 (1989).
  47. I. J. Bermúdez Macias, S. Düsterer, R. Ivanov, J. Liu, G. Brenner, J. Rönsch-Schulenburg, M. K. Czwalinna, and M. V. Yurkov, Study of temporal, spectral, arrival time and energy fluctuations of sase FEL pulses, Opt. Express 29, 10491 (2021).
  48. A. A. Zholents, Method of an enhanced self-amplified spontaneous emission for x-ray free electron lasers, Phys. Rev. ST Accel. Beams 8, 040701 (2005).

Outline

Information

Phys. Rev. Research 7, 043296– Published 15 December, 2025
  • Received 18 March 2025
  • Accepted 24 November 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