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Extreme focusing of hard X-ray free-electron laser pulses enables 7 nm focus width and 1022 W cm2 intensity


By illuminating matter with bright and intense light, researchers gain insights into material composition and properties. In the regime of extremely short wavelengths, X-ray free-electron lasers (XFELs) with exceptional peak brilliance have unveiled crucial details about the structures, dynamics and physics of various materials. Although X-ray focusing optics to enhance the intensity have progressed, achieving a single-nanometre focal spot that fully exploits the source performance remains elusive. Aberrations arising from reflective optical schemes noticeably degrade the focal spot, even in the presence of inevitably slight angular transition and pointing errors. Here we present an approach that directly forms a source image in an extremely small focal spot, achieving 7 nm focusing, in both transverse dimensions, of 9.1 keV XFELs with the extremely high intensity of 1.45 × 1022 W cm2. This was made possible by a scheme combining concave and convex X-ray mirrors with suppressed aberrations and high angular tolerances. The attained highly intense X-rays, surpassing the previous intensity by a hundred-fold, induced the vigorous ionization of chromium, suggesting the creation of solid-density heavy bare atomic nuclei. Our results, which demonstrate the realization of stable ultraintense XFEL beams by forming demagnified source images, hold immediate significance to a wide range of research fields, including atomic, molecular and optical physics and high-energy-density sciences.

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Fig. 1: XFEL sub-10 nm focusing optics.
Fig. 2: Focus characterization results.
Fig. 3: Achieved intensity.
Fig. 4: Fluorescence emission spectra from Cr.

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Data availability

The source data presented in the figures are provided with this paper. Additional data that support the findings of this study are available from the corresponding authors upon reasonable request. Source data are provided with this paper.

Code availability

All non-standard code used to analyse the data is available from the corresponding authors upon reasonable request.


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We thank H. Takano, H. Mimura, H. Yoneda, S. Goto, T. Hara and H. Tanaka for discussions. We are grateful to A. Ito, K. Shioi, A. Yakushigawa, G. Yamaguchi, Y. Kohmura, T. Ishikawa and all the staff of SACLA for their support. The experiments were carried out at SACLA with the approvals of the Japan Synchrotron Radiation Research Institute (JASRI) (proposal nos. 2020A8131, 2021A8049, 2021B8035, 2022A8033, 2022B8032 and 2023A8045). This research was financially supported by Grants-in-Aid for Scientific Research from Japan Society for the Promotion of Science (JSPS; grant nos. JP23K17149 (J.Y.), JP19K23434 (J.Y.), JP21H05004 (K.Y.), JP22H03877 (I.I.), JP22K18131 (T.O.), JP18H03478 (Y.I.) and JP23H03672 (Y.I.)) and FOREST Program from Japan Science and Technology Agency (JST; grant no. JPMJFR202Y (S.M.)). J.Y. and K.Y. acknowledge the SACLA Basic Development Program. J.Y. acknowledges the special postdoctoral researcher programme of RIKEN.

Author information

Authors and Affiliations



J.Y., M.Y. and K.Y. conceived the project. J.Y. designed the mirrors with advice from all co-authors. J.Y., S.M., T.I. and N.N. performed the mirror characterization and shape correction. J.Y., S.M., I.I., T.O., H.Y., T.K., H.O. and M.Y. developed the apparatus. J.Y., I.I., T.O., Y.I., T.Y., K. Tono, K. Tamasaku and M.Y. designed the commissioning plan with advice from all co-authors. J.Y., S.M., T.I. and Y.T. performed the XFEL experiments. J.Y. analysed the experimental data. J.Y. and M.Y. co-wrote the manuscript with input from all authors. All authors discussed the results and agreed on the published version of the manuscript.

Corresponding author

Correspondence to Jumpei Yamada.

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Nature Photonics thanks David Attwood, Heung-Sik Kang and the other, anonymous, reviewer(s) for their contribution to the peer review of this work.

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Extended data

Extended Data Fig. 1 Design of Wolter-III based AKB mirrors.

(a) Cross-section of the Wolter-III based AKB mirrors designed for sub-10 nm focusing of XFEL. (b) Mirror shapes and radii of curvature of the designed four mirrors. (c) Lateral profiles of multilayer parameters: d-space, Pt-layer thickness, C-layer thickness, and γ parameter. (d) Reflectivities of the multilayers measured and calculated at a photon energy of 8.048 keV (Cu Kα). Results of the film thickness/roughness are summarized in inset tables.

Source data

Extended Data Fig. 2 Results of ptychographic characterization.

(a) Scanning electron microscope image of the sample used in ptychography. Logos of the authors’ affiliations are drawn. (b) Phase image of the sample reconstructed using the single-mode ePIE. (c) Phase image of the sample reconstructed using the OPR-enhanced ePIE. (d) Five components of the reconstructed illumination wavefield obtained via OPR-based ptychography, with their corresponding singular values displayed in the upper right corner of each panel. The hue indicates the phase distribution, while the brightness represents the amplitude. (e) The first row displays four selected wavefields out of the total 196 retrieved wavefields. The second row shows the propagated focus intensities. (f) Illumination position errors along the horizontal and vertical direction, corresponding to the relative positional vibration between the focused beam and the sample.

Extended Data Fig. 3 Comparison of wavefront errors measured by s-GI and ptychography.

The s-GI measurement was performed just after the ptychography scan. The wavefield measured by ptychography was propagated to the same defocus distance as the s-GI measurement. (a) Two-dimensional wavefront errors. (b) One-dimensional averaged profile of (a).

Extended Data Fig. 4 Experiments for the fluorescence emission from Cr.

(a) Schematic of the setup for fluorescence emission measurement. (b, c) Intensity maps of emitted spectra normalized by (b) the incident pulse energy and (c) the sum of the measured emission intensity. The right graphs show the one-dimensional profiles of the summation of the intensity between 5.2 and 7.1 keV.

Extended Data Table 1 Optical design parameters of the Wolter-III based AKB mirrors

Supplementary information

Supplementary Video 1

Results of focus characterization via OPR-based ptychography. For measured 196 pulses, the reconstructed wavefields, back-propagated focused intensities, cross-sections of focused intensity along the horizontal axis and the cross-sections along the vertical axis are shown in a 15 fps movie.

Source data

Source Data Fig. 1

Statistical source data of Fig. 1a,b.

Source Data Fig. 2

Full-length data of Fig. 2a. Full-length data of Fig. 2b amplitude. Full-length data of Fig. 2b phase. Full-length data of Fig. 2c. Full-length data of inset of Fig. 2c. Full-length data of Fig. 2d horizontal (Hor.). Full-length data of Fig. 2d (vertical, Ver.). Statistical source data of Fig. 2e–h.

Source Data Fig. 3

Statistical source data of Fig. 3.

Source Data Fig. 4

Full-length data of Fig. 4a.

Source Data Fig. 5

Statistical source data of Fig. 4a,b.

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Yamada, J., Matsuyama, S., Inoue, I. et al. Extreme focusing of hard X-ray free-electron laser pulses enables 7 nm focus width and 1022 W cm2 intensity. Nat. Photon. (2024).

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