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Focusing of X-ray free-electron laser pulses with reflective optics


X-ray free-electron lasers1,2 produce intense femtosecond pulses that have applications in exploring new frontiers in science. The unique characteristics of X-ray free-electron laser radiation can be enhanced significantly using focusing optics3. However, with such an optical device, even a slight deviation from the ideal design can lead to considerable errors in the focusing properties. Here, we present reflective optics comprising elliptically figured mirrors with nanometre accuracy to preserve a coherent wavefront, successfully focusing a 10 keV X-ray free-electron laser to the small area of 0.95 × 1.20 µm2. The near 100% efficiency of this arrangement allows an enormous 40,000-fold increase in the fluence to a power density of 6 × 1017 W cm−2. This achievement is directly applicable to the generation of a nanometre-size beam with an extreme power density of >1 × 1022 W cm−2, which will play a crucial role in the advance of microscopic research towards ultimate ångstrom resolution, as well as in the development of nonlinear optical sciences under extreme conditions.

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Figure 1: Schematic for the Kirkpatrick–Baez mirror geometry.
Figure 2: Profile of the surface figure error for the horizontal focusing mirror.
Figure 3: Evaluation results for focusing beam performance.
Figure 4: Relationship of focused beam sizes and incident beam sizes with the size of the light source.


  1. Emma, P. et al. First lasing and operation of an ångstrom-wavelength free-electron laser. Nature Photon. 4, 641–647 (2010).

    Article  ADS  Google Scholar 

  2. Ishikawa, T. et al. A compact X-ray free-electron laser emitting in the sub-ångström region. Nature Photon. 6, 540–544 (2012).

    Article  ADS  Google Scholar 

  3. David, C. et al. Nanofocusing of hard X-ray free electron laser pulses using diamond based Fresnel zone plates. Sci. Rep. 1, 57 (2011).

    Article  Google Scholar 

  4. Young, L. et al. Femtosecond electronic response of atoms to ultra-intense X-rays. Nature 466, 56–62 (2010).

    Article  ADS  Google Scholar 

  5. Rohringer, N. et al. Atomic inner-shell X-ray laser at 1.46 nanometres pumped by an X-ray free-electron laser. Nature 481, 488–491 (2012).

    Article  ADS  Google Scholar 

  6. Chapman, H. N. et al. Femtosecond diffractive imaging with a soft X-ray free electron laser. Nature Phys. 2, 839–843 (2006).

    Article  ADS  Google Scholar 

  7. Gaffney, K. J. & Chapman, H. N. Imaging atomic structure and dynamics with ultrafast X-ray scattering. Science 316, 1444–1448 (2007).

    Article  ADS  Google Scholar 

  8. Chapman, H. N. et al. Femtosecond X-ray protein nanocrystallography. Nature 470, 73–77 (2011).

    Article  ADS  Google Scholar 

  9. Seibert, M. M. et al. Single mimivirus particles intercepted and imaged with an X-ray laser. Nature 470, 78–81 (2011).

    Article  ADS  Google Scholar 

  10. Schroer, C. G. et al. Hard X-ray nanoprobe based on refractive X-ray lenses. Appl. Phys. Lett. 87, 124103 (2005).

    Article  ADS  Google Scholar 

  11. Chao, W. et al. Soft X-ray microscopy at a spatial resolution better than 15 nm. Nature 435, 1210–1213 (2005).

    Article  ADS  Google Scholar 

  12. Mimura, H. et al. Efficient focusing of hard X rays to 25 nm by a total reflection mirror. Appl. Phys. Lett. 90, 051903 (2007).

    Article  ADS  Google Scholar 

  13. Kirkpatrick, P. & Baez, A. V. Formation of optical images by X-rays. J. Opt. Soc. Am. 38, 766–774 (1948).

    Article  ADS  Google Scholar 

  14. DiFabrizio, E. et al. High-efficiency multilevel zone plates for keV X-rays. Nature 401, 895–898 (1999).

    Article  ADS  Google Scholar 

  15. The European X-Ray Free-Electron Laser technical design report (2007); available at

  16. Yamauchi, K. et al. Wave-optical evaluation of interference fringes and wavefront phase in a hard-X-ray beam totally reflected by mirror optics. Appl. Opt. 44, 6927–6932 (2005).

    Article  ADS  Google Scholar 

  17. Yamauchi, K. et al. Nearly diffraction-limited line focusing of a hard-X-ray beam with an elliptically figured mirror. J. Synchrotron Rad. 9, 313–316 (2002).

    Article  Google Scholar 

  18. Mimura, H. et al. Breaking the 10 nm barrier in hard-X-ray focusing. Nature Phys. 6, 122–125 (2010).

    Article  ADS  Google Scholar 

  19. Mimura, H. et al. Focusing mirror for X-ray free-electron lasers. Rev. Sci. Instrum. 79, 083104 (2008).

    Article  ADS  Google Scholar 

  20. Yamauchi, K. et al. Single-nanometer focusing of hard X-rays by Kirkpatrick–Baez mirrors. J. Phys. Condens. Matter 23, 394206 (2011).

    Article  Google Scholar 

  21. Yamauchi, K., Mimura, H., Inagaki, K. & Mori, Y. Figuring with subnanometer-level accuracy by numerically controlled elastic emission machining. Rev. Sci. Instrum. 73, 4028–4033 (2002).

    Article  ADS  Google Scholar 

  22. Ohmori, H. & Nakagawa, T. Mirror surface grinding of silicon wafers with electrolytic in-process dressing. CIRP Ann. 39, 329–332 (1990).

    Article  Google Scholar 

  23. Yamauchi, K. et al. Microstitching interferometry for X-ray reflective optics. Rev. Sci. Instrum. 74, 2894–2898 (2003).

    Article  ADS  Google Scholar 

  24. Mimura, H. et al. Relative angle determinable stitching interferometry for hard-X-ray reflective optics. Rev. Sci. Instrum. 76, 045102 (2005).

    Article  ADS  Google Scholar 

  25. Born, M. & Wolf, E. Principles of Optics: Electromagnetic Theory of Propagation, Interference and Diffraction of Light 7th edn, 421–425, 436–439 (Cambridge Univ. Press, 1999).

    Book  Google Scholar 

  26. Inubushi, Y. et al. Determination of the pulse duration of an X-ray free electron laser using highly resolved single-shot spectra. Phys. Rev. Lett. 109, 144801 (2012).

    Article  ADS  Google Scholar 

  27. Chalupský, J. et al. Spot size characterization of focused non-Gaussian X-ray laser beams. Opt. Express 18, 27836–27845 (2010).

    Article  ADS  Google Scholar 

  28. Saleh, B. E. A. & Teich, M. C. Fundamentals of Photonics 2nd edn, 75–86 (Wiley-Interscience, 2007).

    Google Scholar 

  29. Tono, K. et al. Single-shot beam-position monitor for X-ray free electron laser. Rev. Sci. Instrum. 82, 023108 (2011).

    Article  ADS  Google Scholar 

  30. Ayvazyan, V. et al. Generation of GW radiation pulses from a VUV free-electron laser operating in the femtosecond regime. Phys. Rev. Lett. 88, 104802 (2002).

    Article  ADS  Google Scholar 

  31. Singer, A. et al. Spatial and temporal coherence properties of single free-electron laser pulses. Opt. Express 20, 17480–17495 (2012).

    Article  ADS  Google Scholar 

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This research was partially supported by a Grant-in-Aid for Scientific Research (S) (23226004) from the Ministry of Education, Sports, Culture, Science and Technology, Japan (MEXT), CREST from the Japan Science and Technology Agency (JST), the X-ray Free Electron Laser Utilization Research Project of MEXT, and the Proposal Program of SACLA Experimental Instruments of RIKEN. The authors thank Hitachi High-Technologies Corporation for providing scanning electron microscope images for Fig. 3.

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Authors and Affiliations



H.Yu. and M.Y. wrote the first draft of the manuscript. The design of the focusing mirrors and the mirror manipulator, wave-optical analysis and the experiment using XFEL were carried out mainly by H.Yu., H.M., T.Ko., S.M., T.Ki., H.Yo. and J.K. The conditions for this experiment at SACLA were set up by K.T., T.To., Y.I. and T.S. The simulator of the electron-beam dynamics was developed by T.Ta. The mirror substrates were fabricated by Y.H. and H.Ohm. Experimental planning was carried out by Y.S., M.Y., H.Oha., T.I. and K.Y.

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Correspondence to Hirokatsu Yumoto.

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Yumoto, H., Mimura, H., Koyama, T. et al. Focusing of X-ray free-electron laser pulses with reflective optics. Nature Photon 7, 43–47 (2013).

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