Skip to main content

Thank you for visiting You are using a browser version with limited support for CSS. To obtain the best experience, we recommend you use a more up to date browser (or turn off compatibility mode in Internet Explorer). In the meantime, to ensure continued support, we are displaying the site without styles and JavaScript.

Extreme-ultraviolet refractive optics


Refraction is a well-known optical phenomenon that alters the direction of light waves propagating through matter. Microscopes, lenses and prisms based on refraction are indispensable tools for controlling light beams at visible, infrared, ultraviolet and X-ray wavelengths1. In the past few decades, a range of extreme-ultraviolet and soft-X-ray sources has been developed in laboratory environments2,3,4 and at large-scale facilities5,6. But the strong absorption of extreme-ultraviolet radiation in matter hinders the development of refractive lenses and prisms in this spectral region, for which reflective mirrors and diffractive Fresnel zone plates7 are instead used for focusing. Here we demonstrate control over the refraction of extreme-ultraviolet radiation by using a gas jet with a density gradient across the profile of the extreme-ultraviolet beam. We produce a gas-phase prism that leads to a frequency-dependent deflection of the beam. The strong deflection near to atomic resonances is further used to develop a deformable refractive lens for extreme-ultraviolet radiation, with low absorption and a focal length that can be tuned by varying the gas pressure. Our results open up a route towards the transfer of refraction-based techniques, which are well established in other spectral regions, to the extreme-ultraviolet domain.

This is a preview of subscription content, access via your institution

Access options

Buy article

Get time limited or full article access on ReadCube.


All prices are NET prices.

Fig. 1: XUV refractive prism.
Fig. 2: Control over XUV deflection by gas pressure.
Fig. 3: XUV refractive lens.
Fig. 4: Simulation of the XUV focus.

Data availability

The data that support the findings of this study are available from the corresponding authors upon request.


  1. Snigirev, A., Kohn, V., Snigireva, I. & Lengeler, B. A compound refractive lens for focusing high-energy X-rays. Nature 384, 49–51 (1996).

    CAS  ADS  Article  Google Scholar 

  2. Ferray, M. et al. Multiple-harmonic conversion of 1064 nm radiation in rare gases. J. Phys. B 21, L31 (1988).

    CAS  Article  Google Scholar 

  3. Rocca, J. J. Table-top soft X-ray lasers. Rev. Sci. Instrum. 70, 3799–3827 (1999).

    CAS  ADS  Article  Google Scholar 

  4. Giulietti, D. & Gizzi, L. A. X-ray emission from laser-produced plasmas. Riv. Nuovo Cim. 21, 1–93 (1998).

    CAS  Article  Google Scholar 

  5. Marr, G. V. Handbook on Synchrotron Radiation: Vacuum Ultraviolet and Soft X-ray Processes Vol. 2 (Elsevier, Amsterdam, 2013).

    Google Scholar 

  6. Allaria, E. et al. Highly coherent and stable pulses from the Fermi seeded free-electron laser in the extreme ultraviolet. Nat. Photon. 6, 699–704 (2012).

    CAS  ADS  Article  Google Scholar 

  7. Baez, A. V. A self-supporting metal Fresnel zone-plate to focus extreme ultra-violet and soft X-rays. Nature 186, 958 (1960).

    ADS  Article  Google Scholar 

  8. Röntgen, W. C. Über eine neue Art von Strahlen: Vorläufige Mittheilung. Sitzungsber. Phys. Med. Gesell. Würzburg (1895).

  9. Santoro, G. et al. Use of intermediate focus for grazing incidence small and wide angle X-ray scattering experiments at the beamline P03 of PETRA III, DESY. Rev. Sci. Instrum. 85, 043901 (2014).

    CAS  ADS  Article  Google Scholar 

  10. Chollet, M. et al. The X-ray pump–probe instrument at the Linac Coherent Light Source. J. Synchrotron Radiat. 22, 503–507 (2015).

    CAS  Article  Google Scholar 

  11. Heimann, P. et al. Compound refractive lenses as prefocusing optics for X-ray FEL radiation. J. Synchrotron Radiat. 23, 425–429 (2016).

    CAS  Article  Google Scholar 

  12. Lengeler, B. et al. A microscope for hard X-rays based on parabolic compound refractive lenses. Appl. Phys. Lett. 74, 3924–3926 (1999).

    CAS  ADS  Article  Google Scholar 

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

    ADS  Article  Google Scholar 

  14. Meijer, J.-M. et al. Observation of solid–solid transitions in 3D crystals of colloidal superballs. Nat. Commun. 8, 14352 (2017).

    CAS  ADS  Article  Google Scholar 

  15. Schroer, C. G. et al. Coherent X-ray diffraction imaging with nanofocused illumination. Phys. Rev. Lett. 101, 090801 (2008).

    CAS  ADS  Article  Google Scholar 

  16. Wang, Y., Yun, W. & Jacobsen, C. Achromatic Fresnel optics for wideband extreme-ultraviolet and X-ray imaging. Nature 424, 50 (2003).

    CAS  ADS  Article  Google Scholar 

  17. Pan, H. et al. Low chromatic Fresnel lens for broadband attosecond XUV pulse applications. Opt. Express 24, 16788–16798 (2016).

    CAS  ADS  Article  Google Scholar 

  18. Hahn, E. L. Nuclear induction due to free Larmor precession. Phys. Rev. 77, 297–298 (1950).

    CAS  ADS  Article  Google Scholar 

  19. Wu, M., Chen, S., Camp, S., Schafer, K. J. & Gaarde, M. B. Theory of strong-field attosecond transient absorption. J. Phys. B 49, 062003 (2016).

    ADS  Article  Google Scholar 

  20. Bengtsson, S. et al. Space–time control of free induction decay in the extreme ultraviolet. Nat. Photon. 11, 252–258 (2017).

    CAS  ADS  Article  Google Scholar 

  21. Liao, C.-T., Sandhu, A., Camp, S., Schafer, K. J. & Gaarde, M. B. Beyond the single-atom response in absorption line shapes: probing a dense, laser-dressed helium gas with attosecond pulse trains. Phys. Rev. Lett. 114, 143002 (2015).

    ADS  Article  Google Scholar 

  22. Schütte, B., Arbeiter, M., Fennel, T., Vrakking, M. J. J. & Rouzée, A. Rare-gas clusters in intense extreme-ultraviolet pulses from a high-order harmonic source. Phys. Rev. Lett. 112, 073003 (2014).

    ADS  Article  Google Scholar 

  23. Semushin, S. & Malka, V. High density gas jet nozzle design for laser target production. Rev. Sci. Instrum. 72, 2961–2965 (2001).

    CAS  ADS  Article  Google Scholar 

  24. Tzallas, P., Charalambidis, D., Papadogiannis, N. A., Witte, K. & Tsakiris, G. D. Direct observation of attosecond light bunching. Nature 426, 267 (2003).

    CAS  ADS  Article  Google Scholar 

  25. Takahashi, E. J., Lan, P., Mücke, O. D., Nabekawa, Y. & Midorikawa, K. Attosecond nonlinear optics using gigawatt-scale isolated attosecond pulses. Nat. Commun. 4, 2691 (2013).

    ADS  Article  Google Scholar 

  26. Manschwetus, B. et al. Two-photon double ionization of neon using an intense attosecond pulse train. Phys. Rev. A 93, 061402 (2016).

    ADS  Article  Google Scholar 

  27. Barillot, T. R. et al. Towards XUV pump-probe experiments in the femtosecond to sub-femtosecond regime: new measurement of the helium two-photon ionization cross-section. Chem. Phys. Lett. 683, 38–42 (2017).

    CAS  ADS  Article  Google Scholar 

  28. Rupp, D. et al. Coherent diffractive imaging of single helium nanodroplets with a high harmonic generation source. Nat. Commun. 8, 493 (2017).

    ADS  Article  Google Scholar 

  29. Flögel, M. et al. Rabi oscillations in extreme ultraviolet ionization of atomic argon. Phys. Rev. A 95, 021401 (2017).

    ADS  Article  Google Scholar 

  30. Schafer, K. J. & Kulander, K. C. High harmonic generation from ultrafast pump lasers. Phys. Rev. Lett. 78, 638–641 (1997).

    CAS  ADS  Article  Google Scholar 

  31. Frühling, U. et al. Single-shot terahertz-field-driven X-ray streak camera. Nat. Photon. 3, 523 (2009).

    ADS  Article  Google Scholar 

  32. Mauritsson, J. et al. Measurement and control of the frequency chirp rate of high-order harmonic pulses. Phys. Rev. A 70, 021801 (2004).

    ADS  Article  Google Scholar 

  33. Valentin, C. et al. Spectral selection of high harmonics via spatial filtering. In High-Brightness Sources and Light-driven Interactions HW3A.3 (Optical Society of America, 2018).

    Google Scholar 

  34. Neidel, C. et al. Probing time-dependent molecular dipoles on the attosecond time scale. Phys. Rev. Lett. 111, 033001 (2013).

    ADS  Article  Google Scholar 

  35. Drescher, L. et al. Communication: XUV transient absorption spectroscopy of iodomethane and iodobenzene photodissociation. J. Chem. Phys. 145, 011101 (2016).

    CAS  ADS  Article  Google Scholar 

  36. Galbraith, M. C. E. et al. Few-femtosecond passage of conical intersections in the benzene cation. Nat. Commun. 8, 1018 (2017).

    CAS  ADS  Article  Google Scholar 

  37. He, X. et al. Spatial and spectral properties of the high-order harmonic emission in argon for seeding applications. Phys. Rev. A 79, 063829 (2009).

    ADS  Article  Google Scholar 

  38. Gademann, G., Ple, F., Paul, P.-M. & Vrakking, M. J. J. Carrier-envelope phase stabilization of a terawatt level chirped pulse amplifier for generation of intense isolated attosecond pulses. Opt. Express 19, 24922 (2011).

    ADS  Article  Google Scholar 

  39. Born, M. & Wolf, E. Principles of Optics 7th expanded edn (Cambridge Univ. Press, Cambridge, 1999).

    Book  Google Scholar 

  40. Wiese, W. L. Smith, M. W. & Glennon, B. M. Atomic Transition Probabilities: Hydrogen through Neon. Technical report, National Standard Reference Data System. (NBS, 1966).

  41. Wiese, W. L. Smith, M. W. & Miles, B. M. Atomic Transition Probabilities: Sodium through Calcium. Technical report, National Standard Reference Data System (NBS, 1969).

Download references


We thank A. A. Ünal and R. Schumann for their support with the laser systems. This project has received funding from the European Union’s Horizon 2020 research and innovation programme under the Marie-Sklodowska-Curie grant agreement no. 641789 MEDEA.

Reviewer information

Nature thanks J. Cryan, M. Gaarde and the other anonymous reviewer(s) for their contribution to the peer review of this work.

Author information

Authors and Affiliations



L.D. and B.S. performed the prism experiments. B.S. performed the lens experiments. O.K. carried out the simulations. All authors discussed the results and contributed to writing the manuscript.

Corresponding authors

Correspondence to O. Kornilov or B. Schütte.

Ethics declarations

Competing interests

The authors declare no competing interests.

Additional information

Publisher’s note: Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

Drescher, L., Kornilov, O., Witting, T. et al. Extreme-ultraviolet refractive optics. Nature 564, 91–94 (2018).

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI:


  • Extreme Ultraviolet Radiation
  • Refractive Lens
  • Controlling Light Beams
  • FWHM Diameter
  • Backing Pressure

Further reading


By submitting a comment you agree to abide by our Terms and Community Guidelines. If you find something abusive or that does not comply with our terms or guidelines please flag it as inappropriate.


Quick links

Nature Briefing

Sign up for the Nature Briefing newsletter — what matters in science, free to your inbox daily.

Get the most important science stories of the day, free in your inbox. Sign up for Nature Briefing