Skip to main content

Thank you for visiting nature.com. 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.

  • Letter
  • Published:

Extreme-ultraviolet spectral compression by four-wave mixing

Abstract

Extreme-ultraviolet (XUV) sources including high-harmonic generation (HHG), free-electron lasers (FELs), soft-X-ray lasers and laser-driven plasmas are widely used for applications ranging from femtochemistry and attosecond science to coherent diffractive imaging and EUV (or XUV) lithography. The bandwidth of the XUV light emitted by these sources reflects the XUV generation process used. Whereas light from soft-X-ray lasers1 and seeded XUV FELs2 typically has a relatively narrow bandwidth, plasma sources and HHG sources often emit broadband XUV pulses3. Since these characteristic properties of a given source impose limitations on applications, techniques enabling modification of the bandwidth are highly desirable. Here we introduce a concept for efficient spectral compression by four-wave mixing (FWM), exploiting a phase-matching scheme based on closely-spaced resonances. We demonstrate the compression of broadband radiation in the 145–130 nm wavelength range into a narrow-bandwidth XUV pulse at 100.3 nm wavelength in the presence of a broadband near-infrared (NIR) pulse in a krypton gas jet. Our concept provides new possibilities for tailoring the spectral bandwidth of XUV beams.

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

Access options

Buy this article

Prices may be subject to local taxes which are calculated during checkout

Fig. 1: XUV bandwidth compression scheme in krypton.
Fig. 2: Experimental demonstration of XUV compression by means of FWM.
Fig. 3: Comparison of XUV spectral intensities.
Fig. 4: Simulated propagation-dependent intensity of the narrowband feature.

Similar content being viewed by others

Data availability

The data that support the plots within this paper and other findings of this study are available from the corresponding author upon reasonable request.

Code availability

The codes that produced the modelled data within this paper and other findings of this study are available from the corresponding author upon reasonable request.

References

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

    Article  ADS  Google Scholar 

  2. 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).

    Article  ADS  Google Scholar 

  3. Krausz, F. & Ivanov, M. Attosecond physics. Rev. Mod. Phys. 81, 163–234 (2009).

    Article  ADS  Google Scholar 

  4. Poletto, L. et al. Time-delay compensated monochromator for the spectral selection of extreme-ultraviolet high-order laser harmonics. Rev. Sci. Instrum. 80, 123109 (2009).

    Article  ADS  Google Scholar 

  5. Hatayama, M. et al. Wide-range narrowband multilayer mirror for selecting a single-order harmonic in the photon energy range of 40–70 eV. Opt. Express 24, 14546–14551 (2016).

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

  7. Sandberg, R. L. et al. Lensless diffractive imaging using tabletop coherent high-harmonic soft-X-ray beams. Phys. Rev. Lett. 99, 098103 (2007).

    Article  ADS  Google Scholar 

  8. Sie, E. J., Rohwer, T., Lee, C. & Gedik, N. Time-resolved XUV ARPES with tunable 24–33 eV laser pulses at 30 meV resolution. Nat. Commun. 10, 3535 (2019).

    Article  ADS  Google Scholar 

  9. Wagner, C. & Harned, N. Lithography gets extreme. Nat. Photon. 4, 24–26 (2010).

    Article  ADS  Google Scholar 

  10. Dorman, C., Kucukkara, I. & Marangos, J. P. Measurement of high conversion efficiency to 123.6-nm radiation in a four-wave-mixing scheme enhanced by electromagnetically induced transparency. Phys. Rev. A 61, 013802 (1999).

    Article  ADS  Google Scholar 

  11. Liu, Y. et al. Extreme ultraviolet time- and angle-resolved photoemission setup with 21.5 meV resolution using high-order harmonic generation from a turn-key Yb:KGW amplifier. Rev. Sci. Instrum. 91, 013102 (2020).

    Article  ADS  Google Scholar 

  12. Mills, A. K. et al. Cavity-enhanced high harmonic generation for extreme ultraviolet time- and angle-resolved photoemission spectroscopy. Rev. Sci. Instrum. 90, 083001 (2019).

    Article  ADS  Google Scholar 

  13. Benediktovitch, A. et al. Amplified spontaneous emission in the extreme ultraviolet by expanding xenon clusters. Phys. Rev. A 101, 063412 (2020).

    Article  ADS  Google Scholar 

  14. Mercadier, L. et al. Evidence of extreme ultraviolet superfluorescence in xenon. Phys. Rev. Lett. 123, 023201 (2019).

    Article  ADS  Google Scholar 

  15. Harries, J. R. et al. Superfluorescence, free-induction decay, and four-wave mixing: propagation of free-electron laser pulses through a dense sample of helium ions. Phys. Rev. Lett. 121, 263201 (2018).

    Article  ADS  Google Scholar 

  16. Yoneda, H. et al. Atomic inner-shell laser at 1.5-ångström wavelength pumped by an X-ray free-electron laser. Nature 524, 446–449 (2015).

    Article  ADS  Google Scholar 

  17. 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 

  18. Heeg, K. P. et al. Spectral narrowing of x-ray pulses for precision spectroscopy with nuclear resonances. Science 357, 375–378 (2017).

    Article  ADS  Google Scholar 

  19. Hilber, G., Lago, A. & Wallenstein, R. Broadly tunable vacuum-ultraviolet/extreme-ultraviolet radiation generated by resonant third-order frequency conversion in krypton. J. Opt. Soc. Am. B 4, 1753–1764 (1987).

    Article  ADS  Google Scholar 

  20. Cao, W., Warrick, E. R., Fidler, A., Leone, S. R. & Neumark, D. M. Near-resonant four-wave mixing of attosecond extreme-ultraviolet pulses with near-infrared pulses in neon: detection of electronic coherences. Phys. Rev. A 94, 021802 (2016).

    Article  ADS  Google Scholar 

  21. Cao, W., Warrick, E. R., Fidler, A., Neumark, D. M. & Leone, S. R. Noncollinear wave mixing of attosecond XUV and few-cycle optical laser pulses in gas-phase atoms: toward multidimensional spectroscopy involving XUV excitations. Phys. Rev. A 94, 053846 (2016).

    Article  ADS  Google Scholar 

  22. Ding, T. et al. Time-resolved four-wave-mixing spectroscopy for inner-valence transitions. Opt. Lett. 41, 709–712 (2016).

    Article  ADS  Google Scholar 

  23. Harkema, N. et al. Controlling attosecond transient absorption with tunable, non-commensurate light fields. Opt. Lett. 43, 3357–3360 (2018).

    Article  ADS  Google Scholar 

  24. Fidler, A. P. et al. Nonlinear XUV signal generation probed by transient grating spectroscopy with attosecond pulses. Nat. Commun. 10, 1384 (2019).

    Article  ADS  Google Scholar 

  25. Bideau-Mehu, A., Guern, Y., Abjean, R. & Johannin-Gilles, A. Measurement of refractive indices of neon, argon, krypton and xenon in the 253.7–140.4 nm wavelength range. Dispersion relations and estimated oscillator strengths of the resonance lines. J. Quant. Spectrosc. Radiat. Transf. 25, 395–402 (1981).

    Article  ADS  Google Scholar 

  26. Drescher, L. et al. Extreme-ultraviolet refractive optics. Nature 564, 91–94 (2018).

    Article  ADS  Google Scholar 

  27. Saloman, E. B. Energy levels and observed spectral lines of krypton, Kr I through Kr XXXVI. J. Phys. Chem. Ref. Data 36, 215–386 (2007).

    Article  ADS  Google Scholar 

  28. Chu, H.-h & Wang, J. Efficient extreme-UV-to-extreme-UV conversion by four-wave mixing with intense near-IR pulses in highly charged ion plasmas. Phys. Rev. A 97, 053840 (2018).

    Article  ADS  Google Scholar 

  29. Drescher, L. et al. State-resolved probing of attosecond timescale molecular dipoles. J. Phys. Chem. Lett. 10, 265–269 (2019).

    Article  Google Scholar 

  30. Galbraith, M. C. E. et al. XUV-induced reactions in benzene on sub-10 fs timescale: nonadiabatic relaxation and proton migration. Phys. Chem. Chem. Phys. 19, 19822–19828 (2017).

    Article  Google Scholar 

  31. 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).

    Article  ADS  Google Scholar 

  32. Klarsfeld, S. A modified Bates–Damgaard method. J. Phys. B 21, L717–L721 (1988).

    Article  ADS  Google Scholar 

  33. 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).

    Article  ADS  Google Scholar 

  34. Muller, H. An efficient propagation scheme for the time-dependent Schrödinger equation in the velocity gauge. Laser Phys. 9, 138–148 (1999).

    Google Scholar 

Download references

Acknowledgements

We would like to thank A. A. Ünal for his support and M. Ivanov, M. Richter, F. Morales, A. Husakou and S. Patchkovskii for helpful discussions.

Author information

Authors and Affiliations

Authors

Contributions

B.S. had the idea for the bandwidth compression scheme. L.D., B.S. and V.S. performed the measurements. M.V. performed the TDSE and Maxwell equation calculations. L.D. performed the perturbative calculations. L.D., B.S. and O.K. performed the data analysis. All authors contributed to the creation of the manuscript.

Corresponding authors

Correspondence to L. Drescher or B. Schütte.

Ethics declarations

Competing interests

The authors declare no competing interests.

Additional information

Peer review information Nature Photonics thanks the anonymous reviewers for their contribution to the peer review of this work.

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

Extended data

Extended Data Fig. 1 Photoelectron spectrum of Xe ionized by the narrow bandwidth feature around 12.365 eV.

The kinetic energy spectrum is calculated from Abel-inverted photoelectron momentum distribution by angular integration between 85 and 95. A non-linear least squares fit of a Gaussian profile yields a FWHM of 4.0 +/- 0.3 meV (solid line). For more information see Supplementary Information.

Extended Data Fig. 2 Efficiency estimation.

XUV spectra have been recorded for a minimal NIR intensity (destructive interference, blue line) and maximal NIR intensity (constructive interference, orange line). In the maximal NIR intensity, the narrow-bandwidth emission at 12.365 eV is observed, together with a decreased spectral intensity in the region between 9.0 eV and 9.64 eV. To estimate efficiencies, the emission (orange shade) and the incident area between 9 eV and 9.64 eV (blue shade) areas are calculated. For more information see Supplementary Information.

Supplementary information

Supplementary Information

Supplementary Figs. 1–5, discussion and refs. 1–12.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Drescher, L., Kornilov, O., Witting, T. et al. Extreme-ultraviolet spectral compression by four-wave mixing. Nat. Photonics 15, 263–266 (2021). https://doi.org/10.1038/s41566-020-00758-8

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1038/s41566-020-00758-8

This article is cited by

Search

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