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.

Four-wave mixing experiments with extreme ultraviolet transient gratings

Nature volume 520, pages 205–208 (2015)Cite this article

Subjects

Abstract

Four-wave mixing (FWM) processes, based on third-order nonlinear light–matter interactions, can combine ultrafast time resolution with energy and wavevector selectivity, and enable the exploration of dynamics inaccessible by linear methods1,2,3,4,5,6,7. The coherent and multi-wave nature of the FWM approach has been crucial in the development of advanced technologies, such as silicon photonics8, subwavelength imaging9 and quantum communications10. All these technologies operate at optical wavelengths, which limits the spatial resolution and does not allow the probing of excitations with energy in the electronvolt range. Extension to shorter wavelengths—that is, the extreme ultraviolet and soft-X-ray ranges—would allow the spatial resolution to be improved and the excitation energy range to be expanded, as well as enabling elemental selectivity to be achieved by exploiting core resonances5,6,7,11,12,13,14. So far, FWM applications at such wavelengths have been prevented by the absence of coherent sources of sufficient brightness and of suitable experimental set-ups. Here we show how transient gratings, generated by the interference of coherent extreme-ultraviolet pulses delivered by the FERMI free-electron laser15, can be used to stimulate FWM processes at suboptical wavelengths. Furthermore, we have demonstrated the possibility of observing the time evolution of the FWM signal, which shows the dynamics of coherent excitations as molecular vibrations. This result opens the way to FWM with nanometre spatial resolution and elemental selectivity, which, for example, would enable the investigation of charge-transfer dynamics5,6,7. The theoretical possibility of realizing these applications has already stimulated ongoing developments of free-electron lasers16,17,18,19,20: our results show that FWM at suboptical wavelengths is feasible, and we hope that they will enable advances in present and future photon sources.

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

Relevant articles

Open Access articles citing this article.

Access options

Rent or buy this article

Get just this article for as long as you need it

$39.95

Learn more

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

Figure 1: FWM experiments with EUV transient gratings.
Figure 2: FWM signal stimulated by EUV transient gratings.
Figure 3: Time evolution of the FWM signal.
Figure 4: Prospects for EUV/SXR FWM.

References

  1. Bloembergen, N. Nonlinear optics and spectroscopy. Rev. Mod. Phys. 54, 685–695 (1982)

    Article  CAS  ADS  Google Scholar 

  2. Boyd, W. R. Nonlinear Optics (Academic, 2008)

    Google Scholar 

  3. Dhar, L., Rogers, J. A. & Nelson, K. A. Time-resolved vibrational spectroscopy in the impulsive limit. Chem. Rev. 94, 157–193 (1994)

    Article  CAS  Google Scholar 

  4. Cundiff, S. T. & Mukamel, S. Optical multidimensional coherent spectroscopy. Phys. Today 66, 44–49 (2013)

    Article  CAS  Google Scholar 

  5. Bencivenga, F. et al. Multi-colour pulses from seeded free-electron-lasers: towards the development of non-linear core-level coherent spectroscopies. Faraday Discuss. 171, 487–503 (2014)

    Article  CAS  ADS  Google Scholar 

  6. Bencivenga, F. et al. Nanoscale dynamics by short-wavelength four wave mixing experiments. New J. Phys. 15, 123023 (2013)

    Article  ADS  Google Scholar 

  7. Tanaka, S. & Mukamel, S. Coherent X-ray Raman spectroscopy: a nonlinear local probe for electronic excitations. Phys. Rev. Lett. 89, 043001 (2002)

    Article  ADS  Google Scholar 

  8. Foster, M. A. et al. Broad-band optical parametric gain on a silicon photonic chip. Nature 441, 960–963 (2006)

    Article  CAS  ADS  Google Scholar 

  9. Chen, P.-Y. & Al, A. Subwavelength imaging using phase-conjugating nonlinear nanoantenna arrays. Nano Lett. 11, 5514–5518 (2011)

    Article  CAS  ADS  Google Scholar 

  10. Boyer, V., Marino, A. M., Pooser, R. C. & Lett, P. D. Entangled images from four-wave mixing. Science 321, 544–547 (2008)

    Article  CAS  ADS  Google Scholar 

  11. Tanaka, S., Chernyak, V. & Mukamel, S. Time-resolved X-ray spectroscopies: nonlinear response functions and Liouville-space pathways. Phys. Rev. A 63, 063405 (2001)

    Article  ADS  Google Scholar 

  12. Adams, B. Nonlinear X-ray optics: the next phase for X-rays. Nature Phys. 7, 675–676 (2011)

    Article  CAS  ADS  Google Scholar 

  13. Glover, T. E. et al. X-ray and optical wave mixing. Nature 488, 603–608 (2012)

    Article  CAS  ADS  Google Scholar 

  14. Tamasaku, K., Sawada, K., Nishiboro, E. & Ishikawa, T. Visualizing the local optical response to extreme ultraviolet radiation with a resolution of λ/380. Nature Phys. 7, 705–708 (2011)

    Article  CAS  ADS  Google Scholar 

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

    Article  CAS  ADS  Google Scholar 

  16. Allaria, E. et al. Two-colour pump-probe experiments with a twin pulse-seed extreme ultraviolet free-electron laser. Nature Commun. 4, 2476 (2013)

    Article  CAS  ADS  Google Scholar 

  17. Lutman, A. A. et al. Experimental demonstration of femtosecond two-color X-ray free-electron-lasers. Phys. Rev. Lett. 110, 134801 (2013)

    Article  CAS  ADS  Google Scholar 

  18. Hara, T. et al. Two-colour hard X-ray free-electron laser with wide tunability. Nature Commun. 4, 2919 (2013)

    Article  ADS  Google Scholar 

  19. Lutman, A. A. et al. Demonstration of single-crystal self-seeded two-color X-ray free-electron lasers. Phys. Rev. Lett. 113, 254801 (2014)

    Article  CAS  ADS  Google Scholar 

  20. Marcus, G., Penn, G. & Zholents, A. A. Free-electron laser design for four-wave-mixing experiments with soft X-ray pulses. Phys. Rev. Lett. 113, 024801 (2014)

    Article  CAS  ADS  Google Scholar 

  21. Bencivenga, F. & Masciovecchio, C. FEL-based transient grating spectroscopy to investigate nanoscale dynamics. Nucl. Instrum. Methods A 606, 785–789 (2009)

    Article  CAS  ADS  Google Scholar 

  22. Shwartz, S. et al. X-ray second harmonic generation. Phys. Rev. Lett. 112, 163901 (2014)

    Article  CAS  ADS  Google Scholar 

  23. 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  CAS  ADS  Google Scholar 

  24. Beye, M. et al. Stimulated X-ray emission for materials science. Nature 501, 191–194 (2013)

    Article  CAS  ADS  Google Scholar 

  25. Tamasaku, K. et al. X-ray two-photon absorption competing against single and sequential multiphoton processes. Nature Photon. 8, 313–316 (2014)

    Article  CAS  ADS  Google Scholar 

  26. Armstrong, J. A., Bloembergen, N., Ducuing, J. & Pershan, P. S. Interactions between light waves in a nonlinear dielectric. Phys. Rev. 127, 1918–1939 (1962)

    Article  CAS  ADS  Google Scholar 

  27. Tobey, R. I. et al. Transient grating measurement of surface acoustic waves in thin metal films with extreme ultraviolet radiation. Appl. Phys. Lett. 89, 091108 (2006)

    Article  ADS  Google Scholar 

  28. Sistrunk, E. F. et al. Extreme ultraviolet transient grating measurement of insulator-metal transition dynamics of VO2. In 19th International Conference on Ultrafast Phenomenahttp://dx.doi.org/10.1364/UP.2014.09.Wed.P3.44 (Paper 09.Wed.P3.44, Optical Society of America, 2014)

  29. Schirmacher, W. et al. Vibrational excitations in systems with correlated disorder. Phys. Status Solidi C 5, 862–866 (2008)

    Article  CAS  ADS  Google Scholar 

  30. Ferrante, C. et al. Acoustic dynamics of network-forming glasses at mesoscopic wavelengths. Nature Commun. 4, 1793 (2013)

    Article  CAS  ADS  Google Scholar 

  31. Capotondi, F. et al. Coherent imaging using seeded free-electron laser pulses with variable polarization: first results and research opportunities. Rev. Sci. Instrum. 84, 051301 (2013)

    Article  CAS  ADS  Google Scholar 

  32. Zangrando, M. et al. The photon analysis, delivery, and reduction system at the FERMI@Elettra free electron laser user facility Rev. Sci. Instrum. 80, 113110 (2009)

    Google Scholar 

  33. Cucini, R., Bencivenga, F., Zangrando, M. & Masciovecchio, C. Technical advances of the TIMER project. Nucl. Instrum. Methods A 635, S69–S74 (2011)

    Article  CAS  ADS  Google Scholar 

  34. Cucini, R., Bencivenga, F. & Masciovecchio, C. All-reflective femtosecond optical pump-probe setup for transient grating spectroscopy. Opt. Lett. 36, 1032–1034 (2011)

    Article  CAS  ADS  Google Scholar 

  35. Allaria, A. et al. Tunability experiments at the FERMI@Elettra free-electron laser New J. Phys. 14, 113009 (2012)

    Google Scholar 

  36. Danailov, M. B. et al. Towards jitter-free pump-probe measurements at seeded free electron laser facilities. Opt. Express 22, 12869–12879 (2014)

    Article  CAS  ADS  Google Scholar 

  37. Cinquegrana, P. et al. Optical beam transport to remote location for low jitter pump-probe experiments with free electron laser. Phys. Rev. ST Accel. Beams 17, 040702 (2014)

    Article  ADS  Google Scholar 

  38. Gahl, C. et al. A femtosecond X-ray/optical cross-correlator. Nature Photon. 2, 165–169 (2008)

    Article  CAS  ADS  Google Scholar 

  39. Casolari, F. et al. Role of multilayer-like interference effects on the transient optical response of Si3N4 films pumped with free-electron laser pulses. Appl. Phys. Lett. 104, 191104 (2014)

    Article  ADS  Google Scholar 

  40. Ruhman, S., Joly, A. G. & Nelson, K. A. Time resolved observations of coherent molecular vibrational motion and the general occurrence of impulsive stimulated scattering. J. Chem. Phys. 86, 6563–6565 (1987)

    Article  CAS  ADS  Google Scholar 

  41. Kalampounias, A. G., Yannopoulos, S. N. & Papatheodorou, G. N. Temperature-induced structural changes in glassy, supercooled, and molten silica from 77 to 2150 K. J. Chem. Phys. 124, 014504 (2006)

    Article  CAS  ADS  Google Scholar 

  42. Hehlen, B. et al. Hyper-Raman scattering observation of the boson peak in vitreous silica. Phys. Rev. Lett. 84, 5355–5358 (2000)

    Article  CAS  ADS  Google Scholar 

  43. Buchenau, U., Nucker, N. & Dianoux, A. J. Neutron scattering study of the low-frequency vibrations in vitreous silica. Phys. Rev. Lett. 53, 2316–2319 (1984)

    Article  CAS  ADS  Google Scholar 

Download references

Acknowledgements

We acknowledge support from the Italian Ministry of University and Research through grants FIRB-RBAP045JF2 and FIRB-RBAP06AWK3, and from the European Research Council through grant 202804-TIMER. We thank M. Svandrlik and the FERMI-FEL team for support.

Author information

Authors and Affiliations

  1. Elettra-Sincrotrone Trieste, Strada Statale 14 km 163,5 in Area Science Park, I-34012 Basovizza, Trieste, Italy,

    F. Bencivenga, R. Cucini, F. Capotondi, A. Battistoni, R. Mincigrucci, E. Giangrisostomi, A. Gessini, M. Manfredda, I. P. Nikolov, E. Pedersoli, E. Principi, C. Svetina, P. Parisse, F. Casolari, M. B. Danailov, M. Kiskinova & C. Masciovecchio

  2. Dipartimento di Fisica, Università degli Studi di Trieste, Piazzale Europa, I-34127 Trieste, Italy,

    A. Battistoni, E. Giangrisostomi & C. Svetina

  3. Dipartimento di Fisica e Geologia, Università degli Studi di Perugia, Via Pascoli, I-06123 Perugia, Italy,

    R. Mincigrucci

Authors
  1. F. Bencivenga
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. R. Cucini
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. F. Capotondi
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. A. Battistoni
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. R. Mincigrucci
    View author publications

    You can also search for this author in PubMed Google Scholar

  6. E. Giangrisostomi
    View author publications

    You can also search for this author in PubMed Google Scholar

  7. A. Gessini
    View author publications

    You can also search for this author in PubMed Google Scholar

  8. M. Manfredda
    View author publications

    You can also search for this author in PubMed Google Scholar

  9. I. P. Nikolov
    View author publications

    You can also search for this author in PubMed Google Scholar

  10. E. Pedersoli
    View author publications

    You can also search for this author in PubMed Google Scholar

  11. E. Principi
    View author publications

    You can also search for this author in PubMed Google Scholar

  12. C. Svetina
    View author publications

    You can also search for this author in PubMed Google Scholar

  13. P. Parisse
    View author publications

    You can also search for this author in PubMed Google Scholar

  14. F. Casolari
    View author publications

    You can also search for this author in PubMed Google Scholar

  15. M. B. Danailov
    View author publications

    You can also search for this author in PubMed Google Scholar

  16. M. Kiskinova
    View author publications

    You can also search for this author in PubMed Google Scholar

  17. C. Masciovecchio
    View author publications

    You can also search for this author in PubMed Google Scholar

Contributions

C.M. proposed and led the project to extend transient grating methods at suboptical wavelengths. F.B. conceived the experiment and coordinated all activities. F. Capotondi designed the set-up to split and recombine the FEL pulses. A.G. realized the set-up and, together with F. Capotondi, A.B. and R.M., integrated it into the end-station. F.B., R.C., A.B., A.G. and R.M. tested the set-up. I.P.N. and M.B.D. realized the set-up to control the optical pulse. F.B., R.C., F. Capotondi, A.B., R.M., E.G., M.M., E.P., E.P., C.S. and F. Casolari performed the experiment. A.B., R.M., F.B., R.C., F. Capotondi and M.M. carried out the data analysis. P.P., C.S., A.B. and R.M. performed the AFM measurements and analysis. F.B., R.C., F. Capotondi, A.B., M.B.D., M.K. and C.M. discussed the data. F.B. and C.M. prepared the manuscript.

Corresponding authors

Correspondence to F. Bencivenga or C. Masciovecchio.

Ethics declarations

Competing interests

The authors declare no competing financial interests.

Extended data figures and tables

Extended Data Figure 1 Experimental set-up for FEL-based FWM measurements.

a, Top-view layout of the experimental set-up used to split and recombine the FEL beams. b, Top-view layout of the experimental set-up used to control the optical beam. c, Top-view picture of the set-up: the two FEL paths (FP1 and FP2) downstream of M1 and the trajectory of the optical pulse are indicated. d, Sketch of the movements needed to change 2θ keeping ΔtEUV-EUV fixed. e, Sketch of the movements needed to change ΔtEUV-EUV keeping 2θ fixed. See Methods for details of a–e. f, g, Optical reflectivity changes in Si3N4 induced by the FEL beam propagating through FP1 (green dots) and FP2 (magenta dots). In f, the mirrors were displaced with respect to the nominal position; a poor time coincidence and a different fluence level in the interaction region can be seen. g, Same measurements as in f after optimization of the geometry; the superposition of the two traces indicates a large improvement in the time coincidence and a similar FEL fluence in the interaction region.

Extended Data Figure 2 AFM topographies.

AFM topographies of 8 × 8 μm2 areas of the sample surface as follows: in a region that was not irradiated (a), in an area irradiated by ∼300 FEL shots at a fluence larger than 50 mJ cm−2 (b), and in an area continuously irradiated by FEL pulses at low fluence (c). d–f, Representative depth profiles of the sample surface along the green lines shown in a–c, respectively. The power spectral densities (PSD) corresponding to data reported in d–f are shown in g–i, respectively.

Extended Data Figure 3 Time sequence of acquired data.

Black open and crossed circles connected by lines are data shown in Fig. 3; crossed circles correspond to a scan made several hours after the one corresponding to data shown as open circles; in both scans the time delay was continuously increased. Green dots are data collected before these two scans; here we had not yet optimized the FWM signal at Δt = 0 (these data are scaled by a factor to fit the peak intensity of the data shown as black circles). Blue and red lines are the same as shown in Fig. 3.

PowerPoint slides

Source data

Rights and permissions

Reprints and Permissions

About this article

Cite this article

Bencivenga, F., Cucini, R., Capotondi, F. et al. Four-wave mixing experiments with extreme ultraviolet transient gratings. Nature 520, 205–208 (2015). https://doi.org/10.1038/nature14341

Download citation

  • Received:

  • Accepted:

  • Issue Date:

  • DOI: https://doi.org/10.1038/nature14341

This article is cited by

Comments

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.

Search

Advanced 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