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.

  • Letter
  • Published:

Hard X-ray transient grating spectroscopy on bismuth germanate

An Author Correction to this article was published on 11 May 2021

This article has been updated


Optical-domain transient grating (TG) spectroscopy is a versatile background-free four-wave-mixing technique that is used to probe vibrational, magnetic and electronic degrees of freedom in the time domain1. The newly developed coherent X-ray free-electron laser sources allow its extension to the X-ray regime. X-rays offer multiple advantages for TG: their large penetration depth allows probing the bulk properties of materials, their element specificity can address core excited states, and their short wavelengths create excitation gratings with unprecedented momentum transfer and spatial resolution. Here, we demonstrate TG excitation in the hard X-ray range at 7.1 keV. In bismuth germanate (BGO), the non-resonant TG excitation generates coherent optical phonons detected as a function of time by diffraction of an optical probe pulse. This experiment demonstrates the ability to probe bulk properties of materials and paves the way for ultrafast coherent four-wave-mixing techniques using X-ray probes and involving nanoscale TG spatial periods.

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: X-ray TG (XTG) uses the Talbot effect from a phase grating to generate the transient excitation.
Fig. 2: Footprints of the signal beam on the CCD detector.
Fig. 3: The XTG signal at 2-ps time delay as a function of the X-ray intensity at the sample.
Fig. 4: XTG signals from BGO at 7.1 keV with an excitation grating pitch of 770 nm.

Similar content being viewed by others

Data availability

The raw data used in this study are available from the corresponding authors upon request.

Change history


  1. Goodno, G. D., Dadusc, G. & Miller, R. D. Ultrafast heterodyne-detected transient-grating spectroscopy using diffractive optics. J. Opt. Soc. Am. B 15, 1791–1794 (1998).

    Article  ADS  Google Scholar 

  2. Thomson, R., Leburn, C. & Reid, D. (eds) Ultrafast Nonlinear Optics (Springer, 2013).

  3. Mukamel, S. Principles of Nonlinear Optical Spectroscopy 6 (Oxford Univ. Press, 1995).

    Google Scholar 

  4. Hamm, P. & Zanni, M. Concepts and Methods of 2D Infrared Spectroscopy (Cambridge Univ. Press, 2011).

  5. Rogers, J. A., Maznev, A. A., Banet, M. J. & Nelson, K. A. Optical generation and characterization of acoustic waves in thin films: fundamentals and applications. Annu. Rev. Mater. Sci. 30, 117–157 (2000).

    Article  ADS  Google Scholar 

  6. Crimmins, T. F., Stoyanov, N. S. & Nelson, K. A. Heterodyned impulsive stimulated Raman scattering of phonon–polaritons in LiTaO3 and LiNbO3. J. Chem. Phys. 117, 2882–2896 (2002).

    Article  ADS  Google Scholar 

  7. Redman, D. A. et al. Spin dynamics and electronic states of N–V centers in diamond by EPR and four-wave-mixing spectroscopy. Phys. Rev. Lett. 67, 3420–3423 (1991).

    Article  Google Scholar 

  8. West, B. A., Womick, J. M. & Moran, A. M. Probing ultrafast dynamics in adenine with mid-UV four-wave mixing spectroscopies. J. Phys. Chem. A 115, 8630–8637 (2011).

    Article  Google Scholar 

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

    Article  Google Scholar 

  10. Janušonis, J. et al. Transient grating spectroscopy in magnetic thin films: simultaneous detection of elastic and magnetic dynamics. Sci. Rep. 6, 29143 (2016).

    Article  ADS  Google Scholar 

  11. 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 

  12. Johnson, J. A. et al. Direct measurement of room-temperature nondiffusive thermal transport over micron distances in a silicon membrane. Phys. Rev. Lett. 110, 025901 (2013).

    Article  ADS  Google Scholar 

  13. Hua, C. & Minnich, AustinJ. Transport regimes in quasiballistic heat conduction. Phys. Rev. B 89, 094302 (2014).

    Article  ADS  Google Scholar 

  14. Behrens, C. et al. Few-femtosecond time-resolved measurements of X-ray free-electron lasers. Nat. Commun. 5, 3762 (2014).

    Article  ADS  Google Scholar 

  15. Bencivenga, F. et al. Four-wave mixing experiments with extreme ultraviolet transient gratings. Nature 520, 205–208 (2015).

    Article  ADS  Google Scholar 

  16. Bencivenga, F. et al. Nanoscale transient gratings excited and probed by extreme ultraviolet femtosecond pulses. Sci. Adv. 5, eaaw5805 (2019).

    Article  ADS  Google Scholar 

  17. Schweigert, I. V. & Mukamel, S. Coherent ultrafast core-hole correlation spectroscopy: X-ray analogues of multidimensional NMR. Phys. Rev. Lett. 99, 163001 (2007).

    Article  ADS  Google Scholar 

  18. Svetina, C. et al. Towards X-ray transient grating spectroscopy. Opt. Lett. 44, 574–577 (2019).

    Article  ADS  Google Scholar 

  19. Milne, C. J. et al. SwissFEL: the Swiss X-ray free electron laser. Appl. Sci. 7, 720 (2017).

    Article  Google Scholar 

  20. Ingold, G. et al. Experimental station Bernina at SwissFEL: condensed matter physics on femtosecond time scales investigated by X-ray diffraction and spectroscopic methods. J. Synchrotron Radiat. 26, 874–886 (2019).

    Article  Google Scholar 

  21. Raymond, S. G. & Townsend, P. D. The influence of rare-earth ions on the low-temperature thermoluminescence of Bi4Ge3O12. J. Phys. Condens. Matter 12, 2103–122 (2000).

    Article  ADS  Google Scholar 

  22. Williams, P. A. et al. Optical, thermo-optic, electro-optic and photoelastic properties of bismuth germanate (Bi4Ge3O12). Appl. Opt. 35, 3562–3569 (1996).

    Article  ADS  Google Scholar 

  23. Kaminskii, A. A. et al. Growth, spectral and luminescence study of cubic Bi4Ge3O12:Pr3+ crystals. Phys. Status Solidi A 85, 553–567 (1984).

    Article  ADS  Google Scholar 

  24. Brunner, S. E. & Schaart, D. R. BGO as a hybrid scintillator/Cherenkov radiator for cost-effective time-of-flight PET. Phys. Med. Biol. 62, 4421–4439 (2017).

    Article  Google Scholar 

  25. Tao, L., Coffee, R. N., Jeong, D. & Levin, C. S. Ionizing photon interactions modulate the optical properties of crystals with femtosecond scale temporal resolution. Phys. Med. Biol. 66, 045032 (2021).

    Article  Google Scholar 

  26. Kamada, O. & Kakishita, K. Electro-optical effect of Bi4Ge3O12 crystals for optical voltage sensors. Jpn J. Appl. Phys. 32, 4288–4291 (1993).

    Article  ADS  Google Scholar 

  27. Kaminskii, A. A. et al. Growth, spectroscopy and stimulated emission of cubic Bi4Ge3O12 crystals doped with Dy3+, Ho3+, Er3+, Tm3+ or Yb3+ ions. Phys. Status Solidi A 56, 725–736 (1979).

    Article  ADS  Google Scholar 

  28. Li, C. & Yoshino, T. Simultaneous measurement of current and voltage by use of one bismuth germanate crystal. Appl. Opt. 41, 5391–5397 (2002).

    Article  ADS  Google Scholar 

  29. Chen, Z., Gao, Y., Minch, B. C. & DeCamp, M. F. Coherent optical phonon generation in Bi3Ge4O12. J. Phys. Condens. Matter 23, 385402 (2011).

    Article  ADS  Google Scholar 

  30. Couzi, M., Vignalou, J. R. & Boulon, G. Infrared and Raman study of the optical phonons in Bi4Ge3O12 single crystal. Solid State Commun. 20, 461–465 (1976).

    Article  ADS  Google Scholar 

  31. Maznev, A. A. et al. Generation of coherent phonons by coherent extreme ultraviolet radiation in a transient grating experiment. Appl. Phys. Lett. 113, 221905 (2018).

    Article  Google Scholar 

  32. Norman, P. & Dreuw, A. Simulating X-ray spectroscopies and calculating core-excited states of molecules. Chem. Rev. 118, 7208–7248 (2018).

    Article  Google Scholar 

  33. Miao, H., Gomella, A. A., Chedid, N., Chen, L. & Wen, H. Fabrication of 200-nm period hard X-ray phase gratings. Nano Lett. 14, 3453–3458 (2014).

    Article  ADS  Google Scholar 

  34. Vila-Comamala, J. et al. Ultra-high resolution zone-doubled diffractive X-ray optics for the multi-keV regime. Opt. Express 19, 175–184 (2011).

    Article  ADS  Google Scholar 

  35. Lynch, S. K. et al. Fabrication of 200-nm period centimeter area hard X-ray absorption gratings by multilayer deposition. J. Micromech. Microeng. 22, 105007 (2012).

    Article  ADS  Google Scholar 

  36. Cho, J., Hwang, T. Y. & Zewail, A. H. Visualization of carrier dynamics in p(n)-type GaAs by scanning ultrafast electron microscopy. Proc. Natl Acad. Sci. USA 111, 2094–2099 (2014).

    Article  ADS  Google Scholar 

  37. Gorfien, M. et al. Nanoscale thermal transport across an GaAs/AlGaAs heterostructure interface. Struct. Dyn. 7, 025101 (2020).

    Article  Google Scholar 

  38. Grilj, J. et al. Self-referencing heterodyne transient grating spectroscopy with short wavelength. Photonics 2, 392–401 (2015).

    Article  Google Scholar 

  39. Katayama, K., Yamaguchi, M. & Sawada, T. Lens-free heterodyne detection for transient grating experiments. Appl. Phys. Lett. 82, 2775–2777 (2003).

    Article  ADS  Google Scholar 

  40. 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 

  41. Makita, M. et al. Fabrication of diamond diffraction gratings for experiments with intense hard X-rays. Microelectron. Eng. 176, 75–78 (2017).

    Article  Google Scholar 

Download references


This study was supported by the Swiss National Science Foundation (SNSF, grant no. 200021_165550/1), the SNSF research instrument NCCR Molecular Ultrafast Science and Technology (NCCR MUST, grants 51NF40-183615 and 200021_169017), the ERC Grant ‘DYNAMOX’ (ERC-2015-AdG-694097) and the EU-H2020 Research and Innovation Programme under the Marie Skłodowska-Curie grant agreements (701647, 654360 NFFA-Europe, 801459-FP-RESOMUS and 871124 Laserlab-Europe). The contribution of the MIT participants A.A.M. and K.A.N. was supported by the US Department of Energy award DE-SC0019126. We thank M. Dzambegovic for the graphical rendering of Fig. 1a.

Author information

Authors and Affiliations



C.S. conceptualized the framework of the experiment. J.R.R. and C.S. designed the experiment. G.S. and C.D. fabricated the diamond gratings. B.R. carried out the optical microscopy of the static printed gratings. All members of the team participated in the experiment and were involved in the discussions. J.R.R., D.F. and E.F. carried out the data reduction. J.R.R., D.F. and C.S. performed the data analysis. C.S., J.R.R. and D.F. wrote the manuscript.

Corresponding authors

Correspondence to Jérémy R. Rouxel or Cristian Svetina.

Ethics declarations

Competing interests

The authors declare no competing interests.

Additional information

Peer review information Nature Photonics thanks Ryan Coffee and the other, anonymous, reviewer(s) 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.

Supplementary information

Supplementary Information

Supplementary Figs. 1–11, Discussion and Tables 1–3.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Rouxel, J.R., Fainozzi, D., Mankowsky, R. et al. Hard X-ray transient grating spectroscopy on bismuth germanate. Nat. Photon. 15, 499–503 (2021).

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI:

This article is cited by


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