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.

  • Article
  • Published:

X-ray and optical wave mixing

Abstract

Light–matter interactions are ubiquitous, and underpin a wide range of basic research fields and applied technologies. Although optical interactions have been intensively studied, their microscopic details are often poorly understood and have so far not been directly measurable. X-ray and optical wave mixing was proposed nearly half a century ago as an atomic-scale probe of optical interactions but has not yet been observed owing to a lack of sufficiently intense X-ray sources. Here we use an X-ray laser to demonstrate X-ray and optical sum-frequency generation. The underlying nonlinearity is a reciprocal-space probe of the optically induced charges and associated microscopic fields that arise in an illuminated material. To within the experimental errors, the measured efficiency is consistent with first-principles calculations of microscopic optical polarization in diamond. The ability to probe optical interactions on the atomic scale offers new opportunities in both basic and applied areas of science.

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

Access options

Rent or buy this article

Prices vary by article type

from$1.95

to$39.95

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

Figure 1: X-ray/optical SFG experiment.
Figure 2: Wave equation simulations.
Figure 3: Density functional theory calculations of real-space valence charge density in diamond.

Similar content being viewed by others

References

  1. Freund . I & Levine, B. F. Optically modulated X-ray diffraction. Phys. Rev. Lett. 25, 1241–1245 (1970)

    Article  ADS  Google Scholar 

  2. Eisenberger, P. M. & McCall, S. L. Mixing of X-ray and optical photons. Phys. Rev. A 3, 1145–1151 (1971)

    Article  ADS  Google Scholar 

  3. Jackson, J. D. Classical Electrodynamics (Wiley, 1975)

    MATH  Google Scholar 

  4. Arya, K. & Jha, S. S. Microscopic optical fields and mixing coefficients of x-ray and optical frequencies in solids. Pramana 2, 116–125 (1974)

    Article  ADS  CAS  Google Scholar 

  5. Adler, S. L. Quantum theory of the dielectric constant in real solids. Phys. Rev. 126, 413–420 (1962)

    Article  ADS  MathSciNet  Google Scholar 

  6. Pine, A. S. Self-consistent-field theory of linear and nonlinear crystalline dielectrics including local-field effects. Phys. Rev. 139, A901–A911 (1965)

    Article  ADS  Google Scholar 

  7. Woo, J. W. F. & Jha, S. S. Inelastic scattering of x rays from optically induced charge-density oscillations. Phys. Rev. B 6, 4081–4082 (1972)

    Article  ADS  Google Scholar 

  8. Freund, I. Nonlinear X-ray diffraction: determination of valence electron charge distributions. Chem. Phys. Lett. 12, 583–588 (1972)

    Article  ADS  CAS  Google Scholar 

  9. Van Vechten, J. A. &. Martin, R. M. Calculation of local effective fields: optical spectrum of diamond. Phys. Rev. Lett. 28, 446–449 (1972)

    Article  ADS  CAS  Google Scholar 

  10. Freund, I. &. Levine, B. F. Surface effects in the nonlinear interaction of X-ray and optical fields. Phys. Rev. B 6, 3059–3060 (1973)

  11. Arya, K. & Jha, S. S. Microscopic optical fields in diamond and germanium: molecular-orbital approach. Phys. Rev. B 10, 4485–4487 (1974)

    Article  ADS  CAS  Google Scholar 

  12. Johnson, D. L. Local field effects and the dielectric response matrix of insulators: A model. Phys. Rev. B 9, 4475–4484 (1974)

    Article  ADS  Google Scholar 

  13. 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 

  14. Tanaka, S. & Mukamel, S. Probing exciton dynamics using Raman resonances in femtosecond X-ray four-wave mixing. Phys. Rev. A 67, 033818 (2003)

    Article  ADS  Google Scholar 

  15. Nazarkin, A., Podorov, S., Uschmann, I., Forster, E. & Sauerbrey, R. Nonlinear optics in the angstrom regime: hard-X-ray frequency doubling in perfect crystals. Phys. Rev. A 67, 041804(R) (2003)

    Article  ADS  Google Scholar 

  16. 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 

  17. Hudis, E., Shkolnikov, P. L. & Kaplan, A. E. X-ray stimulated Raman scattering in Li and He. Appl. Phys. Lett. 64, 818–820 (1994)

    Article  ADS  CAS  Google Scholar 

  18. Freund, I. & Levine, B. F. Parametric conversion of X rays. Phys. Rev. Lett. 23, 854–857 (1969)

    Article  ADS  Google Scholar 

  19. Eisenberger, P. & McCall, S. L. X-ray parametric conversion. Phys. Rev. Lett. 26, 684–688 (1971)

    Article  ADS  CAS  Google Scholar 

  20. Danino, H. & Freund, I. Parametric down conversion of X rays into the extreme ultraviolet. Phys. Rev. Lett. 46, 1127–1130 (1981)

    Article  ADS  CAS  Google Scholar 

  21. Yoda, Y., Suzuki, T., Zhang, X. W., Hirano, K. & Kikuta, S. X-ray parametric scattering by a diamond crystal. J. Synchrotron Radiat. 5, 980–982 (1998)

    Article  CAS  Google Scholar 

  22. Adams, B. et al. Parametric down conversion of X-ray photons. J. Synchrotron Radiat. 7, 81–88 (2000)

    Article  ADS  CAS  Google Scholar 

  23. Tamasaku, K. Sawada, K. Nishibori, 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  ADS  CAS  Google Scholar 

  24. Platzman, P. M. & Isaacs, E. D. Resonant inelastic X-ray scattering. Phys. Rev. B 57, 11107–11114 (1998)

    Article  ADS  CAS  Google Scholar 

  25. Kotani, A. & Shin, S. Resonant inelastic X-ray scattering spectra for electrons in solids. Rev. Mod. Phys. 73, 203–246 (2001)

    Article  ADS  CAS  Google Scholar 

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

    Article  ADS  CAS  Google Scholar 

  27. Palik, E. D., ed. Handbook of Optical Constants of Solids 313–334 (Academic, 1998)

    Book  Google Scholar 

  28. Spackman, M. A. The electron distribution in diamond: a comparison between experiment and theory. Acta Crystallogr. A 47, 420–427 (1991)

    Article  Google Scholar 

  29. Shen, Y. R. The Principles of Nonlinear Optics 5–40 (Wiley, 1984)

  30. Phillips, J. C. Covalent bond in crystals. I. Elements of a structural theory. Phys. Rev. 166, 832–838 (1968)

    Article  ADS  CAS  Google Scholar 

  31. Levine, B. F. Electrodynamic bond-charge calculation of nonlinear optical susceptibilities. Phys. Rev. Lett. 22, 787–790 (1969)

    Article  ADS  CAS  Google Scholar 

  32. Giannozzi, P. et al. Quantum Espresso: a modular and open-source software project for quantum simulations of materials. J. Phys. Condens. Matter 21, 395502 (2009)

    Article  Google Scholar 

  33. Souza, I. Iniguez, J. & Vanderbilt, D. First principles approach to insulators in finite electric fields. Phys. Rev. Lett. 89, 117602 (2002)

    Article  ADS  Google Scholar 

  34. Ihee, H. et al. Ultrafast X-ray diffraction of transient molecular structures in solution. Science 309, 1223–1227 (2005)

    Article  ADS  CAS  Google Scholar 

  35. Möhr-Vorobeva, E. et al. Nonthermal melting of a charge density wave in TiSe2 . Phys. Rev. Lett. 107, 036403 (2011)

    Article  ADS  Google Scholar 

  36. Lindenberg, A. M. et al. Time-resolved X-ray diffraction from coherent phonons during a laser-induced phase transition. Phys. Rev. Lett. 84, 111–114 (2000)

    Article  ADS  CAS  Google Scholar 

  37. Cavalleri, A. et al. Tracking the motion of charges in a terahertz light field by femtosecond X-ray diffraction. Nature 442, 664–666 (2006)

    Article  ADS  CAS  Google Scholar 

  38. Fritz, D. M. et al. Ultrafast bond softening in bismuth: mapping a solid’s interatomic potential with X-rays. Science 315, 633–636 (2007)

    Article  ADS  CAS  Google Scholar 

  39. Wu, J. S., Spence, J. C. H., O’Keeffe, M. & Groy, T. L. Application of a modified Oszlanyi and Suto ab initio charge-flipping algorithm to experimental data. Acta Crystallogr. A 60, 326–330 (2004)

    Article  ADS  CAS  Google Scholar 

  40. Coppens, P. X-Ray Charge Densities and Chemical Bonding (Oxford Univ. Press, 1997)

    Google Scholar 

Download references

Acknowledgements

We thank J. D. Jackson, D. Vanderbilt, and J. C. H. Spence for commenting on various aspects of this work. T.E.G. was supported by the Office of Science, Office of Basic Energy Sciences, of the US Department of Energy under contract no. DE-AC02-05CH11231. The work of S.E.H. and S.S. was supported by the US Air Force Office of Scientific Research and the US Army Research Office. D.A.R. and S.G. were supported as part of the AMOS programme within the Chemical Sciences, Geosciences, and Biosciences Division, Office of Basic Energy Sciences, US Department of Energy. Portions of this research were carried out at the LCLS at SLAC National Accelerator Laboratory. LCLS is an Office of Science User Facility operated for the US Department of Energy Office of Science by Stanford University. Preliminary experiments were performed at the Advanced Light Source at Lawrence Berkeley National Laboratory.

Author information

Authors and Affiliations

Authors

Contributions

T.E.G. and J.B.H. had the idea for the x-ray/optical SFG project. D.M.F., T.E.G., J.B.H., M.C., T.K.A., J.M.F. and D.A.R. contributed to the experiment design. D.M.F., M.C., H.L., D.Z. and R.N.C. were responsible for the X-ray pump–probe instrument and the optical laser. D.M.F., M.C., T.E.G., J.B.H., H.L., D.Z., T.K.A., J.M.F., Y.F., R.N.C., D.A.R., S.S., M.F., S.G. and J.C. collected data. S.E.H., S.S., T.E.G. and T.K.A. contributed to the wave equation calculations. Data analysis was done by T.E.G., H.L. and J.M.F. Construction of the bond charge model was done by T.E.G. Density functional theory calculations were done by S.C. T.E.G. wrote the manuscript. All authors contributed to the work presented here and to the final paper.

Corresponding author

Correspondence to T. E. Glover.

Ethics declarations

Competing interests

The authors declare no competing financial interests.

Supplementary information

Supplementary Information

This file contains Supplementary Text and Data 1-7, Supplementary Figure 1 and additional references (see page 1 for more details). (PDF 1636 kb)

PowerPoint slides

Rights and permissions

Reprints and permissions

About this article

Cite this article

Glover, T., Fritz, D., Cammarata, M. et al. X-ray and optical wave mixing. Nature 488, 603–608 (2012). https://doi.org/10.1038/nature11340

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1038/nature11340

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

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