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X-ray and optical wave mixing


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.

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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.


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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.

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Authors and Affiliations



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.

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Correspondence to T. E. Glover.

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

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Glover, T., Fritz, D., Cammarata, M. et al. X-ray and optical wave mixing. Nature 488, 603–608 (2012).

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