Mixing waves in a diamond

Use of an ultra-high-intensity X-ray laser has allowed X-ray and optical waves to be mixed in a diamond sample. The effect paves the way to studying the microscopic optical response of materials on an atomic scale. See Article p.603

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The invention of the optical laser introduced the field of nonlinear optics — the study of the nonlinear interaction of light with matter. The field kicked off with the observation of second-harmonic generation1, a nonlinear process that converts two photons of identical frequency into a single photon that has twice the frequency of the initial photons. Recently developed X-ray free-electron lasers (XFELs)2,3, which produce ultrashort X-ray pulses of extremely high intensity, hold similar promise in the X-ray domain of the electromagnetic spectrum. On page 603 of this issue, Glover et al.4 report how they have used an XFEL device to observe X-ray and optical sum-frequency generation, a nonlinear optical effect that may allow the microscopic optical properties of materials to be measured with atomic resolution.

If a medium is irradiated with low-intensity light of a specific frequency, the medium's optical response is typically linear. In this regime, the induced electric polarization of the medium has frequency components that match those of the impinging light field — the medium's optically active (polarizable) electric charge density oscillates in phase with the light's electric field. Linear light–matter interactions, which include absorption and scattering, do not alter the medium's optical properties.

However, for light of sufficiently high intensity, the optical properties change and the medium displays a nonlinear response: the induced polarization has frequency components that differ from those of the electric field. As a result, a medium that is irradiated with a laser beam containing, say, two frequency components (w1 and w2) can emit light with a frequency (w) that is either the sum of the components (w = w1 + w2) or the difference between them (w = w1w2). The same effects, known respectively as sum-frequency generation and difference-frequency generation, can occur if two temporally and spatially overlapping laser beams of distinct frequencies (w1 and w2) are shone on the sample. With optical light, the nonlinear response to high orders — emitted light frequencies that are multiples of those of the incident light — has been observed and exploited to create coherent (laser-like), short-wavelength radiation in the ultraviolet and extreme-ultraviolet regimes.

At X-ray wavelengths, the induced polarization is usually too small for sum-frequency generation to occur. Glover et al.4 circumvent this problem by combining optical and X-ray light. They overlapped X-ray pulses from the Linac Coherent Light Source XFEL2 with pulses from an optical laser, shone them on a diamond sample and demonstrated sum-frequency generation of the X-ray and optical pulses. This effect was predicted5 in 1971, but had not previously been observed because there were no X-ray sources of sufficiently high intensity. By measuring the efficiency with which the sum-frequency signal was generated, the authors determined the optically induced microscopic polarization and the associated electric field. They then compared the results with theory, and confirmed the expectation that the optically induced polarization in diamond is associated with charges in the crystal's covalent bonds.

The effect of optical and X-ray wave mixing in crystals can be interpreted as optically modulated X-ray diffraction6. Optical light of frequency w0 induces a polarization in the medium, resulting in a temporally oscillating redistribution of the polarizable charge density. Typically, only valence electrons are polarizable when irradiated with optical light. X-rays of frequency wx interacting with the optically active, oscillatory part of the charge density will scatter off it inelastically, with their frequency being Doppler shifted to w = wx + w0. Most of the X-rays, however, will scatter elastically (their frequency wx is preserved) off the optically unaffected, static component of the charge density. This elastic scattering gives rise to a standard Bragg intensity peak on a detector. The inelastic process generates an intensity peak that is slightly shifted from the elastic Bragg peak (Fig. 1).

Figure 1: Optically modulated X-ray diffraction.

Glover et al.4 directed optical laser light and a beam of X-ray light from the Linac Coherent Light Source into a diamond sample. Most of the beam's X-rays are scattered elastically (their wavelength is preserved) and produce the standard Bragg intensity peak on the detector. The rest of the X-rays undergo inelastic scattering, resulting in optically modulated X-rays which have a frequency that is the sum of the X-ray frequency and the laser frequency. These rays generate an intensity peak that is slightly shifted from the standard peak.

In standard X-ray crystallography, X-ray illumination and scattering at different crystal orientations yield information about a crystal's three-dimensional charge density. In much the same way, the optically modulated, scattered X-rays can allow the three-dimensional, optically induced charge-density changes to be reconstructed5,6. Glover and colleagues' experiment is a first proof of principle of this reconstruction: sum-frequency signals were recorded for only one crystal orientation. But extending the experiment to several crystal orientations, which together will allow determination of the three-dimensional, induced charge-density variation, should be straightforward.

X-ray and optical wave mixing in crystals therefore enables optical polarization to be measured on a microscopic scale. Light-activated microscopic polarization and the associated electric field vary widely on an atomic scale, and determine the overall macroscopic optical properties of materials, including the refractive index. Although conceptually familiar, these microscopic details had never been measured before, because standard optical methods give only a coarse-grained view of them. Glover and colleagues demonstrate that X-rays make it possible to resolve and quantify such details.

The ability to use optical and X-ray sum-frequency generation to probe light–matter interactions at a microscopic scale will potentially advance the fields of optics, energy research and materials science. If optical lasers that emit pulses at high repetition rates (on the megahertz regime) are available at X-ray synchrotron facilities, it may be possible to explore the effect using these more accessible X-ray sources instead of an XFEL. This would allow extensive studies of stationary, microscopic optical properties. But to resolve dynamic light-induced microscopic processes in real time — a challenge that still lies ahead of us — the power of XFELs is indispensable.


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Correspondence to Nina Rohringer.

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Rohringer, N. Mixing waves in a diamond. Nature 488, 598–599 (2012). https://doi.org/10.1038/488598a

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