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.Light-matter interactions have advanced our understanding of atoms, molecules and materials, and are also central to a number of areas of applied science. Although optical interactions have received a great deal of study, the microscopic details of how light manipulates matter are poorly understood in many circumstances. A material's optical response is complex, being determined by coupled many-body interactions that vary on the scale of atoms rather than on the scale of a long-wavelength applied field. Data are needed to combat this complexity, and so far it has not been possible to probe the microscopic details of light-matter interactions. X-ray and optical wave mixing, specifically sum-frequency generation (SFG), was proposed nearly half a century ago as an atomic-scale probe of light-matter interactions 1,2 . The process is, in essence, optically modulated X-ray diffraction: X-rays inelastically scatter from optically induced charge oscillations and probe optically polarized charge in direct analogy to how standard X-ray diffraction probes ground-state charge. Furthermore, the optically induced microscopic field is determined because it is closely related to the induced charge [3][4][5][6] . So far it has not been possible to measure these two quantities directly. X-ray and optical wave mixing has frequently been discussed 1,2,4,[7][8][9][10][11][12] , but it has not yet been demonstrated owing to a lack of sufficiently intense X-ray sources. More generally, although there have been theoretical studies of nonlinear X-ray scattering [13][14][15][16][17][18] , experimental observations have largely been confined to the spontaneous processes of X-ray parametric down-conversion [19][20][21][22][23] and resonant inelastic X-ray scattering 24,25 . X-ray free-electron lasers offer unprecedented brightness and new scientific opportunities 26 . Here we use an X-ray laser to demonstrate X-ray/optical SFG through the nonlinear interaction of the two fields in single-crystal diamond. Optically modulated X-ray diffract...

Compton spectra of atoms at high x-ray intensity

“…The brightness of XFELs is many orders of magnitude higher than that of synchrotron sources [12]. Unprecedentedly ultraintense x-ray pulses enable us to study nonlinear x-ray physics [13,14,15,16], including nonlinear two-photon x-ray Compton scattering [17,18]. The features of ultraintense and ultrashort XFEL pulses are useful to create warm dense matter [19], and the inelastic x-ray scattering technique has been developed to measure characteristics (density and temperature) of high energy density plasma [20,21,22,23].…”

X-Ray Probe Targets Interfaces

“…Prior to the development of free electron lasers (FELs), only parametric downconversion had been observed [17]. While the advent of XFELs has recently enabled second-and third-order nonlinear spectroscopies at hard x-ray energies, including SHG [2], SFG [1], two-photon absorption [4], and inelastic Compton scattering [18], current hard x-ray FELs lack the longitudinal and temporal coherence necessary for efficiently satisfying the phase-matching conditions required for nonlinear spectroscopies, thus, making the exploitation of some of these techniques difficult [19,20]. Furthermore, the shorter hard x-ray wavelengths (λ < 0.2 nm) induce second harmonic and sum frequency generation even within centrosymmetric media, as the observed response depends on material inhomogeneity on the length scale of the x-ray wavelength, similar to how SHG is seen in a plasma, and effectively making this method a bulk probe [21].…”

“…At infrared, visible, and ultraviolet wavelengths, secondorder nonlinear spectroscopies have become important tools in surface science, as symmetry considerations within the dipole approximation constrain signal generation to regions lacking centrosymmetry, such as surfaces and interfaces [9][10][11][12]. In contrast, at hard x-ray wavelengths, second harmonic and sum frequency generation (SFG) have been observed in centrosymmetric materials with a nonuniform electron density and are essentially bulk probes [1,2]. As soft x-ray wavelengths fall in between the hard x-ray and UV regimes, there has been uncertainty regarding the interface specificity of soft x-ray SHG.…”

“…This technique and the associated theoretical framework demonstrate the ability to selectively probe interfaces, including those that are buried, with elemental specificity, providing a new tool for a range of scientific problems. DOI: 10.1103/PhysRevLett.120.023901 Nonlinear optics has recently been extended from visible and near UV wavelengths to new regimes with the development of x-ray free electron lasers (XFELs) capable of delivering x-ray pulses with high brightness, ultrashort pulse duration, and high coherence [1][2][3][4][5][6][7]. One fundamental nonlinear probe is second harmonic generation (SHG), a secondorder process which combines two photons of the same energy to generate a single photon with twice the energy [8].…”

“…When hard x-ray SFG was performed by using an optical laser pulse combined with an x-ray laser, the pump intensities were ∼10 10 W=cm 2 for the optical laser and 10 11 W=cm 2 for the x-ray laser [1]. Additionally, as a soft x-ray SHG requires significantly smaller fields than does a hard x-ray SHG, such damage-free SHG measurements may be achievable by exploiting higher repetition rate FELs (LCLS-II, FLASH2020) and more efficient detection (better spectrometer, spatial separation, etc.…”