Observation of strong nonlinear interactions in parametric down-conversion of X-rays into ultraviolet radiation

Nonlinear interactions between X-rays and long wavelength radiation can be used as a powerful atomic-scale probe for light-matter interactions and for properties of valence electrons. However, reported X-ray nonlinear effects were small and their observations required tremendous efforts. Here we report the observation of strong nonlinearities in parametric down-conversion (PDC) of X-rays to long wavelength radiation in gallium arsenide and lithium niobate crystals, with efficiencies about 4 orders of magnitude stronger than the efficiencies measured in any material studied before. Furthermore, we show that the efficiency in the ferroelectric phase of strontium barium niobite is two orders of magnitude stronger than in its paraelectric phase. This observation suggests that the lack of inversion symmetry is the origin for the strong observed nonlinearity. Additionally, we demonstrate the ability to use the effect for the investigation of the spectral response of non-centrosymmetric materials at wavelengths ranging from infrared to soft X-rays.


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(1) We acquire the signal count ratewith the 2D detector at various angles of the sample (2) We sum over the counts in a region of interest to obtain the rocking curve.
(3) We repeat this process for various idler energies to get the corresponding rocking curves.
(4) We use the maximum values of each rocking curves to reconstruct the spectral dependence of the process.
Supplementary Note 1 -Rocking curves 45 We provide further description on our procedures for the data analysis and for the 46 validation of the measurements of the PDC signal. First, we show several examples of 47 the measured rocking curves that show the agreement with the calculated phase 48 matching angles and nonlinearity, thus constitute conclusive evidence that the 49 measured signal is indeed PDC. We recall that the angular dependence of the PDC 50 efficiency is determined by the phase matching condition and by the nonlinearity.

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Thus, we expect that the maximal efficiency of the effect will be observed near the 52 phase matching angles and when the nonlinearity is the largest. The equation that 53 describes the phase matching is p + = s + i . In order to estimate the shift from 54 the phase matching condition, we use the phase mismatch, which is defined as 55 Δk z L where Δk z is the deviation from the phase matching condition in the propagation 56 direction and L is the length of the crystal, which is defined by the shortest absorption 57 length. We use the wave vectors at the peak of the rocking curve to evaluate the phase 58 mismatch. In the case of PDC of X-rays into UV radiation, the short length is the 59 absorption length of the UV wavelength. The phase mismatch describes the 60 dependence of the efficiency of the PDC process on the deviation from the exact 61 phase matching condition. which is much smaller than π. 65 We continue with the rocking curve for theLiNbO 3 (0 0 6) atomic planes for idler The calculated phase mismatch is -1.221, which is also smaller than π. 72 We next show the rocking curve measured for the (3 1 1) atomic planes in 73 supplementary figure 4. The calculated phase mismatch is -0.1, which is again much 74 smaller than π. 75 We note that in addition to the uncertainties regarding the short UV absorption 76 lengths, there are also experimental uncertainties that emerge from the bandwidth and 77 the acceptance angles of the input monochromator and the analyzers. We estimate the 78 overall energy precision to be 0.3 eV at ESRF and 1 eV at the Diamond Light Source.

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For the estimation of the efficiencies we take the peak of the rocking curve for the 96 chosen atomic planes and sum over a region of interest that is defined by the full 97 width at half the maximum of the signal PDC counts on the camera (while filtering 98 any residual elastic scattering by removing them from the region of interest).