Hard x-ray intensity autocorrelation using direct two-photon absorption

An intensity autocorrelation measurement is demonstrated to characterize a pulse duration of 9-keV x-ray free-electron laser (XFEL) pulses from a split-delay optical (SDO) system with four-bounce silicon 220 reflections in each branch. XFEL pulse replicas with variable time delays are generated by the SDO system itself. High intensity of $>2\times {10}^{16}\mathrm{W}/\mathrm{c}{\mathrm{m}}^2$ achieved in a self-seeding operation and careful data analysis allow the measurement with direct two-photon absorption. The autocorrelation trace gave a duration of $7.6\pm 0.8\mathrm{fs}$ in full width at half maximum for a Gaussian assumption. Furthermore, the trace shows good agreement with a simulation of the XFEL pulse shape propagating through the SDO system, irrespective of spectral chirps in the original XFEL pulses. Our results open the door toward direct temporal characterization of narrowband XFELs at the hard x-ray regime, such as self-seeded and future cavity-based XFELs, and indicate a solid way for temporal tailoring of ultrafast x-ray pulses with perfect crystals.

Figure 1

Schematic illustration of the setup (not scaled). See text for details.

Figure 2

(a) Converted spectra for $6.5\mu \mathrm{J}<I_{\mathrm{sum}}<8.5\mu \mathrm{J}$. The peak (E) at 9 keV is over the range. (b) Pulse-energy dependence of Kα yields. Each plot is separated from the others by adding a vertical offset. Error bar represents the statistical error. Solid line is the fitted quadratic function at each delay. (c) Delay-time dependence of the nonlinearity of two-photon absorption (TPA; circle), which is normalized by the base value of the fitted Gaussian. The triangle point represents the nonlinearity measured with spatially separated beams. Error bar is the fitting error. Dashed and solid lines show the fitted Gaussian and the autocorrelation function of a simulated pulse shape (shown in Fig. 4), respectively.

Figure 3

Examples of single-shot spectra of (a) the split pulses and (b)–(e) the original self-seeded XFEL pulses in a 4-eV range. Vertical and horizontal axes represent the photon energy and spatial position along the horizontal direction, respectively. Scale bar denotes 1 eV. Dashed line shows the spectral range of 0.5 eV reflected by the split-delay optical (SDO) system. The self-seeding amplification was successful for (b)–(d) but misfired for (e).

Figure 4

Simulated x-ray free-electron laser (XFEL) pulse shapes $I_{\mathrm{out}}\left(t\right)$. Black line represents the average over 500 simulated shapes (gray). Each shape is normalized by the peak value. The full width at half maximum (FWHM) duration of the main peak distributed from 7.2 to 7.8 fs in the simulation.