Generation of highly mutually coherent hard-x-ray pulse pairs with an amplitude-splitting delay line

Beam splitters and delay lines are among the key building blocks of modern-day optical laser technology. Progress in x-ray free electron laser source development and applications over the past decade is calling for their counterpart operating at the Angstrom wavelength regime. Recent efforts in x-ray optics development demonstrate relatively stable delay lines that most often adopt the division-of-wavefront approach for the beam splitting and recombination. However, the two exit beams in such configurations struggle to achieve sufficient mutual coherence to enable applications such as interferometry, correlation spectroscopy, and nonlinear spectroscopy. We present an experimental realization of the generation of highly mutually coherent pulse pairs using an amplitude-split delay line design based on transmission grating beam splitters and channel-cut crystals. The performance of the prototype system was analyzed in the context of x-ray coherent scattering and correlation spectroscopy, where nearly identical high-contrast speckle patterns from both branches were observed. We show in addition the high level of dynamical stability during continuous delay scans, a capability essential for high sensitivity ultrafast measurements.

Figure 1

(a) Layout of the experiment setup. The x-ray pulse propagates from left to right, sequentially through, the upstream diamond monochromator (Mono), the first diamond grating (G1), the optical table for the split-delay device (SD table), the second diamond grating (G2), two JJ-x-ray slits (Slit), the compound refractive lens (CRL), the sample or the beam profile monitor assembly (Scintillator & Sample), and the ePix100 x-ray direct detector (ePix100). (b) Schematics and beam paths of channel-cut crystals on the SD table. (c) A photograph of the SD table. (d) A photograph of G1 with a holder. (e) An electron microscopy image of the grating.

Figure 2

(a) Interference fringes with varying time delay. The number on the lower left corner is the corresponding delay time in fs. (b) Visibility of the interference fringes versus the relative delay time between the two pulses. Green dots are visibility for each single interference pattern, red stars are mean values of single pattern visibility values, and the black curve is the simulation value.

Figure 3

(a) The vector relation between wave vectors from a fixed and delayed branch. The ${\vec{k}}_D$ represents the output wave vector of the delayed branch. The ${\vec{k}}_F$ represents the output wave vector of the fixed branch. The $\vec{k}$ is the incident wave vector, ${\vec{g}}_1$ is the photon momentum transfer from G1 to the fixed branch, ${\vec{g}}_2$ is the photon momentum transfer from G2 to the delayed branch, $\vec{p}$ is the photon momentum transfer from the prism to the fixed branch, and ${\mathrm{\Delta }}_{+}$ is the photon momentum transfer from asymmetric Bragg reflections. We assume that $|{\vec{g}}_1|=|{\vec{g}}_2|$. Therefore, when G1 and G2 are perfectly aligned with each other, and $\vec{p}$ and ${\mathrm{\Delta }}_{+}$ are in the $x-z$ plane, the interference fringe should be parallel to the $y$ axis. (b) Interference fringe observed with the prism inserted into the fixed branch. The value on the lower left corners of the images indicate the deviation of the roll angle of G2 from the optimal value in degree.

Figure 4

(a) Pulse energy measurement with the upstream gas monitor showing beam delivery interruptions (denoted with arrows) during the long term beam stability measurement. (b) Single branch beam positions and their relative positions over 2 h. Each data point reflects the average beam position over 1 s. The yellow dashed arrow and line across (a) and (b) highlights the coincidence between the beam drop and sudden change of the beam positions.

Figure 5

Averaged speckles from delayed (a), fixed (b), and both (c) branches from 50 and 25 frames from single and both branches, respectively. The scale bar in (a) is shared by all three plots and corresponds to 0.000665 Å${}^{-1}$. (d) Measured effective overlap $\mu$ right after we optimized the spatial overlap for each delay. (e) Effective overlap over a time span of 30 min. (f) Contrast level of the small angle coherent scattering from delayed, fixed, and both branches as a function of the measurement time. The corresponding delay times are written above/below the markers in the unit of ps.

Figure 6

(a) Contrast of the small angle coherent scattering from delayed, fixed, and both branches in the continuous delay scan mode with the calculated effective overlap displayed in (b). The gray dashed line in (a) is the projected contrast curve for $\mu =0$, calculated with the averaged delayed and fixed branch contrast.

Figure 7

(Top) Direct beam intensity profile on the beam profile monitor. We calculate the total intensity within the red boxes. The size of the box is $700\times 512$ pixels. (Bottom) The $-1$, 0, and 1 order of diffraction (left, middle, and right) from the first grating. We calculate the total intensity within the red boxes. The size of the red boxes is $700\times 512$ pixels.

Figure 8

(a) Structure of the glassy carbon prism. (b) Steering angle of the prism for 9.83 keV photons for different incident angle. (c) Interference patterns measured with different prism angles. The numbers on the lower left corner for each image is the estimated incident angle of the prism.

Figure 9

Horizontal motion of the focused delay branch beam during the continuous delay scan.