A beam branching method for timing and spectral characterization of hard X-ray free-electron lasers

We report a method for achieving advanced photon diagnostics of x-ray free-electron lasers (XFELs) under a quasi-noninvasive condition by using a beam-splitting scheme. Here, we used a transmission grating to generate multiple branches of x-ray beams. One of the two primary diffracted branches (+1st-order) is utilized for spectral measurement in a dispersive scheme, while the other (−1st-order) is dedicated for arrival timing diagnostics between the XFEL and the optical laser pulses. The transmitted x-ray beam (0th-order) is guided to an experimental station. To confirm the validity of this timing-monitoring scheme, we measured the correlation between the arrival timings of the −1st and 0th branches. The observed error was as small as 7.0 fs in root-mean-square. Our result showed the applicability of the beam branching scheme to advanced photon diagnostics, which will further enhance experimental capabilities of XFEL.

We report a method for achieving advanced photon diagnostics of x-ray free-electron lasers (XFELs) under a quasi-noninvasive condition by using a beam-splitting scheme. Here, we used a transmission grating to generate multiple branches of x-ray beams. One of the two primary diffracted branches (þ1st-order) is utilized for spectral measurement in a dispersive scheme, while the other (À1st-order) is dedicated for arrival timing diagnostics between the XFEL and the optical laser pulses. The transmitted x-ray beam (0th-order) is guided to an experimental station. To confirm the validity of this timing-monitoring scheme, we measured the correlation between the arrival timings of the À1st and 0th branches. The observed error was as small as 7.0 fs in root-mean-square. Our result showed the applicability of the beam branching scheme to advanced photon diagnostics, which will further enhance experimental capabilities of XFEL. X-ray free-electron lasers (XFELs) 1-3 have promoted researches in a variety of scientific fields such as chemistry, material science, physics, and biology. Coherent x-ray pulses with an unprecedented peak power (>10 GW) and an ultrashort temporal duration (<10 fs) have opened novel opportunities to observe the electronic and structural dynamics of matter with an ång-str€ om and femtosecond spatio-temporal resolution. Owing to these unique properties of XFEL sources, notable scientific progresses have been reported in studies on capturing unstable shortlived species in light-induced chemical reactions, 4-6 elucidating atomic displacements in phonon oscillations, 7,8 creating exotic states of matter with high energy densities, [9][10][11][12][13] and determining damage-free structures of crystallized proteins. [14][15][16] Most of the current XFEL sources operate on the basis of a self-amplified spontaneous emission (SASE) scheme, 17,18 which causes shot-to-shot variations in radiation properties such as a pulse energy, a temporal duration, a spatial profile, a wavefront, and a spectrum. Detailed knowledge of these stochastic fluctuations is critical for conducting accurate data analysis. A transmissive beam monitor, which consists of a nanocrystal diamond film and photodiodes, 19 a) E-mail: tetsuo@spring8.or.jp b) for example, has provided the pulse energy and the center-of-mass position of XFEL light, which are highly useful for normalization of signals.
Furthermore, diagnostics on arrival timings between an XFEL and an optical laser pulses is indispensable to improve the temporal resolution in ultrafast experiments, because an intrinsic temporal resolution that is determined by the temporal duration of x-ray or optical pulse can be significantly deteriorated by a possible timing jitter between these pulses. To solve this issue, X-ray/optical cross-correlators [20][21][22][23][24][25][26][27][28][29] have been developed at the free-electron laser in Hamburg (FLASH) 28,29 and the Linac Coherent Light Source (LCLS). [21][22][23][24][25][26][27] Intense x-ray irradiation induces an ultrafast change of the electronic states in semiconductor materials; a rapid increase of free-carrier density, resulting from photoabsorption and subsequent electron-electron (electronphonon) scattering processes, modifies the complex refractive index (n ¼ 1 À d À ib). This perturbation is probed by a transient modulation of the optical transmittance or reflectivity. Harmand et al. 22 have applied this scheme to determine the relative arrival timing in the hard x-ray regime and achieved an accuracy of sub-10 fs in root-mean-square (RMS).
Recently, Sato et al. 20 have successfully reduced the pulse energy required for arrival timing diagnostics from the sub-millijoule order 22 to 12 lJ at 12 keV by combining line-shaped focused x-rays with a target comprising high-Z materials that have a small penetration depth of x-rays. Although this method is highly efficient even for short-wavelength x-rays, it does not work as a shot-to-shot monitoring tool for pump-probe experiments owing to its photondestructive nature. Also, Inubushi et al. 30 have developed a dispersive spectrometer with a high resolution of 14 meV, while being in a destructive manner.
If one could perform these photon-destructive diagnostics simultaneously with experiments, one would expect to design advanced experiments with greater flexibilities. In this paper, we propose a scheme using a transmission grating to split an x-ray beam into a main branch and several sub-branches, which are dedicated for experiments and diagnostics, respectively. Similar approaches have been used for building a split-and-delay line 7 as well as for spectral monitoring 31,32 combined with a thin bent analyzer crystal. 33 Here, we utilized the þ1st-order and À1st-order branches for measuring the spectrum and the arrival timing jitter, respectively (see Fig. 1(a)), while the 0th-order branch is used for experiments. In Section II, we give a design concept of the optical system implemented at a hard x-ray beamline, BL3, 34 of SPring-8 Angstrom Compact Free Electron Laser (SACLA 2 ). In Section III, we describe the results and discussion of proof-of-principle experiments for investigating the performance. Finally, we give a summary and discuss future perspectives in Section IV.

II. DESIGN CONCEPT OF OPTICAL SYSTEM
A. Transmission grating beam splitter As key optics devices in this scheme, we employ one-dimensional transmission gratings with high aspect ratios, which diffract a small fraction of the incoming x-ray beam into multiple branches ( Fig. 1(a)). The design parameters of the three gratings are listed in Table I. They were fabricated from thin silicon membranes coated with a 20-nm-thick chromium layer and a 200-nm-thick poly-methylmethacrylate (PMMA) resist layer. The grating lines were defined by electron-beam lithography. After exposure and development, the line patterns were transferred into the chromium layer using chlorine-based dry etching. The chromium layer served as a hard mask for the reactive ion etching into the silicon membranes. These gratings were prepared to cover a wide range of photon energy, although the 500-nm-period grating was used in the present study ( Fig. 1(b)). The þ1st-order and À1st-order branches propagate in the vertical plane with the deflection angle given by hs ¼ a sinðk=dÞ, where k is the wavelength and d is the period. At 10 keV (k ¼ 1.24 Å ), the period d ¼ 500 nm gives hs ¼ 0.248 mrad. To control a diffraction efficiency, the grating can be tilted along the vertical axis so as to change its effective thickness (see Fig. 1(a)). 35 A large horizontal acceptance of 8 mm allows us to set a tilt angle up to 65 , corresponding to an increase in an effective aspect ratio by a factor of 2.37. For the present diffractive structures with rectangular profiles and a duty cycle of 0.5 (Table I), the first-order diffraction efficiency DE is given by 35 where z is the effective thickness, k is the wavelength, and b and 1 À d are the imaginary and real parts of the complex refractive index, respectively. Figures 1(c) and 1(d) show the angular dependence of DE measured using synchrotron radiation. We obtained DE in the range of 2.1%-21.6% (91.0%-22.8% in the transmitted 0th order) for the tilt angle range of 0 -65 . We observed that the values of DE were slightly smaller than those calculated using Eq.
(1), which may be caused by a misalignment of the tilt axis from the ideal orientation perpendicular to both the grating structure and the incoming radiation. For arrival timing and spectral diagnostics, the tilt angle of 0 is routinely used. We evaluated an intensity loss of the 0th-order main beam by the grating for various photon energies, as shown in Fig. 1(e). The x-ray transmittance was measured to be 78.0%-96.4% (3.70%-0.62% in DE) for the photon energy range of 7-15 keV. Also, we confirmed that the beam profile and the focusing performance of the main beam were unchanged even with the presence of the grating at a tilt angle range below 45 .

B. Arrival timing monitor
A schematic of the arrival timing monitor is presented in Fig. 2. The x-ray beam in the À1st-order branch is delivered to a flat mirror (M1) located 8.085 m from the grating, which is used for enlarging lateral separation from the 0th-order beam, as shown in Fig. 2(b). Note that M1 has a groove with a cross section of 10 Â 5 mm 2 so as to avoid interference with other branches. After the horizontal reflection, an elliptical mirror (M3), set at a distance of 0.7 m from M1, is utilized to focus the À1st-order branch vertically on a sample surface with an incident angle of 45 . The footprint on the sample surface is 1500 (H) Â 30 (V) lm 2 . The specifications of the mirrors are listed in Table II.
As targets, we use 5-lm-thick gallium arsenide (GaAs) single crystals glued on 500-lm-thick sapphire substrates. As a probe, a synchronized Ti:sapphire laser pulse with a duration of 40 fs and a central wavelength of 800 nm is focused on the sample using a cylindrical lens with a normal incident angle. The full-width at half-maximum (FWHM) spot size is 3500 (H) Â 75 (V) lm 2 . The spatial modulation of the optical transmittance is recorded using a CCD detector (Adimec OPAL 2000D/c) with imaging lenses. The spatial resolution is measured to be 1.1 lm/pixel, which is converted to 2.6 fs/pixel using the optical geometry of the spatial encoding. 20

C. Dispersive spectrometer
The þ1st-order branch is introduced into a dispersive x-ray spectrometer, 30,37 which consists of an elliptical mirror (M2) set at a distance of 8.435 m from the grating, a flat Si analyzer crystal, and a multiport charge-coupled device (MPCCD) detector 38 (see Fig. 2). The mirror M2 enlarges the divergence (Dh d ) of the þ1st-order branch to 2.5 mrad. The analyzer crystal   diffracts x-rays with the wavelength satisfying the Bragg law when the divergent x-rays impinge with different incident angles. The dispersed spectrum is recorded as a spatial intensity distribution on the MPCCD, which has a pixel size of 50 Â 50 lm 2 . The spectral resolution dE E is given by where h B , r, L, x D , E, and p are the Bragg angle, the source size, the distance from the source to the detector, the FWHM width of the Darwin curve, the photon energy, and the pixel size of the MPCCD detector, respectively. The spectral range DE is given by We prepared Si (111) and Si (220) analyzer crystals to vary the resolution and the spectral range (see Table III) with a h B range of 10 -80 . This tunability is useful for conducting various types of experiments 39,40 as well as for optimizing machine parameters.

III. PROOF-OF-PRINCIPLE EXPERIMENTS
To evaluate performance of the system implemented in the beamline, we measured a correlation by performing an independent measurement using the 0th-order branch, which was located at $3 m from the system. The central photon energy, the average pulse energy, and the temporal duration of the XFEL pulses were 10 keV, 360 lJ, and $5 fs, respectively. DE for the grating was 2.1%, corresponding to an average pulse energy of 7.6 lJ in the 61st-order branches. The 0th-order beam was attenuated to 7.8 lJ with a 0.5-mm-thick Si attenuator.
A. Arrival timing diagnostics Figure 3 shows background-subtracted images of three consecutive single shots recorded using the À1st-order and the 0th-order branches. A background image was built from an average of 100 shots taken with optical lasers (without x-rays) and was used as a reference for normalization. The temporal overlaps were projected to the horizontal axes of the images. We integrated the intensities of the pixels between the two white dotted lines in each image along the vertical axis and extracted the projection shown as black circles on the right of the images. The upper and the lower axes represent the pixel number and the relative time, respectively. The positive direction in the relative time indicates the earlier irradiation of x-rays with respect to the optical lasers. The vertical axis is the optical transmittance normalized by that without x-ray illumination. Although the normalization process could not eliminate a considerable deviation from unity in the unexcited region owing to fluctuation of the optical intensity and pointing, we observed a sharp change in transmittance of over 50% after x-ray excitation. To analyze the correlation between the two independent measurements, edge positions were  retrieved by the following procedure. The projections were smoothed by a low-path filter to remove the noise, which are shown as red lines in Fig. 3. We then obtained the blue dotted lines by differentiating the smoothed red lines and fitted the regions around the peaks with Gaussian functions. The resultant fitted curves are shown as green lines. We defined the Gaussian centers obtained as the relative timing values. Note that we determined the conversion coefficient from the pixels to the timings by mapping the average peak positions while scanning the optical delay. The conversion coefficient was determined to be 2.6 fs/pixel, which agreed with a value expected from the optical geometry. The arrival timings, shown as vertical white lines in the images, exhibit shot-to-shot variation because of the intrinsic temporal jitter. We observed an excellent agreement between the two sets of arrival timing values presented in the images. The average error bars of the Gaussian centers in the fitting procedure were 0.14 fs and 0.35 fs for the À1st-order and 0th-order branches, respectively. The temporal width of the change in transmittance, which is the FWHM of the Gaussian profile, was typically $100 fs. This length corresponds to the convolution of the temporal durations of the XFEL and optical laser pulses, and inherent electronic responses of the sample with respect to x-ray excitation.
On the basis of this analysis, we collected 47 220 images and determined the arrival timing for each shot. The scatter plot in Fig. 4(a) presents the correlation between the arrival timings of the À1st-order and 0th-order branches. The temporal jitter can be seen in the top right histogram ( Fig. 4(b)), where the RMS width was 256 fs (FWHM ¼ 603 fs). The correlation between the two diagnostics was obtained by linear least squares fitting. The residual error of the fitting, which is defined as the overall accuracy, is plotted in Fig. 4(c). The systematic error may have originated from mechanical vibrations of the optics and the samples, optical pointing fluctuations, and imperfection of the sample flatness. We note that further correction of this systematic error may be achieved by applying a nonlinear pixel-to-time calibration, as performed in Ref. 22. The error histogram in Fig. 4(d) has the RMS width of 7.0 fs (FWHM ¼ 16.5 fs). This sub-10 fs accuracy should allow the temporal resolution to be improved down to the femtosecond regime, which is mainly governed by the temporal duration of the optical lasers after re-sorting the data to remove the jitter. Moreover, the error variation was stable over 1 h (Fig. 4(e)), assuring a long-term reliable operation of arrival timing diagnostics.
Next, we investigated an applicable range of the photon energy. For this purpose, we simulated the expected signal using the Drude model 41,42 and the Fresnel formula. First, the freecarrier density (N) created in bulk matter was estimated (see Figs. 5(a) and 5(b)). Assuming a uniform distribution of hot carriers (electron and hole pairs) in the medium, the free-carrier density is given by where E 0 , E b , h i , A, l, and l are the incoming pulse energy, the band gap of the target material, the incident angle of the x-ray beam, the footprint size, the sample thickness, and the penetration depth, respectively. Under our experimental conditions, the carrier density in the GaAs crystal was calculated to be 9.3 Â 10 18 cm À3 (white circle in Fig. 5(a)), which is about one order of magnitude higher than that of a silicon nitride (Si 3 N 4 ) membrane with the same thickness (see Fig. 5(b)). The steep edges at 10.367 keV and 11.867 keV in Fig. 5(a) originate from the Ga and As K edge, respectively. Using the free-carrier density, the complex dielectric function in the excited state is given by where e un is the dielectric function in the un-pumped ground state, w elementary charge, and the angular momentum of the probe light, respectively. Using the Fresnel formula and dielectric function, the transmittance of the optical laser T(w) at normal incidence is given by where t 1 , t 2 , c 1 , and c 2 are Fresnel coefficients, and c is the speed of light. By integrating Eq. (8) over the spectral range of the probe (the FWHM bandwidth was 47 nm and the central wavelength was 800 nm), we estimated the transmittance modulation of GaAs as shown in Fig.  5(c). The expected change in the optical transmission was 0.59, which well agreed with the observation. We emphasize that such a significantly high response of the optical transmission (>30%) is simply predicted over a wide photon energy range (5-25 keV) with a pulse energy of less than 10 lJ. For the Si 3 N 4 membrane with the same thickness, a change of 3%-4% was calculated (Fig. 5(d)). A higher photon energy leads to further reduction of the signal intensity. Experimentally, we confirmed an applicability of GaAs to short-wavelength measurements by performing a similar measurement at a photon energy of 15 keV (Fig. 5(e)), which showed a high optical response over 50%.
B. High resolution spectral measurement Figure 6 presents the single-shot spectra of the þ1st-order and 0th-order branches. Using a Si (660) reflecting plane, the spike features of SASE radiation were completely resolved ( Fig.  6(a)). The spectral range of these two spectrometers was 6.4 eV in Table III, while we showed spectra only in an overlap area ($3 eV) between them in Fig. 6(a). We found reasonable agreement in both an energy dispersion (horizontal) and a spatial chirp (vertical) direction between the spectra. These results indicated that the chromatic dispersion effect induced by the diffraction at the grating was negligible in the þ1st-order branch. The average spike width was determined to be 470 meV. Note that we can easily switch the reflecting plane to a lower index of Si (220), for example, in order to cover a wider bandwidth, as shown in Fig. 6(b).

IV. SUMMARY
We have developed a beam branching method for enabling advanced photon diagnostics with small perturbation using a grating beam splitter. The 0th-order transmission branch, which keeps over 90% of the original intensity at 10 keV, is provided for a diverse range of applications. By measuring the correlation between the arrival timings of the À1st-order and 0th-order branches, we found that the RMS error in the arrival timing diagnostics was below 10 fs. The calculation verified the applicability of GaAs for higher photon energies of up to 25 keV with a pulse energy of less than 10 lJ. Further improvement of the temporal resolution will be explored by implementation of an optical laser with a shorter temporal duration.