1. Introduction

X-ray free electron lasers (XFELs) [1–3] have enabled a wide range of previously impossible dynamical studies of atoms, molecules, clusters, and materials in the physical and life sciences and produced many remarkable and influential results covering multiple disciplines due to their femtosecond time resolution, high peak power and near-full spatial coherence [4]. The availability of high-quality x-ray beam splitters at XFELs is expected to have a deep impact on XFEL facilities and experiments by providing the capabilities such as beam sharing, in-situ beam monitoring [5] including spectral [6,7] and wavefront measurements, and outcoupling in cavity-based XFEL schemes [8].

Past development in x-ray beam splitters have primarily been optimized for synchrotron or compact extreme ultraviolet (EUV) laser applications which range from EUV [9] to soft x-rays [10], and to hard x-rays [11,12]. Many different beam splitting techniques for these sources have been explored and demonstrated, including Bragg reflection from crystals [13–15], Laue diffraction through crystals [16], transmission and reflection from multilayer mirrors [17], diffraction from reflection gratings [18,19] and diffraction from transmission gratings [12,20,21]. However, the high peak and average power characteristic of new high repetition rate XFELs impose new technical challenges on survivability of the optics, and the technology developed for synchrotrons is not always directly translatable.

An ideal XFEL compatible beam splitter would not only survive the beam but would have high and tunable [12,22,23] diffraction efficiency while preserving the wavefront in the split beams. As a result of the survivability requirement, much of the recent work in x-ray FEL beam splitters utilize diamond as the material of choice due to its high thermal conductivity and survivability, and new fabrication methods for diamond-based optics are actively being developed [6,7,21,24,25]. While grating beam splitters based on thin diamond structures have been reported recently [21,24], efficiencies for these structures have been about 2% or less which is lower than what is required for our applications of interest.

In this paper, we report the design, fabrication, and characterization of a XFEL compatible thick diamond grating beam splitter with tunable diffraction efficiencies up to about 30% and wavefront distortions less than $\lambda$/100. We present a new fabrication method that produces high aspect ratio structures with high uniformity and low surface roughness as required for the performance of the device. We then utilize our recently developed Talbot wavefront sensor [26] to quantitatively measure the wavefront. New methods to calibrate and analyze the data for single-shot measurements of diffracted beams are presented. We demonstrate efficiency tunability from the established grating tilting techniques [12,22,23], and we perform additional systematic wavefront measurements, confirming that even under tilted conditions, the grating beam splitter maintains wavefront distortions of less than $\lambda$/100. Future applications of interest for this device include beam sharing among experimental stations, beam splitting for in-situ diagnostic measurements, beam splitting for specific experimental configurations, and outcoupling for cavity based XFEL schemes [8].

2. Experimental setup

The experiments were carried out at the x-ray pump-probe (XPP) instrument at LCLS [27]. A schematic diagram of the experimental setup is shown in Fig. 1. The LCLS was run in self-amplified spontaneous emission (SASE) mode and the beam was sent through a diamond double crystal monochromator to produce a quasi-monochromatic 9.5 keV beam [28]. The diamond beam splitter was placed downstream of the monochromator where the beam width was approximately 400 $\mu$m FWHM. The diamond beam splitter was designed to have a 300 nm half pitch and 2$\times$2 mm$^2$ area and was mounted vertically on a stage that has rotation capability along the horizontal axis perpendicular to beam direction. The rotation provided effective thickness change of the diamond grating, resulting in different phase delays and therefore diffraction efficiency tuning. The beam was then split into multiple diffraction orders and the angle between 0th and 1st orders was 0.22 mrad. Although the experimental results reported here were obtained using monochromatic light, we expect the diffraction grating’s performance to be nearly identical when using the SASE “pink” beam with $\sim$0.2$\%$ relative spectral bandwidth. A single grating Talbot wavefront sensor (WFS) was then placed 6 meters downstream and was large enough to measure the wavefront of the 0, +1, and -1 orders. The Talbot WFS consisted of a large area (1$\times$1 cm$^2$) silicon checkerboard $\pi$-phase shift grating, a cerium-doped yttrium aluminum garnet (YAG:Ce) scintillator, and a visible light microscope/camera. Based on the 14 $\mu$m period of the checkerboard grating, the third Talbot plane was chosen for the location of the YAG scintillator, at a distance of 0.56 m downstream of the checkerboard grating. The setup enabled simultaneous measurements of intensity profile, location, and wavefront distortion of the three beams on a single shot basis.

 

Fig. 1. Experimental schematic. The x-ray beams came from the LCLS FEL, tuned to a quasi-monochromatic 9.5 keV beam using a diamond double crystal monochromator (illustrated as “Source” in the figure). The diamond beam splitter was mounted vertically to give a horizontal diffraction spectrum. The diamond beam splitter can be tilted around the horizontal axis perpendicular to the beam direction as shown by the arrow in the figure. After the diamond beam splitter, the direct beam was split into multiple orders, mainly 0th and $\pm$1st orders. The wavefront sensor (WFS) was placed 6 m downstream of the beam splitter and consisted of a checkerboard grating large enough to capture all three main diffracted beams. A YAG:Ce scintillator at 0.56 m (third Talbot plane) downstream of the checkerboard grating converted x-rays into visible light, and an optical microscope recorded Talbot images of the three beams.

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3. Grating fabrication

The diamond grating was fabricated on a 1$\times$1 cm$^2$ square 100 $\mu$m thick CVD diamond plate (Diamond Materials GmbH). First, the metal electroplating base layer, 5 nm Cr and 10nm Au, which also serves as a charge dissipating layer during e-beam lithography, was electron beam evaporated onto the diamond plate. This was followed by spin coating 2-$\mu$m-thick 950K Polymethyl methacrylate (PMMA) as the resist for e-beam lithography. The resist layer was then baked at 180 $^\circ$C for 30 minutes and patterned with a 100-keV JEOL 6300 electron beam lithography system. To eliminate the field stitching error for exposing large area grating patterns, 2 by 2 pass field averaging was used for the e-beam lithography [29]. This writing method allows us to achieve an average patterning error of less than a few nanometers across the large area grating, as evidenced by the <$\lambda$/100 wavefront distortion between direct and diffracted beams, shown in the next section. The patterned resist was then developed in 7:3 isopropyl alcohol (IPA): deionized (DI) water at room temperature for 65 seconds and then rinsed in IPA. An oxygen descum etch was performed to remove any residual PMMA. To make the hard mask for diamond etch, the patterned PMMA grating was metallized via gold electroplating followed by removal of resist in heated Remover PG (MicroChem Corp). A final oxygen reactive ion etch (RIE) was used to etch the diamond with electroplated hard mask with the following parameters: 20 sccm $\mathrm {O_2}$ gas flow, 3 mTorr pressure, 200W RF power, and 20 $^\circ$C electrode temperature. The DC electrode bias voltage reading was about 650V. The average etch rate is about 14 nm/minute, and thus an etch time of 3 to 6 hours is required in order to etch 3 to 5 $\mu$m into the diamond. Since diamond etches much faster in open area than small trenches, the diamond grating was cleaved across for inspection and thickness measurements. SEM images of the diamond grating are shown in Figs. 2(a)–(d). Figure 2(a) is an overview of the cross sectional profile of the 300-nm-half-pitch diamond grating showing very good uniformity in etch depth. Figure 2(b) shows a 3.8 $\mu$m deep diamond grating etch was obtained after 4.5 h etch. Compared Fig. 2(b) with (d), we see that open area (grating edge) was etched faster than grating trenches, therefore a cleaved cross section rather than a view at the grating edge gives the real grating thickness. Figure 2(c) is an SEM Moire pattern [30] over a 500 $\mu$m field (multiple times of the 60 $\mu$m ebeam writing field), exhibiting very high uniformity. Figure 2(d) is a tilted view of the grating edge, showing the etched diamond surface (etchfront) is very smooth. The RMS roughness measurement of the diamond etchfront with a profilometer is 2.8 nm. Low roughness and high uniformity contribute to the wavefront preserving capability.

 

Fig. 2. SEM images of (a-d) the diamond grating beam splitter and (e, f) checkerboard grating. (a) cleaved cross section of the diamond grating fabricated on diamond plate, (b) zoom-in view of the cross section showing 300 nm half pitch and the thickness of around 3.8 $\mu$m, (c) an SEM Moire pattern image showing the high uniformity over a large area, (d) tilted view of the grating edge, showing the smoothness of the etched diamond surface, (e) top view of the silicon checkerboard grating showing 14 $\mu$m period, and (f) tilted view into the etched silicon showing the thickness of around 12 $\mu$m ($\pi$-phase shift for 9.5 keV x-rays).

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The checkerboard grating, used as part of the Talbot wavefront sensor, was fabricated on 200 $\mu$m thick silicon chips. First, a 20 nm Cr layer was electron beam evaporated onto the silicon chip. Then, a 200 nm thick layer of PMMA resist was spun on the silicon chip and baked for 5 min at 180 $^\circ$C. Electron beam lithography was then used to pattern a 1$\times$1 cm$^2$ area checkerboard pattern with a 14 $\mu$m pitch. The exposure was performed using the same averaging scheme as for the diamond grating to eliminate the field stitching errors. After e-beam exposure, the PMMA was developed at room temperature with 7:3 IPA: DI water for 30 seconds, rinsed in IPA, and dried with nitrogen. An oxygen descum was then used to ensure cleanliness of the pattern in the developed resist. The PMMA pattern was then transferred to the Cr layer via $\mathrm {Cl_2}$/$\mathrm {O_2}$ RIE with the following parameters: 8 sccm $\mathrm {Cl_2}$ gas flow, 2 sccm $\mathrm {O_2}$ gas flow, 20 mTorr pressure, 10W RF power, 10W inductively coupled plasma (ICP) power, 20 $^\circ$C electrode temperature, and an etch time of 6 min. The Cr is then used as the hard mask for etching Si for 12 $\mu$m with Bosch process [31] for 65 cycles. SEM images of the final Si checkerboard grating mask are shown in Figs. 2(e) and (f).

4. Results

4.1 Grating efficiency tunability

The diffraction efficiency and splitting ratio was measured as a function of grating tilt angle (varying x-ray beam incident angle leads to varying effective grating thickness, giving varying phase shift). Using the scintillator and camera, we recorded the intensity profile of the three main diffraction orders (Fig. 3(d) from left to right,-1st, 0th,+1st orders). The absolute diffraction efficiencies were calculated from the intensities of the three diffracted beams Fig. 3(d) and the direct beam Fig. 3(c), and were normalized using the beamline intensity monitor data for the incident beam to compensate the intensity variations between different tilts. We also calculated the diffraction efficiencies by simulating x-ray beam diffracted from the diamond grating with the same cross sectional profile (Fig. 3(e)) as measured with the SEM image (Fig. 2(b)). A multislice method was used to model the interaction between the x-ray beam and the diamond grating with as-fabricated profiles [32]. Effective thickness changes in both the grating and the substrate (absorption change) were taken into account in the simulation. As is shown in Fig. 3(f), the diffraction efficiencies vary with respect to the tilting angle, thus the splitting ratio can be tuned by tilting the grating. The measured efficiency difference between the -1st and +1st orders results from a tiny tilt angle between the x-ray beam direction and the groove sidewall plane. With such a tilt angle of 3 mrad or 0.17$^\circ$, the simulation data agrees well with experimental results. Our diamond grating exhibits high tunable efficiency, for example, ranging from 20% to more than 30% when working at 9.5 keV with a tilting range of 0$^\circ$-37$^\circ$. The tilting capability also makes it an energy tunable beam splitter that can be used for a range of photon energies by adjusting the grating tilt. At normal incidence, about 42% of x-ray energy went into 0th beam and about 22% went into $\pm$1st orders. An equal splitting ratio (1:1:1) among 0th and $\pm$1st orders was obtained with a tilt angle of about 35$^\circ$-37$^\circ$, at which about 28% intensity was diffracted into each of the three beams. In some applications such as in-situ beam monitoring, a smaller efficiency is useful. It can be achieved simply by reducing groove depth in the fabrication process.

 

Fig. 3. The diffraction efficiency is tunable via grating tilting. The diamond grating mounted vertically can be tilted around the horizontal axis perpendicular to the beam direction. (a) When operating at normal incidence, the effective grating thickness is the grating thickness $t_{\mathrm {eff}}=t_0$. (b) When operating at tilted incidence, the effective thickness is increased as a function of tilting angle $t_{\mathrm {eff}}=t_0/\cos \theta$. Using the YAG scintillator and camera but without the checkerboard grating, we recorded the intensity profile of (c) the direct beam without beam splitter and (d) diffracted beams (0th and $\pm$1st orders) with beam splitter at normal incidence. (e) Diamond grating cross sectional profile model geometrized from the SEM image (Fig. 2(b)) used for simulation. Each pillar consists of two trapezoids: a blue tall trapezoid ($h$=3800 nm, $a$=250 nm, $b$=400 nm) for the diamond, and a gold triangular trapezoid ($h$=260 nm, $a$=70 nm, $b$=310 nm) for the hard mask residue. (f) Tunable diffraction efficiency as a function of tilt angle. Simulated results agree well with experimental results. At normal incidence, about 42% of x-ray energy goes into 0th order whereas about 22% goes into $\pm$1st orders. At a tilted incidence, more energy goes into $\pm$1st orders, and at about 35$^\circ$-37$^\circ$ tilt, the equal 1:1:1 split was obtained which means equal amount of x-ray energy goes into each of the three beams. With this configuration, the beam splitter can be used to split the XFEL beam for use at multiple end stations simultaneously.

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Due to the high aspect ratio of our diamond grating, it is no longer considered a thin grating but a volume grating. A tilted incident with respect to the groove sidewall plane would lead to uneven diffraction energy distributions between positive and negative orders. The efficiency difference between the -1st and +1st orders from both the experiment and multislice simulation confirms that slightly tilting the gratings with respect to sidewall plane can be used to adjust the intensity distribution between positive and negative orders, which may also be desirable for some applications and enhances the previously published tunability method from past work [12,22,23].

In this experiment, the 100-$\mu$m-thick diamond grating absorbs only 9% of the 9.5 keV photons when used in normal incidence (Besides the aforementioned 0th and $\pm$1st orders, we estimated about 4-5% were diffracted into higher orders from simulation using the fitted profile geometries). This high level of transparency allows the diamond splitter to take the heat load from not only the current FELs, but also the future high repetition rate FEL sources. For example, a monochromator using 100-$\mu$m-thick diamond is currently being used at LCLS [33], and studies [34] showed that, given adequate thermal transfer mechanism and cooling, 100-$\mu$m-thick diamond can handle high average power x-rays from the 1MHz LCLS II high energy upgrade, to photon energy as low as 3.6 keV.

4.2 Wavefront measurement method

Wavefront measurements were carried out using a Talbot effect [35] based wavefront sensor that has been demonstrated with XFEL radiation [26]. From the Fourier transforms of the Talbot diffraction image [36], we could retrieve the derivatives of the wavefront $\mathbf {S_x=\partial W}/\partial x$ and $\mathbf {S_y=\partial W}/\partial y$, where $\mathbf {W}$ denotes the wavefront. The wavefront can be projected onto a Zernike polynomial basis, a 2D complete orthonormal basis, and thus can be represented in terms of Zernike coefficients: $\mathbf {W=cZ}$, where $\mathbf {c}=[c_0, c_1, c_2,\ldots ]$ is the Zernike coefficients and $\mathbf {Z}=[\mathbf {Z_0, Z_1, Z_2,\ldots }]$ is the Zernike polynomials. The gradients of wavefront $\mathbf {S=(S_x,S_y)}$ can also be represented in terms of Zernike coefficients: $\mathbf {S=cV}$, where $\mathbf {V=(V_x,V_y)}$ is the gradient of the Zernike polynomials [37]. The Zernike coefficients can be then calculated as $\mathbf {c=S V^T [V V^T]^{-1}}$ from the wavefront gradients [38,39]. The retrieved wavefront and the Zernike coefficients of the direct beam without the diamond grating are shown in Fig. 4 labeled as “DB”. The Zernike indices used in this paper follow OSA/ANSI standard indices. The first three Zernike terms $Z_0$, $Z_1$, $Z_2$ represent constant phase and linear phase which are trivial and therefore removed before calculating the Zernike coefficients. As can be seen in Fig. 4, Zernike terms $Z_3$, $Z_4$, $Z_5$ that represent astigmatism and defocus, contribute most to the wavefront.

 

Fig. 4. (a) Recorded Talbot images from the checkerboard grating for diffracted beams (0th and $\pm$1st orders) with beam splitter for wavefront retrieval. (b) Zoom-in view. (c) Retrieved 2D wavefront for direct beam (DB), 0th order beam and $\pm$1st order beams, (d) wavefront decomposed onto Zernike polynomial basis in terms of Zernike coefficients (66 Zernike terms used). Zernike coefficients of the $\pm$1st order beams were corrected for the field distortion to compare with the 0th order beam (See Section 4.3). As can be seen, the main Zernike components are $Z_3$ (oblique astigmatism), $Z_4$ (defocus), and $Z_5$ (vertical astigmatism). There is little differences noticeable between the four beams. The data points are averages from 500 shots and the error bars indicate the standard deviation.

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4.3 Correction of the field-dependent systematic error

The recorded Talbot image of the three diffracted beams is shown in Fig. 4(a). As can be seen, the 0th order beam is located at the center of the camera field, whereas the two $\pm$1st order beams are located at the two edges of the field. This leads to field-dependent systematic error caused by distortions in the recorded images. In order to perform the distortion correction, we moved the microscope to let the same beam (+1st order beam) scan across the field from the left all the way to the right. We tracked the move of the beam shot-to-shot in terms of the horizontal pixel number. At each position, we retrieved the wavefront in terms of Zernike coefficients. In Fig. 5, we show the relations of Zernike coefficients (e.g. $Z_3$, $Z_4$, $Z_5$) vs. horizontal pixel numbers. These curves were used to correct Zernike coefficients for beams that are not located at the center of the field. For example, to compare the wavefronts between the $\pm$1st order beams and the 0th order beam, the difference between the values of the curve at the $\pm$1st order locations and the 0th order location was subtracted.

 

Fig. 5. Field distortion correction curves for $Z_3$, $Z_4$, and $Z_5$. The recorded Talbot image was distorted by the microscope and the camera, which leads to relatively large distortion for $\pm$1st beams that located on the left and right edge, and negligible distortion for the direct beam or the 0th beams that located at the center. We let the + 1st order beam to scan horizontally from the left edge all the way to the right edge of the field. The location of the beam was tracked in terms of horizontal pixel number. We retrieved the wavefront on Zernike basis from shot to shot, and this figure shows how the three main Zernike terms vary as the beam illuminates different horizontal positions (pixel number). Since we used the same beam, these curves can be used to correct retrieved beam wavefronts not at the center of the field (i.e. $\pm$1st order beams) based on its location, to eliminate the field distortion effect from the microscope/camera optics.

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4.4 Corrected results on the three orders showing less than $\lambda$/100

Using the above-mentioned wavefront measurement method, Zernike decomposition algorithm, and field distortion correction, we were able to retrieve the wavefront for all three beams (Fig. 4) and compare them with each other and with the direct beam (Fig. 6). As can be seen from Fig. 4, the three beams look the same, with defocus and astigmatism contributing most to the wavefront. In Fig. 6, we show the wavefront difference between 0th order beam, $\pm$1st order beams and direct beam. The RMS difference between the direct beam and the 0th order beam is 20.8 mrad which means less than $\lambda$/300 wavefront distortion was caused by inserting the diamond grating. The RMS differences between 0th order beam and $\pm$1st order beams are 59.1 mrad and 45.1 mrad respectively. From the gradients of the measured wavefront distortions, we can also calculate the RMS slope errors to be about 12 nrad between the direct beam and the 0th order beam, and 44 nrad and 48 nrad between 0th order beam and $\pm$1st order beams respectively, which are small compared with the state-of-art x-ray mirror with about 100 nrad slope error [40]. This low wavefront distortion will enable us to use such diamond splitter to do real-time beam monitoring or in-situ wavefront sensing, by analyzing a copy of the original beam, and noninvasively sensing the beam.

 

Fig. 6. Wavefront comparison between direct beam (DB), 0th order beam, and $\pm$1st order beams. As can be seen, the RMS difference between 0th order and direct beam is minimal, 20.8 mrad or less than $\lambda$/300. The diamond grating beam splitter imposes very low wavefront distortion on the transmitted beam from the direct beam. The RMS differences between 0th order beam and $\pm$1st beams are both less than 60 mrad. The wavefront distortion between the three split beams is less than level of $\lambda$/100.

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4.5 Consistency of wavefront of all three orders under different tilting angles

The wavefronts of all three beams were also measured using different tilting angles. As can be seen in Fig. 7, there is no noticeable differences of the Zernike coefficients at different tilts. The Zernike coefficient variations from tilting are in the range of standard deviation from shot to shot. The diamond grating beam splitter has exhibited both tunable efficiency via tilting and low wavefront distortion between split beams and between different splitting ratios at different tilts.

 

Fig. 7. (a) Wavefront of 0th order beam at various tilt angles ranging from normal incidence to 35$^\circ$ tilt. Data points are averages from 500 shots and the error bars indicate standard deviations. There is almost no noticeable differences between the Zernike coefficients of wavefront at different tilts. (b) Zernike coefficients $Z_3$, $Z_4$, and $Z_5$ of 0th order beam wavefront at tilting angles from 0$^\circ$ to 35$^\circ$. The error bars indicate the standard deviations over 500 shots at each tilt angle.

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5. Conclusion

We have demonstrated splitting the LCLS hard x-ray FEL beam using a diamond grating as a beam splitter. The diamond grating was nanofabricated with e-beam lithography and reactive ion etching and was designed to have a large area to cover the whole beam and to accommodate the tilting geometry. Diffraction efficiency and splitting ratio were measured showing a high splitting efficiency. A dynamical control over the splitting ratio was obtained via tilting the grating. The grating splitter can also be easily adopted as an energy tunable device at different x-ray energies for a desired splitting ratio. 2D wavefront measurements of the split beams as well as the direct beam were carried out using single grating Talbot interferometry. With calibrations, we achieved low level wavefront distortion between the split beam and the direct beam, all below the level of $\lambda$/100. We have also shown a consistency of the split beam under different tuning angles. This tunable diamond beam splitter has great potential to enable XFEL beam sharing by multiple end stations or in-situ beam monitoring and wavefront measurements.