Research Frontiers 2023 8 1. Introduction Since their discovery by Röntgen in 1895, X-rays have played an indispensable role in a wide range of fields, including basic science, medicine, and engineering. In the fields of life science and material science, in particular, their high permeability to thick materials and their interactions with crystals and atoms have been effectively utilized, providing analytical methods that cannot be reproduced by other means. In recent years, high-brilliance X-ray sources such as SPring-8 have been widely utilized, and most recently, the X-ray free-electron laser has provided spatially coherent ultrashort pulsed X-rays, ushering in a new era of X-ray application technologies. These high brilliance X-ray sources have a significant advantage in increasing the photon density when focused on them because of their small source size and divergence. Consequently, the race to reduce the focus size has intensified worldwide since the late 1990s, and various optical elements, such as zone plates, lenses, and mirrors, have achieved focusing of 100 nm or less. Mirrors have advantages over other elements owing to their high focusing efficiency, large working distance, and low chromatic aberrations. However, the fabrication of mirrors is significantly more difficult than other elements. Since 2000, we have been involved in developing a precision X-ray mirror from the standpoint of optical fabrication and metrology and have achieved the world’s first sub-30-nm focusing and sub-10-nm focusing by compensation optics [1, 2]. This paper discusses the accuracy required on the mirror surface to condense coherent X-rays down to the theoretical limit owing to diffraction and the fabrication and metrology methods to achieve condensation to the limit. Thereafter, it presents the realization of single- nanometer focusing of the Japanese X-ray free electron laser (XFEL), the SPring-8 angstrom compact free electron laser (SACLA), and its application to observe X-ray nonlinear optical phenomena to demonstrate the significance of X-ray condensation. 2. Required shape accuracy of the focusing mirror To focus coherent X-rays under diffraction limitations, all X-rays entering the aperture of the focusing element must be in a constructive interference state at the focal point. T h e m i r r o r s u r f a c e m u s t h a v e extremely high accuracy: according to Rayleigh’s criterion, the wavefront error of the X-rays must be less than λ /4 in peak-to-valley (PV), where λ is the X-ray wavelength. This yields the following equation (1) for grazing incidence mirror optics: d < λ / 8sin θ , (1) where θ is the grazing incidence angle, and d is the shape error of the mirror surface. When the X-ray energy was 10 keV, and the grazing incidence angle was 5 mrad, the acceptable shape error d was 3 nm PV. Because the mirror is several hundred millimeters long, it is extremely difficult to achieve the required accuracy. Shape errors with relatively long periods were related to the formation of unwanted side lobes in the focusing profile. When the distance between the side lobe and the main peak is N times wider than the main peak width, the shape error with a period of 1/N of the mirror length is the origin. Another problem is the speckle noise on the reflected beam, which corresponds to X-rays passing relatively far from the focal point and generates severe intensity fluctuation when the focused X-rays Ultimate condensation of synchrotron radiation X-rays and its application to exploring cutting-edge X-ray science Review Article Fig. 1. STM images of EEM processed Si (001) with view areas of ( a ) 20 nm × 20 nm and ( b ) 100 nm × 100 nm. In (a), each dot corresponds to each atom, the position of which is crystallographically reasonable. The inserted figure in (a) is a LEED spot obtained simultaneously with an electron beam energy of 65 eV. In (b), each atomic layer is color-coded, and 95% of the entire area is seen to be composed of three atomic layers. 〈 〈 11 – 0 〉 〉 (a) (b) Research Frontiers 2023 9 are observed in the far field. This problem has been attributed to short- period shape errors ranging from 0.1 to several millimeters. These errors must be less than 1 nm PV to reduce the speckle noise sufficiently. Furthermore, short-period roughness is related to scattering into wider angular regions; atomic smoothness is required in the X-ray regime. 3. Fabrication technologies We developed elastic emission machining (EEM) [3] as a fabrication m e t h o d a n d r e l a t i v e a n g l e - determinable stitching interferometry (RADSI) [4] as a shape measurement method, both of which are being comprehensively developed to realize a deterministic fabrication system for precision X-ray mirrors. EEM employs fine powder particles that react to workpiece materials. The particles were applied to the surface of the workpiece using ultrapure water. When they come in contact with the workpiece surface, chemical reactions between the interfacial atoms are induced, and when the flow of ultrapure water removes them, atom-by-atom removal proceeds. Figure 1 shows scanning tunneling microscopy (STM) images of an EEM-processed Si (001) surface with view areas of 20 nm × 20 nm and 100 nm × 100 nm. After the EEM processing, the surface was rinsed with ultrapure water, introduced into an ultrahigh-vacuum chamber, and observed by STM without heating. In the 20 nm × 20 nm image, each dot corresponds to each atom, and the position is crystallographically reasonable, meaning that no damage is introduced onto the surface, which is also understood from the low-energy electron diffraction ( L E E D ) i m a g e . T h e i m a g e o f 100 nm × 100 nm is color-coded per atomic layer, and 95% of the observed area is seen to be within the three atomic layers (±1 atomic layer) indicated by blue, green, and yellow. The extremely smooth surface, thus obtained, effectively increases the X-ray reflectivity. An EEM head using a nozzle flow can process a mirror surface with a small footprint of a 50 m m diameter circle and scan over the entire mirror surface to deterministically remove shape errors. An accuracy of more than 1 nm PV was achieved, sufficient to realize diffraction-limited focusing and suppress speckle noise. The shorter period roughness is automatically reduced to the atomic level through the machining principle of EEM. The mirror shape was tested using a stitching Fizeau interferometer called RADSI. In conventional stitching interferometry, the most significant factor that degrades measurement accuracy is the relative angle error between neighboring sub-apertures. The angle is typically estimated to minimize the degree of discrepancy in the common area using the measured shapes of neighboring sub-apertures, although the measured data contain some d e g r e e o f a m b i g u i t y o w i n g t o systematic and/or random errors. I n c o n t r a s t , t h e r e l a t i v e a n g l e was determined in situ during the RADSI measurements. The shapes of the sub-apertures on the curved and flat mirrors were measured simultaneously, as shown in Fig. 2. Then, both mirrors were inclined together at the same angle, and both the neighboring sub-apertures and the shape of the flat mirror were measured again. The difference between the two measurements of the flat mirror gives the relative angles between the neighboring sub- apertures, from which the relative angle can be calculated with an accuracy of nearly 10 –8 rad. When this operation is repeated, the relative angles between all the neighboring sub-apertures can be obtained. The inclination of the flat mirror can be changed independently and adjusted accordingly, such that the density of the interference fringes on the flat mirror is appropriate. Shorter period shapes were measured using a microscopic interferometer and pasted onto the shapes measured by RADSI. With these procedures, shape errors from short periods of less than 10 m m to long periods up to the entire mirror length can be mapped with a precision better than 1 nm PV. The measurement coordinates were related to those of the EEM machine, which was applied to deterministic fabrication. A typical shape-error correction process is shown in Fig. 3. It can be seen that the shape error of several tens of nanometers was improved to 2 nm PV after three cycles of correction processes. Fig. 2. Schematic drawing of RADSI. Flat and curved mirrors are simultaneously measured, inclined together by the tilting stage 2, and measured together again. In this procedure, the shapes of neighboring two sub-apertures on the test mirror and the angle difference between the two sub- apertures are obtained. The angle difference relates to the posture difference of the flat mirror before and after the inclination. The flat mirror can be inclined alone by tilting stage 1, which is set on stage 2 to reset the posture of the flat mirror to have an appropriate density of interference fringes. Reference flat of Fizeau interferometer Flat mirror Curved mirror φ stage 1 which can tilt flat mirror φ stage 2 which can tilt both mirrors θ θ Research Frontiers 2023 10 4. Ultimate focusing of XFEL Here, we present the latest status of XFEL. To date, Kirkpatrick– Baez (KB) mirrors have been used to focus synchrotron radiation X-rays. However, this optical system is prone to coma aberration and very sensitive to errors in the grazing incidence angle. This tendency is particularly pronounced when focusing on a size of 10 nm or less, where an accuracy of 0.1 m rad is required in the grazing incidence angle. This characteristic of KB mirrors makes the optical system unstable, and unfortunately, the practical application of a focused beam down to less than 10 nm is not yet possible. To solve this problem, we propose using Wolter type I or type III optics, which can drastically reduce the coma aberration, and attempts are being made to use type III optics to focus the XFEL of SACLA. The SACLA has a very compact configuration owing to its C-band accelerator and in-vacuum undulator, which are original Japanese technologies. The optical hutch is compact, and focusing optics must be installed inside it. Wolter type III can achieve a sufficiently large demagnification factor even in optics at a short distance from the light source because a convex mirror placed upstream allows the principal plane of the optics to be closer to the focal point. The optical configuration is shown in Fig. 4. The working distance was longer than 40 mm despite the ultimate condensation down to a single nanometer size. The wavefront of the focused beam was evaluated to be better than λ /4 by grating interferometry and ptychography. The focusing profiles were calculated using the measured wavefronts, as shown in Fig. 5. The focus size was approximately 7 nm in horizontal and vertical directions, with an estimated peak intensity of 10 22 W/cm 2 . 5. Nonlinear optical phenomena in a hard X-ray regime When X-rays hit an atom, a vacancy is formed in the inner shell. The upper electron falls into the vacancy, and the energy difference is observed as the energy of the fluorescent X-ray or Auger electron. These phenomena are widely used in condensed matter science. As this process is completed within a time of about femtoseconds, the phenomena can be understood by assuming that an inner-shell vacancy does not exist. In other words, these phenomena occurred in perfect proportion to the intensity of the pump X-rays. However, in the case of intense XFEL irradiation, the excitation by another photon can be observed before the inner-shell vacancy disappears, and the nature of the excitation is not proportional to the pump X-ray intensity. In the early 2010s, we achieved sub-50-nm focusing of the XFEL at SACLA using a conventional KB configuration. The focused beam was successfully used to observe nonlinear optical phenomena in the X-ray regime, such as two-photon absorption in Ge [5], saturable absorption in Fe [6], and inner-shell lasing in Cu [7]. Position (mm) 0 –5 0 5 10 15 20 20 40 60 80 100 Figure Error (nm) Prefigured profile After 1st figuring After 2nd figuring Finished profile Fig. 3. Typical figure correction property through the deterministic figuring process composed of EEM and RADSI. Side view Top view Source Focus Shape: hyperbolic convex Coating: Pt single-layer Shape: elliptical concave Coating: Pt/C multilayer 146.0 m 146.305 m 566.5 mm 118.0 mm 253.0 mm 226.4 mm 416.8 mm 233.4 mm 69.3 mm 77.6 mm Fig. 4. Optical configuration of Wolter type III mirrors installed at SACLA. In the side and top views, blue and orange mirrors condense the X-ray beam in the vertical and horizontal directions, respectively. Research Frontiers 2023 11 Most recently, using Wolter type III optics, fluorescence X-ray spectra from Cr films were observed using an ultimately focused beam with a spot size and peak intensity of 7 × 7 nm 2 and 1 × 10 22 W/cm 2 or higher, respectively. Figure 6 shows the emitted fluorescence spectra. The horizontal axis shows the energy of the fluorescence X-rays, and the vertical axis represents the position of the Cr film along the optical axis. The most intense, minimally focused beam irradiated the Cr film at 0, and a defocused beam was used when the Cr film moved away from the best focus. The bright peak of fluorescence X-ray at the energy of 5415 eV corresponds to the K α line, and many hyper satellites are observed; A and B, respectively, correspond to Ly α and Ly β , which are X-ray fluorescence from the Cr +23 state with only one electron. Interestingly, the intensity decreased when the Cr film was at the best focus, indicating the formation of perfectly bare Cr +24 . This was the world’s first observation under X-ray pumping [8]. This demonstration shows that Wolter optics enable stable operation even with highly focused beams of less than 10 nm. 6. Conclusion This paper reviews our research and development of focusing mirrors for synchrotron X-rays. The latest results were introduced, namely, the ultimate focusing of XFEL at SACLA BL3 down to 7 nm and an observation of Ly α and Ly β emission from a Cr film. The developed single-nanometer X-ray beam will be introduced into BL21XU and used for routine semiconductor evaluation. References [1] H. Mimura et al. : Appl. Phys. Lett. 90 ( 2007) 051903. [2] H. Mimura et al. : Nat. Phys. 6 (2010) 122. [3] K. Arima et al. : Surf. Sci. Lett. 600 (2006) L185. [4] H. Mimura et al. : Rev. Sci. Instrum. 76 (2005) 045102. [5] K. Tamasaku et al. : Nat. Photonics 8 (2014) 313. [6] H. Yoneda et al. : Nat. Commun. 5 (2014) 5080. [7] H. Yoneda et al. : Nature 524 (2015) 446. [8] J. Yamada et al. : Nat. Photonics - in press (2024). Kazuto Yamauchi Osaka University-RIKEN Center for Science and Technology, Osaka University Email: yamauchi.kazuto.ourcst@osaka-u.ac.jp Fig. 5. Beam profiles in (a) horizontal and (b) vertical directions estimated by the measured wavefront. Fig. 6. (a) Experimental setup and (b) fluorescence spectra emitted from a Cr film hit by focused XFEL down to 7 nm. K α peak is at 5415 eV. Horizontal 7 nm FWHM 7 nm FWHM Vertical (a) (b) (a) (b) XFEL Cr film Normalized Intensity (arb. units) Normalized Intensity (arb. units) 0 0 20 5200 7100 –19 0.7 HAPG MPCCD 9.124 keV Emitted Photon Energy (eV) Defocus Distance ( μ μ m) K α He α (5682.1) α Ly (5931.6) He β (6680.4) β Ly (7017.4)
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