[1] P. Emma, R. Akre, J. Arthur, R. Bionta, C. Bostedt, J. Bozek, A. Brachmann, P. Bucksbaum, R. Coffee, F.-J. Decker et al., First lasing and operation of an ångstrom-wavelength free-electron laser, Nat. Photon. 4, 641 (2010).
[2] T. Ishikawa, H. Aoyagi, T. Asaka, Y. Asano, N. Azumi, T. Bizen, H. Ego, K. Fukami, T. Fukui, Y. Furukawa et al., A compact x-ray free-electron laser emitting in the sub-ångström region, Nat. Photon. 6, 540 (2012).
[3] H.-S. Kang, C.-K. Min, H. Heo, C. Kim, H. Yang, G. Kim, I. Nam, S. Y. Baek, H.-J. Choi, G. Mun et al., Hard x-ray free- electron laser with femtosecond-scale timing jitter, Nat. Photon. 11, 708 (2017).
[4] W. Decking, S. Abeghyan, P. Abramian, A. Abramsky, A. Aguirre, C. Albrecht, P. Alou, M. Altarelli, P. Altmann, K. Amyan et al., A MHz-repetition-rate hard x-ray free-electron laser driven by a superconducting linear accelerator, Nat. Photon. 14, 391 (2020).
[5] E. Prat, R. Abela, M. Aiba, A. Alarcon, J. Alex, Y. Arbelo, C. Arrell, V. Arsov, C. Bacellar, C. Beard et al., A compact and cost-effective hard x-ray free-electron laser driven by a high- brightness and low-energy electron beam, Nat. Photon. 14, 748 (2020).
[6] Z. Huang and K.-J. Kim, Review of x-ray free-electron laser theory, Phys. Rev. ST Accel. Beams 10, 034801 (2007).
[7] S. Gerber, S.-L. Yang, D. Zhu, H. Soifer, J. A. Sobota, S. Rebec, J. J. Lee, T. Jia, B. Moritz, C. Jia et al., Femtosecond electron-phonon lock-in by photoemission and x-ray free-electron laser, Science 357, 71 (2017).
[8] K. H. Kim, J. G. Kim, S. Nozawa, T. Sato, K. Y. Oang, T. W. Kim, H. Ki, J. Jo, S. Park, C. Song et al., Direct observation of bond formation in solution with femtosecond x-ray scattering, Nature (London) 518, 385 (2015).
[9] K. Tamasaku, E. Shigemasa, Y. Inubushi, T. Katayama, K. Sawada, H. Yumoto, H. Ohashi, H. Mimura, M. Yabashi, K. Yamauchi, and T. Ishikawa, X-ray two-photon absorption com- peting against single and sequential multiphoton processes, Nat. Photon. 8, 313 (2014).
[10] H. Yoneda, Y. Inubushi, K. Nagamine, Y. Michine, H. Ohashi, H. Yumoto, K. Yamauchi, H. Mimura, H. Kitamura, T. Katayama, T. Ishikawa, and M. Yabashi, Atomic inner-shell laser at 1.5-ångström wavelength pumped by an x-ray free- electron laser, Nature (London) 524, 446 (2015).
[11] See, for example, I. A. Walmsley and C. Dorrer, Characteriza- tion of ultrashort electromagnetic pulses, Adv. Opt. Photon. 1, 308 (2009).
[12] R. Mitzner, A. A. Sorokin, B. Siemer, S. Roling, M. Rutkowski, H. Zacharias, M. Neeb, T. Noll, F. Siewert, W. Eberhardt et al., Direct autocorrelation of soft-x-ray free-electron-laser pulses by time-resolved two-photon double ionization of He, Phys. Rev. A 80, 025402 (2009).
[13] J. A. Armstrong, Measurement of picosecond laser pulse widths, Appl. Phys. Lett. 10, 16 (1967).
[14] J. A. Giordmaine, P. M. Rentzepis, S. L. Shapiro, and K. W. Wecht, Two-photon excitation of fluorescence by picosecond light pulses, Appl. Phys. Lett. 11, 216 (1967).
[15] R. Trebino, K. W. DeLong, D. N. Fittinghoff, J. N. Sweetser, M. A. Krumbügel, B. A. Richman, and D. J. Kane, Measur- ing ultrashort laser pulses in the time-frequency domain using frequency-resolved optical gating, Rev. Sci. Instrum. 68, 3277 (1997).
[16] H. Yoneda, Y. Inubushi, M. Yabashi, T. Katayama, T. Ishikawa, H. Ohashi, H. Yumoto, K. Yamauchi, H. Mimura, and H. Kitamura, Saturable absorption of intense hard x-rays in iron, Nat. Commun. 5, 5080 (2014).
[17] M. Fuchs, M. Trigo, J. Chen, S. Ghimire, S. Shwartz, M. Kozina, M. Jiang, T. Henighan, C. Bray, G. Ndabashimiye et al., Anomalous nonlinear x-ray Compton scattering, Nat. Phys. 11, 964 (2015).
[18] S. Ghimire, M. Fuchs, J. Hastings, S. C. Herrmann, Y. Inubushi, J. Pines, S. Shwartz, M. Yabashi, and D. A. Reis, Nonsequential two-photon absorption from the K shell in solid zirconium, Phys. Rev. A 94, 043418 (2016).
[19] T. Kroll, C. Weninger, R. Alonso-Mori, D. Sokaras, D. Zhu, L. Mercadier, V. P. Majety, A. Marinelli, A. Lutman, M. W. Guetg et al., Stimulated X-Ray Emission Spectroscopy in Transition Metal Complexes, Phys. Rev. Lett. 120, 133203 (2018).
[20] S. Shwartz, M. Fuchs, J. B. Hastings, Y. Inubushi, T. Ishikawa, T. Katayama, D. A. Reis, T. Sato, K. Tono, M. Yabashi, S. Yudovich, and S. E. Harris, X-Ray Second Harmonic Gener- ation, Phys. Rev. Lett. 112, 163901 (2014).
[21] K. Tamasaku, E. Shigemasa, Y. Inubushi, I. Inoue, T. Osaka, T. Katayama, M. Yabashi, A. Koide, T. Yokoyama, and T. Ishikawa, Nonlinear Spectroscopy with X-Ray Two-Photon Absorption in Metallic Copper, Phys. Rev. Lett. 121, 083901 (2018).
[22] T. Osaka, T. Hirano, Y. Morioka, Y. Sano, Y. Inubushi, T. Togashi, I. Inoue, K. Tono, A. Robert, K. Yamauchi, J. B. Hastings, and M. Yabashi, Characterization of temporal coher- ence of hard x-ray free-electron laser pulses with single-shot interferograms, IUCrJ 4, 728 (2017).
[23] D. Zhu, Y. Sun, D. W. Schafer, H. Shi, J. H. James, K. L. Gumerlock, T. O. Osier, R. Whitney, L. Zhang, J. Nicolas et al., Development of a hard x-ray split-delay system at the Linac Coherent Light Source, Proc. SPIE 10237, 102370R (2017).
[24] Y. Sun, N. Wang, S. Song, P. Sun, M. Chollet, T. Sato, T. B. van Driel, S. Nelson, R. Plumley, J. Montana-Lopez et al., Compact hard x-ray split-delay system based on variable-gap channel-cut crystals, Opt. Lett. 44, 2582 (2019).
[25] G. Grübel, G. B. Stephenson, C. Gutt, H. Sinn, and Th. Tschentscher, XPCS at the European x-ray free electron laser facility, Nucl. Instrum. Methods Phys. Res. B 262, 357 (2007).
[26] Y. Shinohara, T. Osaka, I. Inoue, T. Iwashita, W. Dmowski, C. W. Ryu, Y. Sarathchandran, and T. Egami, Split-pulse x-ray photon correlation spectroscopy with seeded x-rays from x-ray laser to study atomic-level dynamics, Nat. Commun. 11, 6213 (2020).
[27] Y. Inubushi, K. Tono, T. Togashi, T. Sato, T. Hatsui, T. Kameshima, K. Togawa, T. Hara, T. Tanaka, H. Tanaka, T. Ishikawa, and M. Yabashi, Determination of the Pulse Dura- tion of an X-Ray Free Electron Laser Using Highly Resolved Single-Shot Spectra, Phys. Rev. Lett. 109, 144801 (2012).
[28] Y. Inubushi, I. Inoue, J. Kim, A. Nishihara, S. Matsuyama, H. Yumoto, T. Koyama, K. Tono, H. Ohashi, K. Yamauchi, and M. Yabashi, Measurement of the x-ray spectrum of a free electron laser with a wide-range high-resolution single-shot spectrome- ter, Appl. Sci. 7, 584 (2017).
[29] C. Gutt, P. Wochner, B. Fischer, H. Conrad, M. Castro-Colin, S. Lee, F. Lehmkhler, I. Steinke, M. Sprung, W. Roseker et al., Single Shot Spatial and Temporal Coherence Properties of the SLAC Linac Coherent Light Source in the Hard X-Ray Regime, Phys. Rev. Lett. 108, 024801 (2012).
[30] C. Behrens, F.-J. Decker, Y. Ding, V. A. Dolgashev, J. Frisch, Z. Huang, P. Krejcik, H. Loos, A. Lutman, T. J. Maxwell et al., Few-femtosecond time-resolved measurements of x-ray free- electron lasers, Nat. Commun. 5, 3762 (2014).
[31] I. Inoue, T. Hara, Y. Inubushi, K. Tono, T. Inagaki, T. Katayama, Y. Amemiya, H. Tanaka, and M. Yabashi, X-ray Hanbury Brown-Twiss interferometry for determination of ultrashort electron-bunch duration, Phys. Rev. Accel. Beams 21, 080704 (2018).
[32] I. Inoue, K. Tamasaku, T. Osaka, Y. Inubushi, and M. Yabashi, Determination of x-ray pulse duration via intensity correlation measurements of x-ray fluorescence, J. Synchrotron Rad. 26, 2050 (2019).
[33] N. Hartmann, G. Hartmann, R. Heider, M. S. Wangner, M. Ilchen, J. Buck, A. O. Lindahl, C. Benko, J. Grünert, J. Krzywinski et al., Attosecond time-energy structure of x-ray free-electron laser pulses, Nat. Photon. 12, 215 (2018).
[34] J. Amann, W. Berg, V. Blank, F.-J. Decker, Y. Ding, P. Emma, Y. Feng, J. Frisch, D. Fritz, J. Hastings et al., Demonstration of self-seeding in a hard-x-ray free-electron laser, Nat. Photon. 6, 693 (2012).
[35] I. Inoue, T. Osaka, T. Hara, T. Tanaka, T. Inagaki, T. Fukui, S. Goto, Y. Inubushi, H. Kimura, R. Kinjo et al., Generation of narrow-band x-ray free-electron laser via reflection self- seeding, Nat. Photon. 13, 319 (2019).
[36] K. Tono, T. Togashi, Y. Inubushi, T. Sato, T. Katayama, K. Ogawa, H. Ohashi, H. Kimura, S. Takahashi, K. Takeshita et al., Beamline, experimental stations and photon beam diagnostics for the hard x-ray free electron laser of SACLA, New. J. Phys. 15, 083035 (2013).
[37] See Supplemental Material at http://link.aps.org/supplemental/ 10.1103/PhysRevResearch.4.L012035 for the details of the re- flection self-seeding mode of operation, the split-delay optical system, and examples of detector images, which includes Refs. [38–43].
[38] T. Osaka, I. Inoue, R. Kinjo, T. Hirano, Y. Morioka, Y. Sano, K. Yamauchi, and M. Yabashi, A micro channel-cut crystal x-ray monochromator for a self-seeded hard x-ray free-electron laser, J. Synchrotron Rad. 26, 1496 (2019).
[39] S. Matsumura, T. Osaka, I. Inoue, S. Matsuyama, M. Yabashi, K. Yamauchi, and Y. Sano, High-resolution micro channel- cut crystal monochromator processed by plasma chemical vaporization machining for a reflection self-seeded x-ray free- electron laser, Opt. Express 28, 25706 (2020).
[40] T. Hirano, T. Osaka, Y. Sano, Y. Inubushi, S. Matsuyama, K. Tono, T. Ishikawa, M. Yabashi, and K. Yamauchi, Development of speckle-free channel-cut crystal optics using plasma chem- ical vaporization machining for coherent x-ray applications, Rev. Sci. Instrum. 87, 063118 (2016).
[41] K. Tono, T. Kudo, M. Yabashi, T. Tachibana, Y. Feng, D. Fritz, J. Hastings, and T. Ishikawa, Single-shot beam-position monitor for x-ray free-electron laser, Rev. Sci. Instrum. 82, 023108 (2011).
[42] T. Hirano, T. Osaka, Y. Morioka, Y. Sano, Y. Inubushi, T. Togashi, I. Inoue, S. Matsuyama, K. Tono, A. Robert et al., Performance of a hard x-ray split-and-delay optical system with a wavefront division, J. Synchrotron Rad. 25, 20 (2018).
[43] S. Shastri, P. Zambianchi, and D. Mills, Dynamical diffraction of ultrashort x-ray free-electron laser pulses, J. Synchrotron Rad. 8, 1131 (2001).
[44] H. Yumoto, H. Mimura, T. Koyama, S. Matsuyama, K. Tono, T. Togashi, Y. Inubushi, T. Sato, T. Tanaka, T. Kimura et al., Fo- cusing of x-ray free-electron laser pulses with reflective optics, Nat. Photon. 7, 43 (2013).
[45] T. Kameshima, S. Ono, T. Kudo, K. Ozaki, Y. Kirihara, K. Kobayashi, Y. Inubushi, M. Yabashi, T. Horigome, A. Holland et al., Development of an x-ray pixel detector with multi-port charge-coupled device for x-ray free-electron laser experiments, Rev. Sci. Instrum. 85, 033110 (2014).
[46] T. Katayama, T. Hirano, Y. Morioka, Y. Sano, T. Osaka, S. Owada, T. Togashi, and M. Yabashi, X-ray optics for ad- vanced ultrafast pump-probe x-ray experiments at SACLA, J. Synchrotron Rad. 26, 333 (2019).
[47] F. Livet, F. Bley, J. Mainville, R. Caudron, S. G. J. Mochrie, E. Geissler, G. Dolino, D. Abernathy, G. Grübel, and M. Sutton, Using direct illumination CCDs as high-resolution area de- tectors for x-ray scattering, Nucl. Instrum. Meth. A 451, 596 (2000).
[48] I. Inoue, Y. Inubushi, T. Osaka, J. Yamada, K. Tamasaku, H. Yoneda, and M. Yabashi, Shortening X-Ray Pulse Dura- tion via Saturable Absorption, Phys. Rev. Lett. 127, 163903 (2021).
[49] A. Authier, Dynamical Theory of X-Ray Diffraction (Oxford University Press, Oxford, 2001).
[50] S. Roling, H. Zacharias, L. Samoylova, H. Sinn, Th. Tschentscher, O. Chubar, A. Buzmakov, E. Schneidmiller, M. V. Yurkov, F. Siewert, S. Braun, and P. Gawlitza, Time-dependent wave front propagation simulation of a hard x-ray split-and- delay unit: towards a measurement of the temporal coherence properties of x-ray free electron lasers, Phys. Rev. ST Accel. Beams 17, 110705 (2014).
[51] S. Huang, Y. Ding, Y. Feng, E. Hemsing, Z. Huang, J. Krzywinski, A. A. Lutman, A. Marinelli, T. J. Maxwell, and D. Zhu, Generating Single-Spike Hard X-Ray Pulses with Non- linear Bunch Compression in Free-Electron Lasers, Phys. Rev. Lett. 119, 154801 (2017).
[52] K.-J. Kim, Yu. Shvyd’ko, and S. Reiche, A Proposal for an X- Ray Free-Electron Laser Oscillator with an Energy-Recovery Linac, Phys. Rev. Lett. 100, 244802 (2008).
[53] G. Marcus, A. Halavanau, Z. Huang, J. Krzywinski, J. MacArthur, R. Margraf, T. Raubenheimer, and D. Zhu, Refrac- tive Guide Switching a Regenerative Amplifier Free-Electron Laser for High Peak and Average Power Hard X Rays, Phys. Rev. Lett. 125, 254801 (2020).
[54] H. Johann, Die Erzeugung lichtstarker Röntgenspektren mit Hilfe von Konkavkristallen, Z. Phys. 69, 185 (1931).
[55] T. Johansson, Über ein neuartiges, genau fokussierendes Rönt- genspektrometer, Z. Phys. 82, 507 (1933).
[56] K. D. Irwin and G. C. Hilton, Transition-Edge Sensors (Springer, Berlin Heidelberg, 2005).
[57] J. Yamada, S. Matsuyama, R. Hirose, Y. Takeda, Y. Kohmura, M. Yabashi, K. Omote, T. Ishikawa, and K. Yamauchi, Compact full-field hard x-ray microscope based on advanced Kirkpatrick-Baez mirrors, Optica 7, 367 (2020).
[58] F. Salin, P. Georges, G. Roger, and A. Brun, Single- shot measurement of a 52-fs pulse, Appl. Opt. 26, 4528 (1987).