Abstract
Free-electron lasers and high-harmonic-generation table-top systems are new sources of extreme-ultraviolet to hard X-ray photons, providing ultrashort pulses that are intense, coherent and tunable. They are enabling a broad range of nonlinear optical and spectroscopic methods at short wavelengths, similar to those developed in the terahertz to ultraviolet regimes over the past 60 years. The extreme-ultraviolet to X-ray wavelengths access core transitions that can provide element and orbital selectivity, structural resolution down to the sub-nanometre scale and, for some methods, high momentum transfers across typical Brillouin zones; the possibilities for polarization control and sub-femtosecond time resolution are opening up new frontiers in research. In this Roadmap, we review the emergence of this field over the past 10 years or so, covering methods such as sum or difference frequency generation and second-harmonic generation, two-photon absorption, stimulated emission or Raman spectroscopy and transient grating spectroscopy. We then discuss the unique opportunities provided by these techniques for probing elementary dynamics in a wide variety of systems.
Key points
-
X-ray free-electron lasers and high-harmonic-generation sources of extreme-ultraviolet (EUV) to hard X-ray photons deliver intense ultrashort pulses and enable the extension of nonlinear methods to much shorter wavelengths.
-
EUV to X-ray wavelengths access core transitions that can provide element and orbital selectivity. These wavelengths also achieve sub-nanometre structural resolution and high momentum transfer, with femtosecond and attosecond time resolution.
-
Nonlinear EUV/X-ray methods that have emerged include sum or difference frequency generation, parametric down-conversion, second-harmonic generation, two-photon absorption, stimulated emission or Raman spectroscopy and transient grating spectroscopy.
-
Nonlinear EUV/X-ray science is developing hand-in-hand with instrumentation, to improve pulse features and enhance accessibility with the use of table-top systems or compact accelerators.
-
These techniques offer unique opportunities for probing dynamical events in a wide variety of systems, including surface and interface processes, chirality, nanoscale transport and multidimensional core-level spectroscopy.
This is a preview of subscription content, access via your institution
Access options
Access Nature and 54 other Nature Portfolio journals
Get Nature+, our best-value online-access subscription
$29.99 / 30 days
cancel any time
Subscribe to this journal
Receive 12 digital issues and online access to articles
$99.00 per year
only $8.25 per issue
Buy this article
- Purchase on SpringerLink
- Instant access to full article PDF
Prices may be subject to local taxes which are calculated during checkout
Similar content being viewed by others
References
Kaiser, W. & Garrett, C. G. B. Two-photon excitation in CaF2:Eu2+. Phys. Rev. Lett. 7, 229–231 (1961).
Franken, P. A., Hill, A. E., Peters, C. W. & Weinreich, G. Generation of optical harmonics. Phys. Rev. Lett. 7, 118–119 (1961).
Bloembergen, N. Nonlinear optics and spectroscopy. Rev. Mod. Phys. 54, 685–695 (1982).
Mukamel, S. Principles of Nonlinear Optical Spectroscopy (Oxford Univ. Press, 1995).
Munn, R. W. & Ironside, C. N. Principles and Applications of Nonlinear Optical Materials (Springer Netherlands, 1993).
Busch, G. E., Jones, R. P. & Rentzepis, P. M. Picosecond spectroscopy using a picosecond continuum. Chem. Phys. Lett. 18, 178–185 (1973).
Eisenthal, K. B. Picosecond relaxation processes in chemistry. In Ultrashort Light Pulses: Picosecond Techniques and Applications (ed. Shapiro, S. L.) 275–315 (Springer, 1977).
Shank, C., Ippen, E. & Bersohn, R. Time-resolved spectroscopy of hemoglobin and its complexes with subpicosecond optical pulses. Science 193, 50 (1976).
Zewail, A. H. Femtochemistry: atomic-scale dynamics of the chemical bond using ultrafast lasers (Nobel Lecture). Angew. Chem. Int. Ed. 39, 2586–2631 (2000).
Ackermann, W. et al. Operation of a free-electron laser from the extreme ultraviolet to the water window. Nat. Photon. 1, 336–342 (2007).
Allaria, E. et al. The FERMI@ Elettra free-electron-laser source for coherent X-ray physics: photon properties, beam transport system and applications. N. J. Phys. 12, 075002 (2010).
Emma, P. et al. First lasing and operation of an angstrom-wavelength free-electron laser. Nat. Photon. 4, 641–647 (2010).
Ishikawa, T. et al. A compact X-ray free-electron laser emitting in the sub-angstrom region. Nat. Photon. 6, 540–544 (2012).
Prat, E. 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, 748–754 (2020).
Lappas, D. G. & L’Huillier, A. Generation of attosecond XUV pulses in strong laser-atom interactions. Phys. Rev. A 58, 4140–4146 (1998).
Corkum, P. B., Burnett, N. H. & Ivanov, M. Y. Subfemtosecond pulses. Opt. Lett. 19, 1870–1872 (1994).
Drescher, M. et al. X-ray pulses approaching the attosecond frontier. Science 291, 1923–1927 (2001).
Christov, I. P., Murnane, M. M. & Kapteyn, H. C. High-harmonic generation of attosecond pulses in the ‘single-cycle’ regime. Phys. Rev. Lett. 78, 1251–1254 (1997).
Chang, Z. H., Rundquist, A., Wang, H. W., Murnane, M. M. & Kapteyn, H. C. Generation of coherent soft X rays at 2.7 nm using high harmonics. Phys. Rev. Lett. 79, 2967–2970 (1997).
Hentschel, M. et al. Attosecond metrology. Nature 414, 509–513 (2001).
Lenzner, M., Schnurer, M., Spielmann, C. & Krausz, F. Extreme nonlinear optics with few-cycle laser pulses. IEICE Trans. Electron. E81C, 112–122 (1998).
Milne, C. J., Penfold, T. J. & Chergui, M. Recent experimental and theoretical developments in time-resolved X-ray spectroscopies. Coord. Chem. Rev. 277, 44–68 (2014).
Chergui, M. & Collet, E. Photoinduced structural dynamics of molecular systems mapped by time-resolved X-ray methods. Chem. Rev. 117, 11025–11065 (2017).
Kraus, P. M., Zürch, M., Cushing, S. K., Neumark, D. M. & Leone, S. R. The ultrafast X-ray spectroscopic revolution in chemical dynamics. Nat. Rev. Chem. 2, 82–94 (2018).
Zong, A., Nebgen, B. R., Lin, S.-C., Spies, J. A. & Zuerch, M. Emerging ultrafast techniques for studying quantum materials. Nat. Rev. Mater. https://doi.org/10.1038/s41578-022-00530-0 (2023).
Rohringer, N. X-ray Raman scattering: a building block for nonlinear spectroscopy. Philos. Trans. R. Soc. Math. Phys. Eng. Sci. 377, 20170471 (2019).
Leone, S. R. & Neumark, D. M. Probing matter with nonlinear spectroscopy. Science 379, 536–537 (2023).
Khan, S. Free-electron lasers. J. Mod. Opt. 55, 3469–3512 (2008).
Schoenlein, R. et al. Recent advances in ultrafast X-ray sources. Philos. Trans. R. Soc. Math. Phys. Eng. Sci. 377, 20180384 (2019).
Biegert, J., Calegari, F., Dudovich, N., Quéré, F. & Vrakking, M. Attosecond technology(ies) and science. J. Phys. B Mol. Opt. Phys. 54, 070201 (2021).
Huang, N., Deng, H., Liu, B., Wang, D. & Zhao, Z. Features and futures of X-ray free-electron lasers. Innovation 2, 100097 (2021).
Pellegrini, C., Marinelli, A. & Reiche, S. The physics of X-ray free-electron lasers. Rev. Mod. Phys. 88, 015006 (2016).
Margaritondo, G. & Rafelski, J. The relativistic foundations of synchrotron radiation. J. Synchrotron Radiat. 24, 898–901 (2017).
Kondratenko, A. M. & Saldin, E. L. Generation of coherent radiation by a relativistic electron beam in an ondulator. Part. Accel. 10, 207–216 (1980).
Allaria, E. et al. Highly coherent and stable pulses from the FERMI seeded free-electron laser in the extreme ultraviolet. Nat. Photon. 6, 699–704 (2012).
Abela, R. et al. Perspective: opportunities for ultrafast science at SwissFEL. Struct. Dyn. 4, 061602 (2017).
Altarelli, M., Brinkmann, R. & Chergui, M. The European X-ray Free-electron Laser (DESY, 2007).
Tschentscher, T. et al. Photon beam transport and scientific instruments at the European XFEL. Appl. Sci. 7, 592 (2017).
Kang, H.-S. et al. Hard X-ray free-electron laser with femtosecond-scale timing jitter. Nat. Photon. 11, 708–713 (2017).
Yu, L.-H. et al. High-gain harmonic-generation free-electron laser. Science 289, 932–934 (2000).
Allaria, E. et al. Two-stage seeded soft-X-ray free-electron laser. Nat. Photon. 7, 913–918 (2013).
Rebernik Ribič, P. et al. Coherent soft X-ray pulses from an echo-enabled harmonic generation free-electron laser. Nat. Photon. 13, 555–561 (2019).
Gianessi, L. & Masciovecchio, C. (eds) FERMI 2.0 Conceptual Design Report (Elettra Sincrotrone Trieste, 2022); https://www.elettra.eu/images/Documents/FERMI%20Machine/Machine/CDR/FERMI2.0CDR.pdf
McPherson, A. et al. Studies of multiphoton production of vacuum-ultraviolet radiation in the rare gases. J. Opt. Soc. Am. B 4, 595–601 (1987).
Ferray, M. et al. Multiple-harmonic conversion of 1064 nm radiation in rare gases. J. Phys. B Mol. Opt. Phys. 21, L31–L35 (1988).
Corkum, P. B. & Krausz, F. Attosecond science. Nat. Phys. 3, 381–387 (2007).
DiChiara, A. D. et al. Scaling of high-order harmonic generation in the long wavelength limit of a strong laser field. IEEE J. Sel. Top. Quantum Electron. 18, 419–433 (2012).
Cousin, S. L. et al. High-flux table-top soft X-ray source driven by sub-2-cycle, CEP stable, 1.85-µm 1-kHz pulses for carbon K-edge spectroscopy. Opt. Lett. 39, 5383–5386 (2014).
Kleine, C. et al. Soft X-ray absorption spectroscopy of aqueous solutions using a table-top femtosecond soft X-ray source. J. Phys. Chem. Lett. 10, 52–58 (2019).
Chang, Z. Enhancing keV high harmonic signals generated by long-wave infrared lasers. OSA Contin. 2, 2131–2136 (2019).
Kroh, T. et al. Enhanced high-harmonic generation up to the soft X-ray region driven by mid-infrared pulses mixed with their third harmonic. Opt. Express 26, 16955–16969 (2018).
Makos, I. et al. Α 10-gigawatt attosecond source for non-linear XUV optics and XUV-pump-XUV-probe studies. Sci. Rep. 10, 3759 (2020).
Pupeza, I. et al. Compact high-repetition-rate source of coherent 100 eV radiation. Nat. Photon. 7, 608–612 (2013).
Hädrich, S. et al. Exploring new avenues in high repetition rate table-top coherent extreme ultraviolet sources. Light Sci. Appl. 4, e320–e320 (2015).
Rossi, G. M. et al. Sub-cycle millijoule-level parametric waveform synthesizer for attosecond science. Nat. Photon. 14, 629–635 (2020).
Geneaux, R., Marroux, H. J. B., Guggenmos, A., Neumark, D. M. & Leone, S. R. Transient absorption spectroscopy using high harmonic generation: a review of ultrafast X-ray dynamics in molecules and solids. Philos. Trans. R Soc. Math. Phys. Eng. Sci. 377, 20170463 (2019).
Park, J., Subramani, A., Kim, S. & Ciappina, M. F. Recent trends in high-order harmonic generation in solids. Adv. Phys. X 7, 2003244 (2022).
Luu, T. T. et al. Extreme–ultraviolet high-harmonic generation in liquids. Nat. Commun. 9, 3723 (2018).
Zeng, A.-W. & Bian, X.-B. Impact of statistical fluctuations on high harmonic generation in liquids. Phys. Rev. Lett. 124, 203901 (2020).
Agostini, P. & DiMauro, L. F. The physics of attosecond light pulses. Rep. Prog. Phys. 67, 813–855 (2004).
Gallmann, L., Cirelli, C. & Keller, U. Attosecond science: recent highlights and future trends. Annu. Rev. Phys. Chem. 63, 447–469 (2012).
Krausz, F. & Ivanov, M. Attosecond physics. Rev. Mod. Phys. 81, 163 (2009).
Frank, F. et al. Invited review article: technology for attosecond science. Rev. Sci. Instrum. 83, 071101 (2012).
Boutu, W., Ducousso, M., Hergott, J.-F. & Merdji, H. Overview on HHG high-flux sources. in Optical Technologies for Extreme-Ultraviolet and Soft X-ray Coherent Sources (eds Canova, F. & Poletto, L.) 63–78 (Springer, 2015).
Franz, D. et al. All semiconductor enhanced high-harmonic generation from a single nanostructured cone. Sci. Rep. 9, 5663 (2019).
Jürgens, P. et al. Origin of strong-field-induced low-order harmonic generation in amorphous quartz. Nat. Phys. 16, 1035–1039 (2020).
Gholam-Mirzaei, S., Beetar, J. E., Chacón, A. & Chini, M. High-harmonic generation in ZnO driven by self-compressed mid-infrared pulses. J. Opt. Soc. Am. B 35, A27–A31 (2018).
Pertot, Y. et al. Time-resolved X-ray absorption spectroscopy with a water window high-harmonic source. Science 355, 264–267 (2017).
Zinchenko, K. S. et al. Sub-7-femtosecond conical-intersection dynamics probed at the carbon K-edge. Science 371, 489–494 (2021).
Gallmann, L. et al. Photoemission and photoionization time delays and rates. Struct. Dyn. 4, 061502 (2017).
Faccialà, D. et al. Time-resolved chiral X-ray photoelectron spectroscopy with transiently enhanced atomic site-selectivity: a free electron laser investigation of electronically excited fenchone enantiomers. Phys. Rev. X 13, 011044 (2022).
Wörner, H. J., Bertrand, J. B., Kartashov, D. V., Corkum, P. B. & Villeneuve, D. M. Following a chemical reaction using high-harmonic interferometry. Nature 466, 604–607 (2010).
Abel, B., Buck, U., Sobolewski, A. L. & Domcke, W. On the nature and signatures of the solvated electron in water. Phys. Chem. Chem. Phys. 14, 22–34 (2012).
Hummert, J. et al. Femtosecond extreme ultraviolet photoelectron spectroscopy of organic molecules in aqueous solution. J. Phys. Chem. Lett. 9, 6649–6655 (2018).
Longetti, L. et al. Ultrafast photoelectron spectroscopy of photoexcited aqueous ferrioxalate. Phys. Chem. Chem. Phys. 23, 25308–25316 (2021).
Arrell, C. A. et al. Laser-assisted photoelectric effect from liquids. Phys. Rev. Lett. 117, 143001 (2016).
Crepaldi, A. et al. Time-resolved ARPES at LACUS: band structure and ultrafast electron dynamics of solids. CHIMIA 71, 273–277 (2017).
Gatti, G. et al. Light-induced renormalization of the Dirac quasiparticles in the nodal-line semimetal ZrSiSe. Phys. Rev. Lett. 125, 076401 (2020).
Fidler, A. P. et al. Nonlinear XUV signal generation probed by transient grating spectroscopy with attosecond pulses. Nat. Commun. 10, 1384 (2019).
Grilj, J. et al. Self referencing heterodyne transient grating spectroscopy with short wavelength. Photonics 2, 392–401 (2015).
Cao, W., Warrick, E. R., Fidler, A., Neumark, D. M. & Leone, S. R. Noncollinear wave mixing of attosecond XUV and few-cycle optical laser pulses in gas-phase atoms: toward multidimensional spectroscopy involving XUV excitations. Phys. Rev. A 94, 053846 (2016).
Mairesse, Y. et al. High-order harmonic transient grating spectroscopy in a molecular jet. Phys. Rev. Lett. 100, 143903 (2008).
Ruf, H. et al. High-harmonic transient grating spectroscopy of NO2 electronic relaxation. J. Chem. Phys. 137, 224303 (2012).
Orfanos, I. et al. Non-linear processes in the extreme ultraviolet. J. Phys. Photon. 2, 042003 (2020).
Senfftleben, B. et al. Highly non-linear ionization of atoms induced by intense high-harmonic pulses. J. Phys. Photon. 2, 034001 (2020).
Drescher, L. et al. Extreme-ultraviolet spectral compression by four-wave mixing. Nat. Photon. 15, 263–266 (2021).
Helk, T. et al. Table-top extreme ultraviolet second harmonic generation. Sci. Adv. 7, eabe2265 (2021).
Shen, Y. R. Principles of Nonlinear Optics (U.S. Department of Energy, 1984).
Boyd, R. W. Nonlinear Optics (Academic Press, 2020).
Corn, R. M. & Higgins, D. A. Optical second harmonic generation as a probe of surface chemistry. Chem. Rev. 94, 107–125 (1994).
Shi, X., Borguet, E., Tarnovsky, A. N. & Eisenthal, K. B. Ultrafast dynamics and structure at aqueous interfaces by second harmonic generation. Chem. Phys. 205, 167–178 (1996).
Wang, H., Borguet, E. & Eisenthal, K. B. Polarity of liquid interfaces by second harmonic generation spectroscopy. J. Phys. Chem. A 101, 713–718 (1997).
Eisenthal, K. B. Liquid interfaces probed by second-harmonic and sum-frequency spectroscopy. Chem. Rev. 96, 1343–1360 (1996).
Almogy, G. & Yariv, A. Resonantly-enhanced nonlinear optics of intersubband transitions. J. Nonlinear Opt. Phys. Mater. 4, 401–458 (1995).
Oudar, J.-L. & Shen, Y. R. Nonlinear spectroscopy by multiresonant four-wave mixing. Phys. Rev. A 22, 1141–1158 (1980).
Begley, R. F., Harvey, A. B. & Byer, R. L. Coherent anti‐stokes Raman spectroscopy. Appl. Phys. Lett. 25, 387–390 (1974).
Giordmaine, J. A. Mixing of light beams in crystals. Phys. Rev. Lett. 8, 19–20 (1962).
Jones, W. J. & Stoicheff, B. P. Inverse Raman spectra: induced absorption at optical frequencies. Phys. Rev. Lett. 13, 657–659 (1964).
Maker, P. D. & Terhune, R. W. Study of optical effects due to an induced polarization third order in the electric field strength. Phys. Rev. 137, A801–A818 (1965).
Duncan, M. D., Reintjes, J. & Manuccia, T. J. Scanning coherent anti-Stokes Raman microscope. Opt. Lett. 7, 350–352 (1982).
Hofmann, F., Short, M. P. & Dennett, C. A. Transient grating spectroscopy: an ultrarapid, nondestructive materials evaluation technique. MRS Bull. 44, 392–402 (2019).
Ernst, R. R., Bodenhausen, G. & Wokaun, A. Principles of Nuclear Magnetic Resonance in One and Two Dimensions Vol. 14 (Clarendon Press, 1987).
Mukamel, S., Tanimura, Y. & Hamm, P. Coherent multidimensional optical spectroscopy. Acc. Chem. Res. 42, 1207–1209 (2009).
Hamm, P. & Zanni, M. Concepts and Methods of 2D Infrared Spectroscopy (Cambridge Univ. Press, 2011).
Brixner, T., Stiopkin, I. V. & Fleming, G. R. Tunable two-dimensional femtosecond spectroscopy. Opt. Lett. 29, 884–886 (2004).
Brixner, T. et al. Two-dimensional spectroscopy of electronic couplings in photosynthesis. Nature 434, 625–628 (2005).
Haddad, A. A. et al. Set-up for broadband Fourier-transform multidimensional electronic spectroscopy. Opt. Lett. 40, 312–315 (2015).
Auböck, G., Consani, C., Mourik, F. & Chergui, M. Ultrabroadband femtosecond two-dimensional ultraviolet transient absorption. Opt. Lett. 37, 2337–2339 (2012).
Consani, C., Aubock, G., van Mourik, F. & Chergui, M. Ultrafast tryptophan-to-haem electron transfer in myoglobins revealed by UV 2D spectroscopy. Science 339, 1586–1589 (2013).
Borrego-Varillas, R. et al. Two-dimensional electronic spectroscopy in the ultraviolet by a birefringent delay line. Opt. Express 24, 28491–28499 (2016).
Freund, I. & Levine, B. F. Parametric conversion of X rays. Phys. Rev. Lett. 23, 854–857 (1969).
Eisenberger, P. & McCall, S. L. X-ray parametric conversion. Phys. Rev. Lett. 26, 684–688 (1971).
Eisenberger, P. M. & McCall, S. L. Mixing of X-ray and optical photons. Phys. Rev. A 3, 1145–1151 (1971).
Woo, J. W. F. & Jha, S. S. Inelastic scattering of X rays from optically induced charge-density oscillations. Phys. Rev. B 6, 4081–4082 (1972).
Freund, I. Nonlinear X-ray spectroscopy. Opt. Commun. 6, 421–423 (1972).
Freund, I. & Levine, B. F. Surface effects in the nonlinear interaction of X-ray and optical fields. Phys. Rev. B 8, 3059–3060 (1973).
Flytzanis, C. Determination of local field in dielectric. C. R. Acad. Sci. Serie B 278, 339–342 (1975).
Danino, H. & Freund, I. Parametric down conversion of X rays into the extreme ultraviolet. Phys. Rev. Lett. 46, 1127–1130 (1981).
Tanaka, S., Chernyak, V. & Mukamel, S. Time-resolved X-ray spectroscopies: nonlinear response functions and Liouville-space pathways. Phys. Rev. A 63, 063405 (2001).
Tanaka, S. & Mukamel, S. Coherent X-ray Raman spectroscopy: a nonlinear local probe for electronic excitations. Phys. Rev. Lett. 89, 043001 (2002).
Tanaka, S. & Mukamel, S. X-ray four-wave mixing in molecules. J. Chem. Phys. 116, 1877–1891 (2002).
Doumy, G. et al. Nonlinear atomic response to intense ultrashort X rays. Phys. Rev. Lett. 106, 083002 (2011).
Serrat, C. Localized core four-wave mixing buildup in the X-ray spectrum of chemical species. J. Phys. Chem. Lett. 12, 1093–1097 (2021).
Serrat, C. Resonantly enhanced difference-frequency generation in the core X-ray absorption of molecules. J. Phys. Chem. A 125, 10706–10710 (2021).
Haber, J. et al. Nonlinear resonant X-ray Raman scattering. Preprint at https://doi.org/10.48550/arXiv.2006.14724 (2020).
Popova-Gorelova, D., Reis, D. A. & Santra, R. Theory of X-ray scattering from laser-driven electronic systems. Phys. Rev. B 98, 224302 (2018).
Misoguti, L., Christov, I. P., Backus, S., Murnane, M. M. & Kapteyn, H. C. Nonlinear wave-mixing processes in the extreme ultraviolet. Phys. Rev. A 72, 063803 (2005).
Maznev, A. A., Nelson, K. A. & Rogers, J. A. Optical heterodyne detection of laser-induced gratings. Opt. Lett. 23, 1319–1321 (1998).
Katayama, K., Yamaguchi, M. & Sawada, T. Lens-free heterodyne detection for transient grating experiments. Appl. Phys. Lett. 82, 2775–2777 (2003).
Sorokin, A. A. et al. Photoelectric effect at ultrahigh intensities. Phys. Rev. Lett. 99, 213002 (2007).
Kanter, E. P. et al. Unveiling and driving hidden resonances with high-fluence, high-intensity X-ray pulses. Phys. Rev. Lett. 107, 233001 (2011).
Lambropoulos, P. & Tang, X. Multiple excitation and ionization of atoms by strong lasers. J. Opt. Soc. Am. B 4, 821–832 (1987).
Novikov, S. A. & Hopersky, A. N. Two-photon excitation-ionization of the 1s shell of highly charged positive atomic ions. J. Phys. B Mol. Opt. Phys. 34, 4857–4863 (2001).
Sytcheva, A., Pabst, S., Son, S.-K. & Santra, R. Enhanced nonlinear response of Ne8+ to intense ultrafast X rays. Phys. Rev. A 85, 023414 (2012).
Tamasaku, K. et al. X-ray two-photon absorption competing against single and sequential multiphoton processes. Nat. Photon. 8, 313–316 (2014).
Ghimire, S. et al. Nonsequential two-photon absorption from the K shell in solid zirconium. Phys. Rev. A 94, 043418 (2016).
Tamasaku, K. et al. Nonlinear spectroscopy with X-ray two-photon absorption in metallic copper. Phys. Rev. Lett. 121, 083901 (2018).
Powers, P. E. & Haus, J. W. Fundamentals of Nonlinear Optics (CRC Press, 2017).
Paschotta, R. & Keller, U. Passive mode locking with slow saturable absorbers. Appl. Phys. B 73, 653–662 (2001).
Wang, G. et al. Broadband saturable absorption and exciton–exciton annihilation in MoSe2 composite thin films. Opt. Mater. Express 9, 483–496 (2019).
Kumar, S. et al. Femtosecond carrier dynamics and saturable absorption in graphene suspensions. Appl. Phys. Lett. 95, 191911 (2009).
Bob, Nagler et al. Turning solid aluminium transparent by intense soft X-ray photoionization. Nat. Phys. 5, 693–696 (2009).
Yoneda, H. et al. Ultra-fast switching of light by absorption saturation in vacuum ultra-violet region. Opt. Express 17, 23443–23448 (2009).
Yoneda, H. et al. Saturable absorption of intense hard X-rays in iron. Nat. Commun. 5, 5080 (2014).
Hoffmann, L. et al. Saturable absorption of free-electron laser radiation by graphite near the carbon K-edge. J. Phys. Chem. Lett. 13, 8963–8970 (2022).
Rohringer, N. et al. Atomic inner-shell X-ray laser at 1.46 nanometres pumped by an X-ray free-electron laser. Nature 481, 488–491 (2012).
Beye, M. et al. Stimulated X-ray emission for materials science. Nature 501, 191–194 (2013).
Jonnard, P. et al. EUV stimulated emission from MgO pumped by FEL pulses. Struct. Dyn. 4, 054306 (2017).
Yoneda, H. et al. Atomic inner-shell laser at 1.5-ångström wavelength pumped by an X-ray free-electron laser. Nature 524, 446–449 (2015).
Glatzel, P. & Bergmann, U. High resolution 1s core hole X-ray spectroscopy in 3d transition metal complexes — electronic and structural information. Coord. Chem. Rev. 249, 65–95 (2005).
Zhang, W. et al. Tracking excited-state charge and spin dynamics in iron coordination complexes. Nature 509, 345–348 (2014).
Kinschel, D. et al. Femtosecond X-ray emission study of the spin cross-over dynamics in haem proteins. Nat. Commun. 11, 4145 (2020).
Bacellar, C. et al. Spin cascade and doming in ferric hemes: femtosecond X-ray absorption and X-ray emission studies. Proc. Natl Acad. Sci. USA 117, 21914–21920 (2020).
March, A. M. et al. Probing transient valence orbital changes with picosecond valence-to-core X-ray emission spectroscopy. J. Phys. Chem. C 121, 2620–2626 (2017).
Ledbetter, K. et al. Excited state charge distribution and bond expansion of ferrous complexes observed with femtosecond valence-to-core X-ray emission spectroscopy. J. Chem. Phys. 152, 074203 (2020).
Kroll, T. et al. Stimulated X-ray emission spectroscopy in transition metal complexes. Phys. Rev. Lett. 120, 133203 (2018).
Kroll, T. et al. Observation of seeded Mn Kβ stimulated X-ray emission using two-color X-ray free-electron laser pulses. Phys. Rev. Lett. 125, 037404 (2020).
Duris, J. et al. Tunable isolated attosecond X-ray pulses with gigawatt peak power from a free-electron laser. Nat. Photon. 14, 30–36 (2020).
McCamant, D. W., Kukura, P. & Mathies, R. A. Femtosecond stimulated Raman study of excited-state evolution in bacteriorhodopsin. J. Phys. Chem. B 109, 10449–10457 (2005).
Kukura, P., McCamant, D. W. & Mathies, R. A. Femtosecond stimulated Raman spectroscopy. Annu. Rev. Phys. Chem. 58, 461–488 (2007).
Hahn, A. W. et al. Probing the valence electronic structure of low-spin ferrous and ferric complexes using 2p3d resonant inelastic X-ray scattering (RIXS). Inorg. Chem. 57, 9515–9530 (2018).
Van Kuiken, B. E. et al. Electronic spectra of iron–sulfur complexes measured by 2p3d RIXS spectroscopy. Inorg. Chem. 57, 7355–7361 (2018).
Ågren, H., Luo, Y., Gelmukhanov, F. & Jensen, H. J. A. Screening in resonant X-ray emission of molecules. J. Electron Spectrosc. Relat. Phenom. 82, 125–134 (1996).
Cho, D., Rouxel, J. R., Mukamel, S., Kin-Lic Chan, G. & Li, Z. Stimulated X-ray Raman and absorption spectroscopy of iron–sulfur dimers. J. Phys. Chem. Lett. 10, 6664–6671 (2019).
Schweigert, I. V. & Mukamel, S. Probing valence electronic wave-packet dynamics by all X-ray stimulated Raman spectroscopy: a simulation study. Phys. Rev. A 76, 012504 (2007).
Harbola, U. & Mukamel, S. Coherent stimulated X-ray Raman spectroscopy: attosecond extension of resonant inelastic X-ray Raman scattering. Phys. Rev. B 79, 085108 (2009).
Hua, W. et al. Monitoring conical intersections in the ring opening of furan by attosecond stimulated X-ray Raman spectroscopy. Struct. Dyn. 3, 023601 (2016).
Weninger, C. Stimulated electronic X-ray Raman scattering. Phys. Rev. Lett. 111, 233902 (2013).
Weninger, C. & Rohringer, N. Stimulated resonant X-ray Raman scattering with incoherent radiation. Phys. Rev. A 88, 053421 (2013).
Kimberg, V. & Rohringer, N. Stochastic stimulated electronic X-ray Raman spectroscopy. Struct. Dyn. 3, 034101 (2016).
O’Neal, J. T. et al. Electronic population transfer via impulsive stimulated X-ray Raman scattering with attosecond soft-X-ray pulses. Phys. Rev. Lett. 125, 073203 (2020).
Higley, D. J. et al. Stimulated resonant inelastic X-ray scattering in a solid. Commun. Phys. 5, 1–12 (2022).
Arya, K. & Jha, S. S. Microscopic optical fields and mixing coefficients of X-ray and optical frequencies in solids. Pramana 2, 116–125 (1974).
Pine, A. S. Self-consistent-field theory of linear and nonlinear crystalline dielectrics including local-field effects. Phys. Rev. 139, A901–A911 (1965).
Schweigert, I. V. & Mukamel, S. Coherent ultrafast core-hole correlation spectroscopy: X-ray analogues of multidimensional NMR. Phys. Rev. Lett. 99, 163001 (2007).
Nazarkin, A., Podorov, S., Uschmann, I., Förster, E. & Sauerbrey, R. Nonlinear optics in the angstrom regime: hard-X-ray frequency doubling in perfect crystals. Phys. Rev. A 67, 041804 (2003).
Glover, T. E. et al. X-ray and optical wave mixing. Nature 488, 603–608 (2012).
Tamasaku, K. & Ishikawa, T. Interference between Compton scattering and X-ray parametric down-conversion. Phys. Rev. Lett. 98, 244801 (2007).
Tamasaku, K., Sawada, K. & Ishikawa, T. Determining X-ray nonlinear susceptibility of diamond by the optical Fano effect. Phys. Rev. Lett. 103, 254801 (2009).
Tamasaku, K., Sawada, K., Nishibori, E. & Ishikawa, T. Visualizing the local optical response to extreme-ultraviolet radiation with a resolution of λ/380. Nat. Phys. 7, 705–708 (2011).
Schori, A. et al. Parametric down-conversion of X rays into the optical regime. Phys. Rev. Lett. 119, 253902 (2017).
Shwartz, S. et al. X-ray second harmonic generation. Phys. Rev. Lett. 112, 163901 (2014).
Lam, R. K. et al. Soft X-ray second harmonic generation as an interfacial probe. Phys. Rev. Lett. 120, 023901 (2018).
Yamamoto, S. et al. Element selectivity in second-harmonic generation of GaFeO3 by a soft-X-ray free-electron laser. Phys. Rev. Lett. 120, 223902 (2018).
Berger, E. et al. Extreme ultraviolet second harmonic generation spectroscopy in a polar metal. Nano Lett. 21, 6095–6101 (2021).
Schwartz, C. P. et al. Angstrom-resolved interfacial structure in buried organic–inorganic junctions. Phys. Rev. Lett. 127, 096801 (2021).
Sistrunk, E. et al. Extreme ultraviolet transient grating measurement of insulator–metal transition dynamics of VO2. In 19th International Conference on Ultrafast Phenomena (OSA, 2014); https://doi.org/10.1364/UP.2014.09.Wed.P3.44.
Gaynor, J. D. et al. Solid state core-exciton dynamics in NaCl observed by tabletop attosecond four-wave mixing spectroscopy. Phys. Rev. B 103, 245140 (2021).
Rottke, H. et al. Probing electron and hole colocalization by resonant four-wave mixing spectroscopy in the extreme ultraviolet. Sci. Adv. 8, eabn5127 (2022).
Sander, M. et al. Spatiotemporal coherent control of thermal excitations in solids. Phys. Rev. Lett. 119, 075901 (2017).
Pudell, J.-E. et al. Full spatiotemporal control of laser-excited periodic surface deformations. Phys. Rev. Appl. 12, 024036 (2019).
Frazer, T. D. et al. Optical transient grating pumped X-ray diffraction microscopy for studying mesoscale structural dynamics. Sci. Rep. 11, 19322 (2021).
Bencivenga, F. et al. Four-wave mixing experiments with extreme ultraviolet transient gratings. Nature 520, 205–208 (2015).
Foglia, L. et al. First evidence of purely extreme-ultraviolet four-wave mixing. Phys. Rev. Lett. 120, 263901 (2018).
Bencivenga, F. et al. Nanoscale transient gratings excited and probed by extreme ultraviolet femtosecond pulses. Sci. Adv. 5, eaaw5805 (2019).
Maznev, A. A. et al. Generation of coherent phonons by coherent extreme ultraviolet radiation in a transient grating experiment. Appl. Phys. Lett. 113, 221905 (2018).
Maznev, A. A. et al. Generation and detection of 50 GHz surface acoustic waves by extreme ultraviolet pulses. Appl. Phys. Lett. 119, 044102 (2021).
Bohinc, R. et al. Nonlinear XUV-optical transient grating spectroscopy at the Si L2,3-edge. Appl. Phys. Lett. 114, 181101 (2019).
Naumenko, D. et al. Thermoelasticity of nanoscale silicon carbide membranes excited by extreme ultraviolet transient gratings: implications for mechanical and thermal management. ACS Appl. Nano Mater. 2, 5132–5139 (2019).
Ksenzov, D. et al. Nanoscale transient magnetization gratings created and probed by femtosecond extreme ultraviolet pulses. Nano Lett. 21, 2905–2911 (2021).
Yao, K. et al. All-optical switching on the nanometer scale excited and probed with femtosecond extreme ultraviolet pulses. Nano Lett. 22, 4452–4458 (2022).
Rouxel, J. R. et al. Hard X-ray transient grating spectroscopy on bismuth germanate. Nat. Photon. 15, 499–503 (2021).
Svetina, C. et al. Towards X-ray transient grating spectroscopy. Opt. Lett. 44, 574–577 (2019).
Chen, Z., Gao, Y., Minch, B. C. & DeCamp, M. F. Coherent optical phonon generation in Bi 3 Ge 4 O 12. J. Phys. Condens. Matter 23, 385402 (2011).
Peters, W. et al. Hard X-ray–optical transient grating. In 2021 Conference on Lasers and Electro-Optics (CLEO) 1–2 (CLEO, 2021).
Shi, H. & Zhu, D. Multi-axis nanopositioning system for the hard X-ray split-delay system at the LCLS. Synchrotron Radiat. News 31, 15–20 (2018).
Ukleev, V. et al. Effect of intense X-ray free-electron laser transient gratings on the magnetic domain structure of Tm:YIG. J. Appl. Phys. 133, 123902 (2023).
Keefer, D. et al. Ultrafast X-ray probes of elementary molecular events. Ann. Rev. Phys. Chem. 74, 73–97 (2023).
Roemelt, M., Maganas, D., DeBeer, S. & Neese, F. A combined DFT and restricted open-shell configuration interaction method including spin–orbit coupling: application to transition metal L-edge X-ray absorption spectroscopy. J. Chem. Phys. 138, 204101 (2013).
Norman, P. & Dreuw, A. Simulating X-ray spectroscopies and calculating core-excited states of molecules. Chem. Rev. 118, 7208–7248 (2018).
Vidal, M. L., Feng, X., Epifanovsky, E., Krylov, A. I. & Coriani, S. New and efficient equation-of-motion coupled-cluster framework for core-excited and core-ionized states. J. Chem. Theory Comput. 15, 3117–3133 (2019).
Montorsi, F., Segatta, F., Nenov, A., Mukamel, S. & Garavelli, M. Soft X-ray spectroscopy simulations with multiconfigurational wave function theory: spectrum completeness, sub-eV accuracy, and quantitative reproduction of line shapes. J. Chem. Theory Comput. 18, 1003–1016 (2022).
Tully, J. C. Molecular dynamics with electronic transitions. J. Chem. Phys. 93, 1061–1071 (1990).
Meyer, H.-D., Manthe, U. & Cederbaum, L. S. The multi-configurational time-dependent Hartree approach. Chem. Phys. Lett. 165, 73–78 (1990).
Ben-Nun, M. & Martinez, T. J. Ab initio quantum molecular dynamics. Adv. Chem. Phys. 121, 439–512 (2002).
Makhov, D. V., Glover, W. J., Martinez, T. J. & Shalashilin, D. V. Ab initio multiple cloning algorithm for quantum nonadiabatic molecular dynamics. J. Chem. Phys. 141, 054110 (2014).
Richter, M., Marquetand, P., González-Vázquez, J., Sola, I. & González, L. SHARC: ab initio molecular dynamics with surface hopping in the adiabatic representation including arbitrary couplings. J. Chem. Theory Comput. 7, 1253–1258 (2011).
Reiter, S., Keefer, D. & de Vivie-Riedle, R. Exact quantum dynamics (wave packets) in reduced dimensionality. in Quantum Chemistry and Dynamics of Excited States 355–381 (John Wiley & Sons, Ltd, 2020).
Helmich-Paris, B. Simulating X-ray absorption spectra with complete active space self-consistent field linear response methods. Int. J. Quantum Chem. 121, e26559 (2021).
Casanova, D. Restricted active space configuration interaction methods for strong correlation: Recent developments. WIREs Comput Mol Sci. 12, e1561 (2022).
Autschbach, J., Ziegler, T., van Gisbergen, S. J. A. & Baerends, E. J. Chiroptical properties from time-dependent density functional theory. I. Circular dichroism spectra of organic molecules. J. Chem. Phys. 116, 6930–6940 (2002).
Lopata, K., Van Kuiken, B. E., Khalil, M. & Govind, N. Linear-response and real-time time-dependent density functional theory studies of core-level near-edge X-ray absorption. J. Chem. Theory Comput. 8, 3284–3292 (2012).
Andersen, J. H., Nanda, K. D., Krylov, A. I. & Coriani, S. Probing molecular chirality of ground and electronically excited states in the UV–vis and X-ray regimes: an EOM-CCSD study. J. Chem. Theory Comput. 18, 1748–1764 (2022).
Nanda, K. D. & Krylov, A. I. Cherry-picking resolvents: a general strategy for convergent coupled-cluster damped response calculations of core-level spectra. J. Chem. Phys. 153, 141104 (2020).
Freund, I. Nonlinear X-ray diffraction. Determination of valence electron charge distributions. Chem. Phys. Lett. 12, 583–588 (1972).
Shwartz, E. & Shwartz, S. Difference-frequency generation of optical radiation from two-color X-ray pulses. Opt. Express 23, 7471–7480 (2015).
Rohringer, N. & Santra, R. X-ray nonlinear optical processes using a self-amplified spontaneous emission free-electron laser. Phys. Rev. A 76, 033416 (2007).
Santra, R., Kryzhevoi, N. V. & Cederbaum, L. S. X-ray two-photon photoelectron spectroscopy: a theoretical study of inner-shell spectra of the organic para-aminophenol molecule. Phys. Rev. Lett. 103, 013002 (2009).
Motomura, K. et al. Sequential multiphoton multiple ionization of atomic argon and xenon irradiated by X-ray free-electron laser pulses from SACLA. J. Phys. B Mol. Opt. Phys. 46, 164024 (2013).
Mazza, T. et al. Sensitivity of nonlinear photoionization to resonance substructure in collective excitation. Nat. Commun. 6, 6799 (2015).
Popova-Gorelova, D., Guskov, V. & Santra, R. Microscopic electron dynamics in nonlinear optical response of solids. Preprint at https://doi.org/10.48550/arXiv.2009.07527 (2020).
Popova-Gorelova, D. & Santra, R. Atomic-scale imaging of laser-driven electron dynamics in solids using subcycle-resolved X-ray-optical wave mixing. Preprint at https://doi.org/10.48550/arXiv.2012.10334 (2020).
Keefer, D. et al. Monitoring molecular vibronic coherences in a bichromophoric molecule by ultrafast X-ray spectroscopy. Chem. Sci. 12, 5286–5294 (2021).
Bennett, K., Kowalewski, M., Rouxel, J. R. & Mukamel, S. Monitoring molecular nonadiabatic dynamics with femtosecond X-ray diffraction. Proc. Natl Acad. Sci. USA 115, 6538–6547 (2018).
Shakya, Y., Inhester, L., Arnold, C., Welsch, R. & Santra, R. Ultrafast time-resolved X-ray absorption spectroscopy of ionized urea and its dimer through ab initio nonadiabatic dynamics. Struct. Dyn. 8, 034102 (2021).
List, N. H., Dempwolff, A. L., Dreuw, A., Norman, P. & Martínez, T. J. Probing competing relaxation pathways in malonaldehyde with transient X-ray absorption spectroscopy. Chem. Sci. 11, 4180–4193 (2020).
Keefer, D., Schnappinger, T., de Vivie-Riedle, R. & Mukamel, S. Visualizing conical intersection passages via vibronic coherence maps generated by stimulated ultrafast X-ray Raman signals. Proc. Natl Acad. Sci. USA 117, 24069–24075 (2020).
Nenov, A., Segatta, F., Bruner, A., Mukamel, S. & Garavelli, M. X-ray linear and non-linear spectroscopy of the ESCA molecule. J. Chem. Phys. 151, 114110 (2019).
Kowalewski, M. Catching conical intersections in the act: monitoring transient electronic coherences by attosecond stimulated X-ray Raman signals. Phys. Rev. Lett. 115, 193003 (2015).
Rouxel, J. R., Kowalewski, M., Bennett, K. & Mukamel, S. X-ray sum frequency diffraction for direct imaging of ultrafast electron dynamics. Phys. Rev. Lett. 120, 243902 (2018).
Neville, S. P., Chergui, M., Stolow, A. & Schuurman, M. S. Ultrafast X-ray spectroscopy of conical intersections. Phys. Rev. Lett. 120, 243001 (2018).
Keefer, D. et al. Imaging conical intersection dynamics during azobenzene photoisomerization by ultrafast X-ray diffraction. Proc. Natl Acad. Sci. USA 118, e2022037118 (2021).
Amann, J. et al. Demonstration of self-seeding in a hard-X-ray free-electron laser. Nat. Photon. 6, 693–698 (2012).
Cavaletto, S. M., Keefer, D. & Mukamel, S. High temporal and spectral resolution of stimulated X-ray Raman signals with stochastic free-electron-laser pulses. Phys. Rev. X 11, 011029 (2021).
Biggs, J. D., Zhang, Y., Healion, D. & Mukamel, S. Watching energy transfer in metalloporphyrin heterodimers using stimulated X-ray Raman spectroscopy. Proc. Natl Acad. Sci. USA 110, 15597–15601 (2013).
Kimberg, V. et al. Stimulated X-ray Raman scattering — a critical assessment of the building block of nonlinear X-ray spectroscopy. Faraday Discuss. 194, 305–324 (2016).
Gschwendtner, E. & Muggli, P. Plasma wakefield accelerators. Nat. Rev. Phys. 1, 246–248 (2019).
Wang, W. et al. Free-electron lasing at 27 nanometres based on a laser wakefield accelerator. Nature 595, 516–520 (2021).
Galletti, M. et al. Stable operation of a free-electron laser driven by a plasma accelerator. Phys. Rev. Lett. 129, 234801 (2022).
Labat, M. et al. Seeded free-electron laser driven by a compact laser plasma accelerator. Nat. Photon. 17, 150–156 (2023).
Trebino, R. Frequency-Resolved Optical Gating: The Measurement of Ultrashort Laser Pulses: The Measurement of Ultrashort Laser Pulses (Springer Science & Business Media, 2000).
Peters, W. K. et al. All-optical single-shot complete electric field measurement of extreme ultraviolet free electron laser pulses. Optica 8, 545–550 (2021).
Gauthier, D. et al. Spectrotemporal shaping of seeded free-electron laser pulses. Phys. Rev. Lett. 115, 114801 (2015).
Prince, K. C. et al. Coherent control with a short-wavelength free-electron laser. Nat. Photon. 10, 176–179 (2016).
Cavaletto, S. M. et al. Unveiling the spatial distribution of molecular coherences at conical intersections by covariance X-ray diffraction signals. Proc. Natl Acad. Sci. USA 118, e2105046118 (2021).
Ratner, D., Cryan, J. P., Lane, T. J., Li, S. & Stupakov, G. Pump–probe ghost imaging with SASE FELs. Phys. Rev. X 9, 011045 (2019).
Kayser, Y. et al. Core-level nonlinear spectroscopy triggered by stochastic X-ray pulses. Nat. Commun. 10, 4761 (2019).
Driver, T. et al. Attosecond transient absorption spectroscopy: a ghost imaging approach to ultrafast absorption spectroscopy. Phys. Chem. Chem. Phys. 22, 2704–2712 (2020).
Gorobtsov, O. Y. et al. Seeded X-ray free-electron laser generating radiation with laser statistical properties. Nat. Commun. 9, 4498 (2018).
Li, K. et al. Ghost-imaging-enhanced noninvasive spectral characterization of stochastic X-ray free-electron-laser pulses. Commun. Phys. 5, 1–8 (2022).
Kalz, K. F. et al. Future challenges in heterogeneous catalysis: understanding catalysts under dynamic reaction conditions. ChemCatChem 9, 17–29 (2017).
Yang, Y. et al. Operando methods in electrocatalysis. ACS Catal. 11, 1136–1178 (2021).
Singh, J., Lamberti, C. & van Bokhoven, J. A. Advanced X-ray absorption and emission spectroscopy: in situ catalytic studies. Chem. Soc. Rev. 39, 4754–4766 (2010).
Beye, M. et al. Non-linear soft X-ray methods on solids with MUSIX — the multi-dimensional spectroscopy and inelastic X-ray scattering endstation. J. Phys. Condens. Matter 31, 014003 (2019).
Chakraborti, P. et al. Higher-order X-ray — optical wave mixing. SPring-8/SACLA利用研究成果集 https://doi.org/10.18957/rr.10.4.409 (2022).
Alagna, L. et al. X-ray natural circular dichroism. Phys. Rev. Lett. 80, 4799–4802 (1998).
Peacock, R. D. & Stewart, B. Natural circular dichroism in X-ray spectroscopy. J. Phys. Chem. B 105, 351–360 (2001).
Turchini, S. et al. Core electron transitions as a probe for molecular chirality: natural circular dichroism at the carbon K-edge of methyloxirane. J. Am. Chem. Soc. 126, 4532–4533 (2004).
Tanaka, M., Nakagawa, K., Agui, A., Fujii, K. & Yokoya, A. First observation of natural circular dichroism for biomolecules in soft X-ray region studied with a polarizing undulator. Phys. Scr. 2005, 873 (2005).
Rouxel, J. R. et al. Hard X-ray helical dichroism of disordered molecular media. Nat. Photon. 16, 570–574 (2022).
Mincigrucci, R. et al. Element- and enantiomer-selective visualization of molecular motion in real-time. Nat. Commun. 14, 386 (2023).
Byers, J. D., Yee, H. I., Petralli-Mallow, T. & Hicks, J. M. Second-harmonic generation circular-dichroism spectroscopy from chiral monolayers. Phys. Rev. B 49, 14643–14647 (1994).
Petralli-Mallow, T., Wong, T. M., Byers, J. D., Yee, H. I. & Hicks, J. M. Circular dichroism spectroscopy at interfaces: a surface second harmonic generation study. J. Phys. Chem. 97, 1383–1388 (1993).
Kauranen, M., Verbiest, T., Maki, J. J. & Persoons, A. Second‐harmonic generation from chiral surfaces. J. Chem. Phys. 101, 8193–8199 (1994).
Verbiest, T., Kauranen, M., Van Rompaey, Y. & Persoons, A. Optical activity of anisotropic achiral surfaces. Phys. Rev. Lett. 77, 1456–1459 (1996).
Verbiest, T., Kauranen, M. & Persoons, A. Second-order nonlinear optical properties of chiral thin films. J. Mater. Chem. 9, 2005–2012 (1999).
Belkin, M. A., Han, S. H., Wei, X. & Shen, Y. R. Sum-frequency generation in chiral liquids near electronic resonance. Phys. Rev. Lett. 87, 113001 (2001).
Belkin, M. A., Shen, Y. R. & Flytzanis, C. Coupled-oscillator model for nonlinear optical activity. Chem. Phys. Lett. 363, 479–485 (2002).
Belkin, M. A. & Shen, Y. R. Non-linear optical spectroscopy as a novel probe for molecular chirality. Int. Rev. Phys. Chem. 24, 257–299 (2005).
Fischer, P., Beckwitt, K., Wise, F. W. & Albrecht, A. C. The chiral specificity of sum-frequency generation in solutions. Chem. Phys. Lett. 352, 463–468 (2002).
Lee, T., Rhee, H. & Cho, M. Femtosecond vibrational sum-frequency generation spectroscopy of chiral molecules in isotropic liquid. J. Phys. Chem. Lett. 9, 6723–6730 (2018).
Song, Z., Zhang, T., Fang, Z. & Fang, C. Quantitative mappings between symmetry and topology in solids. Nat. Commun. 9, 3530 (2018).
Gatti, G. et al. Radial spin texture of the Weyl fermions in chiral tellurium. Phys. Rev. Lett. 125, 216402 (2020).
Cochran, T. A. et al. Visualizing higher-fold topology in chiral crystals. Phys. Rev. Lett. 130, 066402 (2023).
Rouxel, J. R., Kowalewski, M. & Mukamel, S. Photoinduced molecular chirality probed by ultrafast resonant X-ray spectroscopy. Struct. Dyn. 4, 044006 (2017).
Rouxel, J. R., Zhang, Y. & Mukamel, S. X-ray Raman optical activity of chiral molecules. Chem. Sci. 10, 898–908 (2019).
Bencivenga, F. et al. Four-wave-mixing experiments with seeded free electron lasers. Faraday Discuss. 194, 283–303 (2016).
Rouxel, J. R. & Mukamel, S. Molecular chirality and its monitoring by ultrafast X-ray pulses. Chem. Rev. 122, 16802–16838 (2022).
Rouxel, J. R., Rajabi, A. & Mukamel, S. Chiral four-wave mixing signals with circularly polarized X-ray pulses. J. Chem. Theory Comput. 16, 5784–5791 (2020).
Schenkl, S. et al. Insights into excited-state and isomerization dynamics of bacteriorhodopsin from ultrafast transient UV absorption. Proc. Natl Acad. Sci. USA 103, 4101–4106 (2006).
Polli, D. et al. Conical intersection dynamics of the primary photoisomerization event in vision. Nature 467, 440–443 (2010).
Schreier, W. J., Gilch, P. & Zinth, W. Early events of DNA photodamage. Annu. Rev. Phys. Chem. 66, 497–519 (2015).
Ebadi, H. Tracking of azobenzene isomerization by X-ray emission spectroscopy. J. Phys. Chem. A 118, 7832–7837 (2014).
Hua, W., Mukamel, S. & Luo, Y. Transient X-ray absorption spectral fingerprints of the S1 dark state in uracil. J. Phys. Chem. Lett. 10, 7172–7178 (2019).
Nam, Y. et al. Time-resolved optical pump-resonant X-ray probe spectroscopy of 4-thiouracil: a simulation study. J. Chem. Theory Comput. 18, 3075–3088 (2022).
Segatta, F. et al. Exploring the capabilities of optical pump X-ray probe NEXAFS spectroscopy to track photo-induced dynamics mediated by conical intersections. Faraday Discuss. 221, 245–264 (2020).
Chang, K. F. et al. Revealing electronic state-switching at conical intersections in alkyl iodides by ultrafast XUV transient absorption spectroscopy. Nat. Commun. 11, 4042 (2020).
Timmers, H. et al. Disentangling conical intersection and coherent molecular dynamics in methyl bromide with attosecond transient absorption spectroscopy. Nat. Commun. 10, 3133 (2019).
Nam, Y. et al. Conical intersection passages of molecules probed by X-ray diffraction and stimulated Raman spectroscopy. J. Phys. Chem. Lett. 12, 12300–12309 (2021).
Freixas, V. M., Keefer, D., Tretiak, S., Fernandez-Alberti, S. & Mukamel, S. Ultrafast coherent photoexcited dynamics in a trimeric dendrimer probed by X-ray stimulated-Raman signals. Chem. Sci. 13, 6373–6384 (2022).
Polishchuk, S. et al. Nanoscale-resolved surface-to-bulk electron transport in CsPbBr3 perovskite. Nano Lett. 22, 1067–1074 (2022).
Consani, C., Bram, O., van Mourik, F., Cannizzo, A. & Chergui, M. Energy transfer and relaxation mechanisms in cytochrome c. Chem. Phys. 396, 108–115 (2012).
Chenu, A. & Scholes, G. D. Coherence in energy transfer and photosynthesis. Annu. Rev. Phys. Chem. 66, 69–96 (2015).
Bacellar, C. et al. Ultrafast energy transfer from photoexcited tryptophan to the haem in cytochrome c. J. Phys. Chem. Lett. 14, 2425–2432 (2023).
Zeiger, H. J. et al. Theory for displacive excitation of coherent phonons. Phys. Rev. B 45, 768–778 (1992).
Mukamel, S., Healion, D., Zhang, Y. & Biggs, J. D. Multidimensional attosecond resonant X-ray spectroscopy of molecules: lessons from the optical regime. Annu. Rev. Phys. Chem. 64, 101–127 (2013).
Al-Haddad, A. et al. Observation of site-selective chemical bond changes via ultrafast chemical shifts. Nat. Commun. 13, 7170 (2022).
El Nahhas, A. et al. X-ray absorption spectroscopy of ground and excited rhenium-carbonyl diimine-complexes: evidence for a two-center electron transfer. J. Phys. Chem. A 117, 361–369 (2013).
Bencivenga, F. & Masciovecchio, C. FEL-based transient grating spectroscopy to investigate nanoscale dynamics. Nucl. Instrum. Methods Phys. Res. Sect. Accel. Spectrometers Detect. Assoc. Equip. 606, 785–789 (2009).
Johnson, J. A. et al. Direct measurement of room-temperature nondiffusive thermal transport over micron distances in a silicon membrane. Phys. Rev. Lett. 110, 025901 (2013).
Acknowledgements
S.M. gratefully acknowledges the support of the Chemical Sciences, Geosciences and Biosciences Division, Office of Basic Energy Sciences, Office of Science, U.S. Department of Energy through Award No. DE-FG02-04ER15571 and of the National Science Foundation (Grant No. CHE-2246379). M.C. thanks the Swiss NSF NCCR:MUST and the ERC Advanced Grant DYNAMOX for support. All authors are deeply grateful to their former students and postdocs and to their collaborators for making this work possible.
Author information
Authors and Affiliations
Contributions
M.C. researched data for the article. All authors contributed substantially to discussion of the content. M.C. and S.M. wrote the article. All authors reviewed and/or edited the manuscript before submission.
Corresponding author
Ethics declarations
Competing interests
The authors declare no competing interests.
Peer review
Peer review information
Nature Reviews Physics thanks Nora Berrah and the other, anonymous, reviewer(s) for their contribution to the peer review of this work.
Additional information
Publisher’s note Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Rights and permissions
Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
About this article
Cite this article
Chergui, M., Beye, M., Mukamel, S. et al. Progress and prospects in nonlinear extreme-ultraviolet and X-ray optics and spectroscopy. Nat Rev Phys 5, 578–596 (2023). https://doi.org/10.1038/s42254-023-00643-7
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1038/s42254-023-00643-7
This article is cited by
-
Femtosecond stimulated Raman spectroscopy
Nature Reviews Methods Primers (2024)
-
Transient responses of double core-holes generation in all-attosecond pump-probe spectroscopy
Scientific Reports (2024)