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X-ray two-photon absorption competing against single and sequential multiphoton processes

Abstract

The success1,2 of X-ray free-electron lasers (XFELs) has extended the frontier of nonlinear optics into the hard X-ray region. Recently, sum-frequency generation3 has been reported, as well as parametric downconversion4,5,6. These are of the lowest (second) order, and higher-order processes remain unexplored. Here, we report the first observation of a third-order process: two-photon absorption of a 5.6 keV XFEL beam by germanium. We find that two-photon absorption competes with single and sequential multiphoton processes7,8, but we successfully determine the intrinsic cross-section by analysing the pulse-energy dependence. We also discuss the two-photon absorption cross-section by comparing a new mechanism unique to X-rays with the conventional mechanism and show that the latter is consistent with the present result. The experimental determination and understanding of the cross-section would allow two-photon absorption spectroscopy. Our result indicates that X-ray analogues of other third-order nonlinear optical processes9, such as nonlinear Raman and optical Kerr effects, are available for XFEL applications in spectroscopy, imaging and beam control.

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Figure 1: Schematics of experiment and fluorescence spectrum of germanium.
Figure 2: Pulse-energy dependence of germanium TPA fluorescence.
Figure 3: Simulated population dynamics for electronic configurations of interest.

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References

  1. Emma, P. et al. First lasing and operation of an Angstrom wavelength free-electron laser. Nature Photon. 4, 641–647 (2010).

    Article  ADS  Google Scholar 

  2. Ishikawa, T. et al. A compact X-ray free-electron laser emitting in the sub-Ångström region. Nature Photon. 6, 540–544 (2012).

    Article  ADS  Google Scholar 

  3. Glover, T. E. et al. X-ray and optical wave mixing. Nature 488, 603–608 (2012).

    Article  ADS  Google Scholar 

  4. Eisenberger, P. & McCall, S. L. X-ray parametric conversion. Phys. Rev. Lett. 26, 684–688 (1971).

    Article  ADS  Google Scholar 

  5. Adams B. (ed.) Nonlinear Optics, Quantum Optics, and Ultrafast Phenomena with X-rays (Kluwer Academic, 2003).

    Book  Google Scholar 

  6. Tamasaku, K., Sawada, K., Nishibori, E. & Ishikawa, T. Visualizing the local optical response to extreme-ultraviolet radiation with a resolution of λ/380. Nature Phys. 7, 705–708 (2011).

    Article  ADS  Google Scholar 

  7. Fukuzawa, H. et al. Deep inner-shell multiphoton ionization by intense X-ray free-electron laser pulses. Phys. Rev. Lett. 110, 173005 (2013).

    Article  ADS  Google Scholar 

  8. Tamasaku, K. et al. Double core–hole creation by sequential attosecond photo-ionization. Phys. Rev. Lett. 111, 043001 (2013).

    Article  ADS  Google Scholar 

  9. Boyd, R. W. Nonlinear Optics (Academic Press, 2003).

    Google Scholar 

  10. Doumy, G. et al. Nonlinear atomic response to intense ultrashort X rays. Phys. Rev. Lett. 106, 083002 (2011).

    Article  ADS  Google Scholar 

  11. Novikov, S. A. & Hopersky, A. N. Two-photon excitation-ionization of the 1s shell of highly charged positive atomic ions. J. Phys. B 34, 4857–4863 (2001).

    Article  ADS  Google Scholar 

  12. 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).

    Article  ADS  Google Scholar 

  13. Son, S.-K., Young, L. & Santra, R. Impact of hollow-atom formation on coherent X-ray scattering at high intensity. Phys. Rev. A 83, 033402 (2011).

    Article  ADS  Google Scholar 

  14. Son, S.-K., Chapman, H. N. & Santra, R. Multiwavelength anomalous diffraction at high X-ray intensity. Phys. Rev. Lett. 107, 218102 (2011).

    Article  ADS  Google Scholar 

  15. Lorentz, U., Kabachnik, N. M., Weckert, E. & Vartanyants, I. A. Impact of ultrafast electronic damage in single-particle X-ray imaging experiments. Phys. Rev. E 86, 051911 (2012).

    Article  ADS  Google Scholar 

  16. Zel'dovich, Ya. B. & Raizer, Yu. P. Physics of Shock Waves and High-Temperature Hydrodynamic Phenomena (Dover, 1966).

    Google Scholar 

  17. Veigele, W. J. Photon cross sections from 0.1 keV to 1 MeV for elements with Z = 1 to Z = 94. Atomic Data 5, 51–111 (1973).

    Article  ADS  Google Scholar 

  18. Sakurai, J. J. Advanced Quantum Mechanics (Addison-Wesley, 1967).

    Google Scholar 

  19. Varma, H. R., Ciappina, M. F., Rohringer N. & Santra, R. Above-threshold ionization in the X-ray regime. Phys. Rev. A 80, 053424 (2009).

    Article  ADS  Google Scholar 

  20. Lambropoulos, P. & Tang, X. Multiple excitation and ionization of atoms by strong lasers. J. Opt. Soc. Am. B 4, 821–832 (1987).

    Article  ADS  Google Scholar 

  21. Zernik, W. Two-photon ionization of atomic hydrogen. Phys. Rev. 135, A51–A57 (1964).

    Article  ADS  Google Scholar 

  22. Koval, P., Fritzsche, S. & Surzhykov, A. Relativistic and retardation effects in the two-photon ionization of hydrogen-like ions. J. Phys. B 36, 873–878 (2003).

    Article  ADS  Google Scholar 

  23. Faisal, F. H. M. Theory of Multiphoton Processes (Plenum, 1987).

    Book  Google Scholar 

  24. Amann, J. et al. Demonstration of self-seeding in a hard-X-ray free-electron laser. Nature Photon. 6, 693–698 (2012).

    Article  ADS  Google Scholar 

  25. Bunker, G. Introduction to XAFS (Cambridge Univ. Press, 2010).

    Book  Google Scholar 

  26. Kato, M. et al. Pulse energy measurement at the hard X-ray laser in Japan. Appl. Phys. Lett. 101, 023503 (2012).

    Article  ADS  Google Scholar 

  27. Tono, K. et al. Beamline for X-ray free electron laser of SACLA. J. Phys. 425, 072006 (2013).

    Google Scholar 

  28. Cowan, R. D. The Theory of Atomic Structure and Spectra (Univ. of California Press, 1981).

    Google Scholar 

Download references

Acknowledgements

The authors thank H. Yoneda, T. Hara, T. Tanaka and T. Hatsui for helpful discussions. This work was supported by a grant-in-aid from the Ministry of Education, Culture, Sports, Science and Technology of Japan (23360038 and 23226004). The experiments were performed with the approval of JASRI (proposal no. 2012B8006).

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K.T., E.S. and Y.I. designed the experiment. H.Y., H.O., H.M. and K.Y. designed the focusing optics and the sample chamber. K.T., E.S., Y.I. and T.K. acquired the experimental data. K.T. and K.S. performed theoretical calculations. K.T. analysed data and wrote the manuscript. All authors discussed the results and commented on the manuscript.

Corresponding author

Correspondence to Kenji Tamasaku.

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The authors declare no competing financial interests.

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Tamasaku, K., Shigemasa, E., Inubushi, Y. et al. X-ray two-photon absorption competing against single and sequential multiphoton processes. Nature Photon 8, 313–316 (2014). https://doi.org/10.1038/nphoton.2014.10

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