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Optics Express

Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 16, Iss. 12 — Jun. 9, 2008
  • pp: 8324–8331

Nonlinear optics in the X-ray regime: nonlinear waves and self-action effects

C. Conti, A. Fratalocchi, G. Ruocco, and F. Sette  »View Author Affiliations

Optics Express, Vol. 16, Issue 12, pp. 8324-8331 (2008)

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We study the nonlinear refraction of X-rays in highly ionized condensed matter by using a classical model of a cold electron plasma in a lattice of still ions coupled with Maxwell equations. We discuss the existence and stability of nonlinear waves. As a real-world example, we consider beam self-defocusing in crystalline materials (B, C, Li, Na). We predict that nonlinear processes become comparable to the linear ones for focused beams with powers of the order of mc3/ro (≈10 GW), the classical electron power. As a consequence, nonlinear phenomena are expected in currently exploited X-ray Free-Electron Lasers and in their future developments.

© 2008 Optical Society of America

OCIS Codes
(160.4330) Materials : Nonlinear optical materials
(190.5940) Nonlinear optics : Self-action effects
(340.0340) X-ray optics : X-ray optics

ToC Category:
Nonlinear Optics

Original Manuscript: January 18, 2008
Revised Manuscript: March 11, 2008
Manuscript Accepted: March 18, 2008
Published: May 23, 2008

C. Conti, A. Fratalocchi, G. Ruocco, and F. Sette, "Nonlinear optics in the X-ray regime: nonlinear waves and self-action effects," Opt. Express 16, 8324-8331 (2008)

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  1. R. Dendy, Plasma physics: an in introductory course (Cambridge University Press, Cambridge, 1996).
  2. T. Pfeifer, C. Spielmann, and G. Gerber, "Femtosecond x-ray science," Rep. Prog. Phys. 69,443-505 (2006). [CrossRef]
  3. Techical Design Report of the European XFEL, DESY (2006-097). http://xfel.desy.de/tdr/tdr.
  4. H. Hora, Physics of Laser Driven Plasmas (Wiley-Interscience, New York, 1981).
  5. R. Alkofer, M. B. Hecht, C. D. Roberts, S. M. Schmidt, and D. V. Vinnik, "Pair Creation and an X-Ray Free Electron Laser, " Phys. Rev. Lett. 87, 193902-(4) (2001). [CrossRef] [PubMed]
  6. R. Moshammer Y. H. Jiang, L. Foucar, A. Rudenko, Th. Ergler, C. D. Schrter, S. Ldemann, K. Zrost, D. Fischer, J. Titze, T. Jahnke, M. Schffler, T. Weber, R. Drner, T. J. M. Zouros, A. Dorn, T. Ferger, K. U. Khnel, S. Dsterer, R. Treusch, P. Radcliffe, E. Plnjes, and J. Ullrich, " Few-Photon Multiple Ionization of Ne and Ar by Strong Free-Electron-Laser Pulses," Phys. Rev. Lett. 98, 203001-(4) (2007). [CrossRef] [PubMed]
  7. H. Wabnitz, A. R. B. de Castro, P. Grtler, T. Laarmann, W. Laasch, J. Schulz, and T. Mller, " Multiple Ionization of Rare Gas Atoms Irradiated with Intense VUV Radiation," Phys. Rev. Lett. 94, 023001-(4) (2005). [CrossRef] [PubMed]
  8. Y. Nabekawa, H. Hasegawa, E. J. Takahashi, and K. Midorikawa, " Production of Doubly Charged Helium Ions by Two-Photon Absorption of an Intense Sub-10-fs Soft X-Ray Pulse at 42 eV Photon Energy," Phys. Rev. Lett. 94, 043001-(4) (2005). [CrossRef] [PubMed]
  9. T. Laarmann, A. R. B. de Castro, P. Grtler, W. Laasch, J. Schulz, H. Wabnitz, and T. Mller, " Photoionization of helium atoms irradiated with intense vacuum ultraviolet free-electron laser light. Part I. Experimental study of multiphoton and single-photon processes," Phys. Rev. A 72, 023409-(8) (2005). [CrossRef]
  10. E. P. Benis, D. Charalambidis, T. N. Kitsopoulos, G. D. Tsakiris, and P. Tzallas, " Two-photon double ionization of rare gases by a superposition of harmonics," Phys. Rev. A 74, 051402(R)-(4) (2006). [CrossRef]
  11. T. Sekikawa, A. Kosuge, T. Kanai, and S. Watanabe, "Nonlinear optics in the extreme ultraviolet," Nature (London) 432,605-608 (2004). [CrossRef] [PubMed]
  12. N. Bloembergen, R. K. Chang, S. S. Jha, and C. H. Lee, "Optical Second-Harmonic Generation in Reflection from Media with Inversion Symmetry, " Phys. Rev. 174,813-822 (1968). [CrossRef]
  13. S. S. Jha, and C. S. Warke, "Nonlinear electromagnetic response of Bloch electrons in a magnetic field," Nuovo Cimento 53B,120-135 (1968).
  14. A. Nazarkin, S. Podorov, I. Uschmann, E. Frster, and R. Sauerbrey, "Nonlinear optics in the angstrom regime: Hard-x-ray frequency doubling in perfect crystals," Phys. Rev. A 67, 041804-(4) (2003). [CrossRef]
  15. S. S. Jha, and J. W. F. Woo, "Nonlinear Response of Bound Electrons to X Rays," Phys. Rev. B 5,4210-4212 (1972). [CrossRef]
  16. N. Bloembergen, "Wave propagation in nonlinear electromagnetic media," Proceedings of the IEEE 51,124-131 (1963). [CrossRef]
  17. R. W. Boyd, Nonlinear Optics (Academic Press, New York, 2002).
  18. R. Neutze, R. Wouts, D. Spoel, E. Weckert, and J. Hajdu, "Potential for biomolecular imaging with femtosecond X-ray pulses," Nature (London) 406,752-757 (2000). [CrossRef] [PubMed]
  19. K. Sakoda, Optical Properties of Photonic Crystals (Springer & Verlag, Berlin, 2001).
  20. T. Inui, Y. Tanabe, and Y. Onodera, Group theory and its applications in Physics (Springer & Verlag, Berlin, 1990). [CrossRef]
  21. C. A. Balanis, Advanced Engineering Electromagnetics (Jhon Wiley & Sons, Toronto, 1989).
  22. Y. S. Kivshar and G. P. Agrawal, Optical Solitons: from Fibers to Photonic Crystals (Academic Press, San Diego, 2003).
  23. D. Vaughan, X-Ray Data Booklet (Lawrence Berkely Laboratory, Berkely, 1986). [CrossRef]

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