The European Physical Journal D

, Volume 55, Issue 2, pp 475–481 | Cite as

Controlling the divergence of high harmonics from solid targets: a route toward coherent harmonic focusing

  • R. HörleinEmail author
  • S. G. Rykovanov
  • B. Dromey
  • Y. Nomura
  • D. Adams
  • M. Geissler
  • M. Zepf
  • F. Krausz
  • G. D. Tsakiris
Topical issue: Fundamental Physics and Ultra-High Laser Fields


Harmonic generation from relativistically oscillating plasma surfaces formed during the interaction of high contrast lasers with solid-density targets has been shown to be an efficient source of extreme ultraviolet (XUV) and X-ray radiation. Recent work has demonstrated that the exceptional coherence properties of the driving laser can be mirrored in the emitted radiation, permitting diffraction limited performance and attosecond phase locking of the harmonic radiation. These unique properties may allow the coherent harmonic focusing (CHF) of high harmonics generated from solid density targets to intensities on the order of the Schwinger limit of 1029 W cm-2 with laser systems available in the near future [Phys. Rev. Lett. 93, 115002 (2004)] and thus pave the way for unique experiments exploring the nonlinear properties of vacuum on ultra-fast timescales. In this paper we investigate experimentally as well as numerically the prospect of focusing high harmonics under realistic experimental conditions and demonstrate, using particle in cell (PIC) simulations, that precise control of the wavefronts and thus the focusability of the generated harmonics is possible with pre-shaped targets.


42.65.Ky Frequency conversion; harmonic generation, including higher-order harmonic generation 42.65.Re Ultrafast processes; optical pulse generation and pulse compression 52.59.Ye Plasma devices for generation of coherent radiation 52.65.Rr Particle-in-cell method 


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  1. 1.
    J. Schwinger, Phys. Rev. 82, 664 (1951)zbMATHCrossRefMathSciNetADSGoogle Scholar
  2. 2.
    N. Narozhny, S. Bulanov, V. Mur, V. Popov, Phys. Lett. A 330, 1 (2004)zbMATHCrossRefADSGoogle Scholar
  3. 3.
    N. Narozhny, S. Bulanov, V. Mur, V. Popov, JETP Lett. 80, 382 (2004)CrossRefADSGoogle Scholar
  4. 4.
    M. Marklund, P.K. Shukla, Rev. Mod. Phys. 78, 591 (2006)CrossRefADSGoogle Scholar
  5. 5.
    R. Schützhold, G. Schaller, D. Habs, Phys. Rev. Lett. 97, 121302 (2006)CrossRefADSGoogle Scholar
  6. 6.
    A. Di Piazza, K.Z. Hatsagortsyan, C.H. Keitel, Phys. Plasmas 14, 032102 (2007)CrossRefADSGoogle Scholar
  7. 7.
    L.C.B. Crispino, A. Higuchi, G.E.A. Matsas, Rev. Mod. Phys. 80, 787 (2008)CrossRefMathSciNetADSGoogle Scholar
  8. 8.
    S. Gordienko, A. Pukhov, O. Shorokhov, T. Baeva, Phys. Rev. Lett. 93, 115002 (2004)CrossRefADSGoogle Scholar
  9. 9.
    T. Baeva, S. Gordienko, A. Pukhov, Phys. Rev. E 74, 046404 (2006)CrossRefADSGoogle Scholar
  10. 10.
    G.D. Tsakiris, K. Eidmann, J. Meyer-ter-Vehn, F. Krausz, New J. Phys. 8, 19 (2006)CrossRefADSGoogle Scholar
  11. 11.
    S.V. Bulanov, N.M. Naumova, F. Pegoraro, Phys. Plasmas 1, 745 (1994)CrossRefADSGoogle Scholar
  12. 12.
    R. Lichters, J. Meyer-ter-Vehn, A. Pukhov, Phys. Plasmas 3, 3425 (1996)CrossRefADSGoogle Scholar
  13. 13.
    S. Gordienko, A. Pukhov, O. Shorokhov, T. Baeva, Phys. Rev. Lett. 94, 103903 (2005)CrossRefADSGoogle Scholar
  14. 14.
    F. Quéré, C. Thaury, P. Monot, S. Dobosz, P. Martin, J.-P. Geindre, P. Audebert, Phys. Rev. Lett. 96, 125004 (2006)CrossRefADSGoogle Scholar
  15. 15.
    B. Dromey, M. Zepf, A. Gopal, K. Lancaster, M.S. Wei, K. Krushelnick, M. Tatarakis, N. Vakakis, S. Moustaizis, R. Kodama, M. Tampo, C. Stoeckl, R. Clarke, H. Habara, D. Neely, S. Karsch, P. Norreys, Nat. Phys. 2, 456 (2006)CrossRefGoogle Scholar
  16. 16.
    B. Dromey, S. Kar, C. Bellei, D.C. Carroll, R.J. Clarke, J.S. Green, S. Kneip, K. Markey, S.R. Nagel, P.T. Simpson, L. Willingale, P. McKenna, D. Neely, Z. Najmudin, K. Krushelnick, P.A. Norreys, M. Zepf, Phys. Rev. Lett. 99, 085001 (2007)CrossRefADSGoogle Scholar
  17. 17.
    Y. Nomura, R. Hörlein, P. Tzallas, B. Dromey, S. Rykovanov, Z. Major, J. Osterhoff, S. Karsch, L. Veisz, M. Zepf, D. Charalambidis, F. Krausz, G.D. Tsakiris, Nat. Phys. 5, 124 (2009)CrossRefGoogle Scholar
  18. 18.
    P. Agostini, L.F. DiMauro, Rep. Prog. Phys. 67, 813 (2004)CrossRefADSGoogle Scholar
  19. 19.
    P.B. Corkum, F. Krausz, Nat. Phys. 3, 381 (2007)CrossRefGoogle Scholar
  20. 20.
    W. Ackermann et al., Nature Photonics 1, 336 (2007)CrossRefADSGoogle Scholar
  21. 21.
    A.J. Langley, E.J. Divall, C.H. Hooker, M.H.R. Hutchinson, A.J.-M.P. Lecot, D. Marshall, M.E. Payne, P.F. Taday, Technical report, Rutherford Appleton Laboratory, 2000Google Scholar
  22. 22.
    H. Kapteyn, M. Murnane, A. Szoke, R. Falcone, Opt. Lett. 16, 490 (1991)CrossRefADSGoogle Scholar
  23. 23.
    B. Dromey, S. Kar, M. Zepf, P. Foster, Rev. Sci. Instrum. 75, 645 (2004)CrossRefADSGoogle Scholar
  24. 24.
    D. Neely, D. Chambers, C. Danson, P. Norreys, S. Preston, F. Quinn, M. Roper, J. Wark, M. Zepf, AIP Conf. Proc. 426, 479 (1998)ADSCrossRefGoogle Scholar
  25. 25.
    R. Hörlein, B. Dromey, D. Adams, Y. Nomura, S. Kar, K. Markey, P.S. Foster, D. Neely, F. Krausz, G.D. Tsakiris, M. Zepf, New J. Phys. 10, 083002 (2008)Google Scholar
  26. 26.
    B. Dromey, D. Adams, R. Hörlein, Y. Nomura, S.G. Rykovanov, D.C. Caroll, P.S. Foster, S. Kar, K. Markey, P. McKenna, D. Neely, M. Geissler, G.D. Tsakiris, M. Zepf, Nat. Phys. 5, 146 (2009)CrossRefGoogle Scholar
  27. 27.
    D. An der Brügge, A. Pukhov, Phys. Plasmas 14, 093104 (2007)Google Scholar
  28. 28.
    S. Rykovanov, M. Geissler, J. Meyer-ter-Vehn, G.D. Tsakiris, New J. Phys. 10, 025025 (2008)Google Scholar
  29. 29.
    M. Geissler, S. Rykovanov, J. Schreiber, J. Meyer-ter-Vehn, G.D. Tsakiris, New J. Phys. 9, 218 (2007)CrossRefADSGoogle Scholar
  30. 30.
    N.M. Naumova, J.A. Nees, I.V. Sokolov, B. Hou, G.A. Mourou, Phys. Rev. Lett. 92, 063902 (2004)CrossRefADSGoogle Scholar
  31. 31.
    M. Born, E. Wolf, Principles of optics, 7th edn. (Cambridge University Press, 1999)Google Scholar
  32. 32.
    T. Morishita, S. Watanabe, C.D. Lin, Phys. Rev. Lett. 98, 083003 (2007)CrossRefADSGoogle Scholar
  33. 33.
    J. Feist, S. Nagele, R. Pazourek, E. Persson, B.I. Schneider, L.A. Collins, J. Burgdörfer, Phys. Rev. A 77, 043420 (2008)CrossRefADSGoogle Scholar
  34. 34.
    J.J. Honrubia, J. Meyer-ter-Vehn, Nucl. Fusion 46, L25 (2006)CrossRefADSGoogle Scholar
  35. 35.
    R. Hörlein, Y. Nomura, J. Osterhoff, Z. Major, S. Karsch, F. Krausz, G.D. Tsakiris, Plasma Phys. Contr. Fusion 50, 124002 (2008)Google Scholar

Copyright information

© EDP Sciences, SIF, Springer-Verlag Berlin Heidelberg 2009

Authors and Affiliations

  • R. Hörlein
    • 1
    • 2
    Email author
  • S. G. Rykovanov
    • 1
    • 3
  • B. Dromey
    • 4
  • Y. Nomura
    • 1
  • D. Adams
    • 4
  • M. Geissler
    • 4
  • M. Zepf
    • 4
  • F. Krausz
    • 1
    • 2
  • G. D. Tsakiris
    • 1
  1. 1.Max-Planck-Institut für QuantenoptikGarchingGermany
  2. 2.Sektion Physik der Ludwig-Maximilians-Universität MünchenGarchingGermany
  3. 3.Moscow Physics Engineering InstituteMoscowRussia
  4. 4.Department of Physics and AstronomyQueens University BelfastBelfastUK

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