Light bullets from femtosecond filamentation

  • A. CouaironEmail author


A model for the propagation of femtosecond laser pulses in transparent media and the formation of light bullets is proposed. This model enable us to generalize Marburger’s formula for the position of the nonlinear focus of the beam in the presence of delayed Kerr effect. It is shown that an instantaneous higher-order saturation tuned to mimic the defocusing effect due to the plasma generated by multiphoton ionization does not properly represent the dynamics of femtosecond filamentation as it violates causality and artificially promotes long distance propagation in the form of periodic oscillations around a spatial soliton. A causal description of multiphoton ionization leads to an extended moving focus model from which the formation of a synchronized structure exhibiting several focusing-defocusing cycles before eventual diffraction can be inferred.


Soliton Laser Pulse Femtosecond Laser Periodic Oscillation Distance Propagation 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    A. Braun, G. Korn, X. Liu, D. Du, J. Squier, G. Mourou, Opt. Lett. 20, 73 (1995)Google Scholar
  2. 2.
    E.T.J. Nibbering, P.F. Curley, G. Grillon, B.S. Prade, M.A. Franco, F. Salin, A. Mysyrowicz, Opt. Lett. 21, 62 (1996)Google Scholar
  3. 3.
    B. La Fontaine, F. Vidal, Z. Jiang, C.Y. Chien, D. Comtois, A. Desparois, T.W. Johnston, J.-C. Kieffer, H. Pépin, Phys. Plasmas 6, 1615 (1999)CrossRefGoogle Scholar
  4. 4.
    J. Schwarz, P. Rambo, J.-C. Diels, M. Kolesik, E.M. Wright, J.V. Moloney, Opt. Commun. 180, 383 (2000)CrossRefGoogle Scholar
  5. 5.
    S. Tzortzakis, B. Lamouroux, A. Chiron, M. Franco, B.S. Prade, A. Mysyrowicz, S.D. Moustaizis, Opt. Lett. 25, 1270 (2000)Google Scholar
  6. 6.
    S. Tzortzakis, B. Lamouroux, A. Chiron, S.D. Moustaizis, D. Anglos, M. Franco, B. Prade, A. Mysyrowicz, Opt. Commun. 197, 131 (2001)CrossRefGoogle Scholar
  7. 7.
    D. Mikalauskas, A. Dubietis, R. Danielus, Appl. Phys. B 75, 899 (2002)Google Scholar
  8. 8.
    V.P. Kandidov, O.G. Kosareva, S.A. Shlenov, Quant. Electron. 24, 905 (1994)Google Scholar
  9. 9.
    M. Mlejnek, E.M. Wright, J.V. Moloney, Opt. Lett. 23, 382 (1998)Google Scholar
  10. 10.
    M. Mlejnek, E.M. Wright, J.V. Moloney, Opt. Expr. 7, 223 (1999)Google Scholar
  11. 11.
    M. Mlejnek, M. Kolesik, J.V. Moloney, E.M. Wright, Phys. Rev. Lett. 83, 2938 (1999)CrossRefGoogle Scholar
  12. 12.
    A. Chiron, B. Lamouroux, R. Lange, J.-F. Ripoche, M. Franco, B. Prade, G. Bonnaud, G. Riazuelo, A. Mysyrowicz, Eur. Phys. J. D 6, 383 (1999)CrossRefGoogle Scholar
  13. 13.
    J.V. Moloney, M. Kolesik, M. Mlejnek, E.M. Wright, Chaos 10, 559 (2000)CrossRefzbMATHGoogle Scholar
  14. 14.
    M. Nurhuda, A. Suda, M. Hatayama, K. Nagasaka, K. Midorikawa, Phys. Rev. A 66, 023811 (2002)CrossRefGoogle Scholar
  15. 15.
    A. Couairon, S. Tzortzakis, L. Bergé, M. Franco, B. Prade, A. Mysyrowicz, J. Opt. Soc. Am. B 19, 1117 (2002)Google Scholar
  16. 16.
    A. Couairon, L. Bergé, Phys. Rev. Lett. 88, 135003 (2002)CrossRefGoogle Scholar
  17. 17.
    A. Couairon, Phys. Rev. A 68, 015801 (2003)CrossRefGoogle Scholar
  18. 18.
    R.Y. Chiao, E. Garmire, C.H. Townes, Phys. Rev. Lett. 13, 479 (1964)CrossRefGoogle Scholar
  19. 19.
    J.H. Marburger, E. Dawes, Phys. Rev. Lett. 21, 556 (1968)CrossRefGoogle Scholar
  20. 20.
    V.I. Bespalov, V.I. Talanov, JETP Lett. 3, 307 (1966)Google Scholar
  21. 21.
    F. Vidal, D. Comtois, C.-Y. Chien, A. Desparois, B. La Fontaine, T.W. Johnston, J.-C. Kieffer, H.P. Mercure, F.A. Rizk, IEEE Trans. Plasma Sci. 28, 418 (2000)CrossRefGoogle Scholar
  22. 22.
    L. Wöste, C. Wedekind, H. Wille, P. Rairoux, B. Stein, S. Nikolov, C. Werner, S. Neirdeimer, F. Ronneberger, H. Schilinger, R. Sauerbrey, Las. Optoelectr. 29, 51 (1997)Google Scholar
  23. 23.
    P. Rairoux, H. Schillinger, S. Neirdeimer, M. Rodriguez, F. Ronneberger, R. Sauerbrey, B. Stein, D. Waite, C. Wedekind, H. Wille, L. Wöste, C. Ziener, Appl. Phys. B 71, 573 (2000)CrossRefGoogle Scholar
  24. 24.
    E. Frejafon, J. Kasparian, P. Rambaldi, B. Vezin, V. Boutou, J. Yu, M. Ulbricht, D. Weidauer, B. Ottobrini, E. de Saeger, B. Krämer, T. Leisner, P. Rairoux, L. Wöste, J.-P. Wolf, Eur. Phys. J. D 4, 231 (1998)CrossRefGoogle Scholar
  25. 25.
    Y. Silberberg, Opt. Lett. 15, 1282 (1990)Google Scholar
  26. 26.
    P. Goorjian, Y. Silberberg, J. Opt. Soc. Am. B 14, 3253 (1997)Google Scholar
  27. 27.
    J.X. Xin, Physica D 135, 345 (2000)CrossRefMathSciNetzbMATHGoogle Scholar
  28. 28.
    T. Brabec, F. Krausz, Phys. Rev. Lett. 78, 3282 (1997)CrossRefGoogle Scholar
  29. 29.
    A.L. Gaeta, Phys. Rev. Lett. 84, 3582 (2000)CrossRefGoogle Scholar
  30. 30.
    A. Brodeur, C.Y. Chien, F.A. Ilkov, S.L. Chin, O.G. Kosareva, V.P. Kandidov, Opt. Lett. 22, 304 (1997)Google Scholar
  31. 31.
    J.F. Ripoche, G. Grillon, B.S. Prade, M.A. Franco, E. Nibbering, H.R. Lange, A. Mysyrowicz, Opt. Commun. 135, 310 (1997)CrossRefGoogle Scholar
  32. 32.
    E. Yablonovitch, N. Bloembergen, Phys. Rev. Lett. 29, 907 (1972)CrossRefGoogle Scholar
  33. 33.
    L.V. Keldysh, ZhETF 47, 1945 (1964)zbMATHGoogle Scholar
  34. 34.
    D. Anderson, M. Bonnedal, Phys. Fluids 22, 105 (1979)CrossRefMathSciNetGoogle Scholar
  35. 35.
    P. Sprangle, J.R. Peñano, B. Hafizi, Phys. Rev. E 66, 046418 (2002)CrossRefGoogle Scholar
  36. 36.
    S. Tzortzakis, L. Sudrie, M. Franco, B. Prade, A. Mysyrowicz, A. Couairon, L. Bergé, Phys. Rev. Lett. 87, 213902 (2001)Google Scholar
  37. 37.
    L. Sudrie, A. Couairon, M. Franco, B. Lamouroux, B. Prade, S. Tzortzakis, A. Mysyrowicz, Phys. Rev. Lett. 89, 186601 (2002)CrossRefGoogle Scholar
  38. 38.
    P. Chernev, V. Petrov, Opt. Lett. 17, 172 (1992)Google Scholar
  39. 39.
    J.E. Rothenberg, Opt. Lett. 17, 583 (1992)Google Scholar
  40. 40.
    G.G. Luther, J.V. Moloney, A.C. Newell, E.M. Wright, Opt. Lett. 19, 862 (1994)Google Scholar
  41. 41.
    S. Henz, J. Herrmann, Phys. Rev. E 53, 4092 (1996)Google Scholar
  42. 42.
    N. Aközbek, C.M. Bowden, A. Talebpour, S. Chin, Phys. Rev. E 61, 4540 (2000)CrossRefGoogle Scholar
  43. 43.
    J. Schwarz, J.-C. Diels, Phys. Rev. A 65, 013806 (2001)CrossRefGoogle Scholar
  44. 44.
    Y.R. Shen, The principles of nonlinear optics (Wiley, New-York, 1984)Google Scholar
  45. 45.
    J.H. Marburger, Prog. Quant. Electr. 4, 35 (1975)CrossRefGoogle Scholar
  46. 46.
    H.R. Lange, G. Grillon, J.-F. Ripoche, M.A. Franco, B. Lamouroux, B.S. Prade, A. Mysyrowicz, Opt. Lett. 23, 120 (1998)Google Scholar
  47. 47.
    M. Mlejnek, E.M. Wright, J.V. Moloney, IEEE J. Quant. Electron. 35, 697 (1999)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin/Heidelberg 2003

Authors and Affiliations

  1. 1.Centre de Physique ThéoriqueÉcole Polytechnique (UMR 7644 du CNRS)Palaiseau CedexFrance

Personalised recommendations