Generation of the Quasi-solitons in the Lasers: Computer Algebra Approach to an Analysis

  • Vladimir L. Kalashnikov
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 2630)


The recent progress in the generation of the extremely short laser pulses has allowed to reach the pulse durations of few femtoseconds and the peak intensities higher than 1015 W/cm2 (for review see [1]). Their applications cover the range from the technology and the medicine to the sophisticated spectroscopical researches and the nuclear fusion. The femtosecond lasers possess the rich nonlinear properties, which dramatically complicate the field dynamics. There are two main approaches to the theoretical analysis of the femtosecond pulse dynamics. In fact, these approaches reproduce the mainstreams of the nonlinear physics in general.


Femtosecond Laser Saturable Absorber Ultrashort Pulse Soliton Model Semiconductor Saturable Absorber 
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.
    Brabec, T., Krausz, F. (2000): Intense few-cycle laser fields: frontiers of nonlinear optics. Rev. Mod. Physics, 72, 545–591CrossRefGoogle Scholar
  2. 2.
    Haus, H.A., Fujimoto, J.G., Ippen, E.P. (1992): Analytic theory of additive pulse and Kerr lens mode locking. IEEE J. Quantum Electron., 28, 2086–2096CrossRefGoogle Scholar
  3. 3.
    Aranson, I.S., Kramer, L. (2002): The world of the complex Ginzburg-Landau equation. Rev. Modern Physics, 74, 99–143CrossRefMathSciNetGoogle Scholar
  4. 4.
    Akhmediev, N.N., Afanasjev, V.V., Soto-Crespo, J.M. (1996): Singularities and special soliton solutions of the cubic-quintic complex Ginzburg-Landau equation. Phys. Rev. E, 53, 1190–1201CrossRefGoogle Scholar
  5. 5.
    Kalashnikov, V.L., Poloyko, I.G., Mikhailov, V.P., von der Linde, D. (1997): Regular, quasi-periodic and chaotic behaviour in cw solid-state Kerr-lens mode-locked lasers. J. Opt. Soc. Am. B, 14, 2691–2695CrossRefGoogle Scholar
  6. 6.
    Akhmanov, S.A., Vysloukh, V.A., and Chirkin, A.S. (1992): Optics of femtosecond laser pulses. Springer, New YorkGoogle Scholar
  7. 7.
    Kalashnikov, V.L., Kalosha, V.P., Mikhailov, V.P., Poloyko, I.G. (1995): Self-mode locking of four-mirror cavity solid-state lasers by Kerr self-focusing. J. Opt. Soc. Am. B, 12, 462–467CrossRefGoogle Scholar
  8. 8.
    Xing, Q., Chai, L., Zhang, W., Wang, Ch.-yue (1999): Regular, period-doubling, quasi-periodic, and chaotic behavior in a self-mode-locked Ti:sapphire laser. Optics Commun. 162, 71–74CrossRefGoogle Scholar
  9. 9.
    Kalosha, V.P., Müller, M., Herrmann, J., and Gatz, S. (1998): Spatiotemporal model of femtosecond pulse generation in Kerr-lens mode-locked solid-state lasers. J. Opt. Soc. Am. B, 15, 535–550CrossRefGoogle Scholar
  10. 10.
    Sergeev, A.M., Vanin, E.V., Wise, F.W. (1997): Stability of passively modelocked lasers with fast saturable absorbers. Optics Commun. 140, 61–64CrossRefGoogle Scholar
  11. 11.
    Jasapara, J., Kalashnikov, V.L., Krimer, D.O., Poloyko, I.G., Lenzner, M., Rudolph, W. (2000): Automodulations in cw Kerr-lens modelocked solid-state lasers. J. Opt. Soc. Am. B, 17, 319–326CrossRefGoogle Scholar
  12. 12.
    Kalashnikov, V.L., Krimer, D.O., Poloyko, I.G. (2000): Soliton generation and picosecond collapse in solid-state lasers with semiconductor saturable absorber. J. Opt. Soc. Am. B, 17, 519–523CrossRefGoogle Scholar
  13. 13.
    Kärtner, F.X., Yung, I.D., Keller, U. (1996): Soliton mode-locking with saturable absorbers. IEEE J. Sel. Top. Quantum Electron., 2, 540–556CrossRefGoogle Scholar
  14. 14.
    Haus, H.A. (1975): Theory of mode locking with a slow saturable absorber. IEEE J. Quantum Electron., 11, 736–746CrossRefGoogle Scholar
  15. 15.
  16. 16.
    Kalosha, V.P., Müller, M., Herrmann, J. (1999): Theory of solid-state laser mode locking by coherent semiconductor quantum-well absorbers. J. Opt. Soc. Am. B, 16, 323–338CrossRefGoogle Scholar
  17. 17.
    Kalashnikov, V.L. (2001): Theory of sub-10 fs generation in Kerr-lens mode-locked solid-state lasers with a coherent semiconductor absorber. Optics Commun., 192, 323–331CrossRefGoogle Scholar
  18. 18.
    Allen, L., Eberly, J.H. (1975): Optical resonance and two-level atoms. Wiley, New YorkGoogle Scholar
  19. 19.
    Kalashnikov V.L. (2002): Mathematical ultrashort-pulse laser physics. arXiv:physics/0009056Google Scholar
  20. 20.
    Marcq, P., Chaté, H., Conte, R. (1994): Exact solitons of the one-dimensional quintic complex Ginzburg-Landau equation. Physica D, 73, 305–317zbMATHCrossRefMathSciNetGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2003

Authors and Affiliations

  • Vladimir L. Kalashnikov
    • 1
  1. 1.Institut für PhotonikTU WienViennaAustria

Personalised recommendations