Skip to main content
SpringerLink
Log in

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

  • Conference paper
  • First Online:
Symbolic and Numerical Scientific Computation (SNSC 2001)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 2630))

  • 528 Accesses

Abstract

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.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 39.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 54.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Brabec, T., Krausz, F. (2000): Intense few-cycle laser fields: frontiers of nonlinear optics. Rev. Mod. Physics, 72, 545–591

    Article  Google Scholar 

  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, 2086–2096

    Article  Google Scholar 

  3. Aranson, I.S., Kramer, L. (2002): The world of the complex Ginzburg-Landau equation. Rev. Modern Physics, 74, 99–143

    Article  MathSciNet  Google Scholar 

  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, 1190–1201

    Article  Google Scholar 

  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, 2691–2695

    Article  Google Scholar 

  6. Akhmanov, S.A., Vysloukh, V.A., and Chirkin, A.S. (1992): Optics of femtosecond laser pulses. Springer, New York

    Google Scholar 

  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, 462–467

    Article  Google Scholar 

  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, 71–74

    Article  Google Scholar 

  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, 535–550

    Article  Google Scholar 

  10. Sergeev, A.M., Vanin, E.V., Wise, F.W. (1997): Stability of passively modelocked lasers with fast saturable absorbers. Optics Commun. 140, 61–64

    Article  Google Scholar 

  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, 319–326

    Article  Google Scholar 

  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, 519–523

    Article  Google Scholar 

  13. Kärtner, F.X., Yung, I.D., Keller, U. (1996): Soliton mode-locking with saturable absorbers. IEEE J. Sel. Top. Quantum Electron., 2, 540–556

    Article  Google Scholar 

  14. Haus, H.A. (1975): Theory of mode locking with a slow saturable absorber. IEEE J. Quantum Electron., 11, 736–746

    Article  Google Scholar 

  15. Maple 6 computer algebra realization can be found on http://www.mapleapps.com/categories/science/physics/worksheets/Ultrashort_PulseLaser.mws. (Maple V version: http://www.mapleapps.com/categories/mathematics/desolving/worksheets/soliton.mws)

  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, 323–338

    Article  Google Scholar 

  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, 323–331

    Article  Google Scholar 

  18. Allen, L., Eberly, J.H. (1975): Optical resonance and two-level atoms. Wiley, New York

    Google Scholar 

  19. Kalashnikov V.L. (2002): Mathematical ultrashort-pulse laser physics. arXiv:physics/0009056

    Google Scholar 

  20. Marcq, P., Chaté, H., Conte, R. (1994): Exact solitons of the one-dimensional quintic complex Ginzburg-Landau equation. Physica D, 73, 305–317

    Article  MATH  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Institut für Photonik, TU Wien, Gusshausstr. 27/387, A-1040, Vienna, Austria

    Vladimir L. Kalashnikov

Authors
  1. Vladimir L. Kalashnikov
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. RISC-Linz, Johannes Kepler University Linz, Altenberger Str. 69, 4040, Linz, Austria

    Franz Winkler

  2. Institute of Computational Mathematics, Johannes Kepler University Linz, Altenberger Str. 69, 4040, Linz, Austria

    Ulrich Langer

Rights and permissions

Reprints and permissions

Copyright information

© 2003 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Kalashnikov, V.L. (2003). Generation of the Quasi-solitons in the Lasers: Computer Algebra Approach to an Analysis. In: Winkler, F., Langer, U. (eds) Symbolic and Numerical Scientific Computation. SNSC 2001. Lecture Notes in Computer Science, vol 2630. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-45084-X_18

Download citation

  • DOI: https://doi.org/10.1007/3-540-45084-X_18

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-40554-2

  • Online ISBN: 978-3-540-45084-9

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation