Skip to main content
SpringerLink
Log in

A polynomial expansion method for solving the laser Fokker-Planck equation

  • Published:
Zeitschrift für Physik B Condensed Matter

Abstract

Distribution functions of the laser amplitude and intensity can be determined by solving the laser Fokker-Planck equation. By a suitable expansion of the distribution functions in Laguerre polynomials, a system of ordinary differential equations for the coefficients of the expansion is derived and is shown to have the form of a recurrence relation with length four. Applying it to the transient solution, the averaged amplitude and the first four cumulants of the intensity distribution are obtained even for those pump parameters where the hitherto known numerical solution is not applicable.

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

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Risken, H.: Z. Physik186, 85 (1965)

    Google Scholar 

  2. Haken, H.: Handbuch der Physik, Bd. XXV/2c. Berlin, Heidelberg, New York: Springer 1970

    Google Scholar 

  3. Risken, H.: In: Progress in Optics. Wolf, E. (ed.), Vol. VIII, p. 239. Amsterdam: North Holland 1970

    Google Scholar 

  4. Risken, H., Vollmer, H.D.: Z. Physik204, 240 (1967)

    Google Scholar 

  5. Gordon, J.P., Aslaksen, E.W.: IEEE J. Quantum Electron6, 428 (1970)

    Google Scholar 

  6. Arecchi, F.T., Degiorgio, V.: Phys. Rev. A3, 1108 (1971)

    Google Scholar 

  7. Suzuki, M.: Prog. Theor. Phys.56, 77 (1976);56, 477 (1976)

    Google Scholar 

  8. Arimitsu, T., Suzuki, M.: Physica A (Amsterdam)86, 622 (1977);90, 303 (1978)

    Google Scholar 

  9. Haake, F.: Phys. Rev. Lett. 41 (1978, 1685

    Google Scholar 

  10. Suzuki, M.: In: Synergetics far from Equilibrium. Pacault, A., Vidal, C. (eds.), p. 94. Berlin, Heidelberg, New York: Springer 1979

    Google Scholar 

  11. De Pasquale, F., Tartaglia, P., Tombesi, P.: Physica A (Amsterdam)99, 581 (1979)

    Google Scholar 

  12. Meltzer, D., Mandel, L.: Phys. Rev. Lett.25, 1151 (1970)

    Google Scholar 

  13. Seybold, K., Risken, H.: Z. Physik267, 323 (1974)

    Google Scholar 

  14. Magnus, W., Oberhettinger, F., Soni, R.: Formulas and Theorems for Special Functions of Mathematical Physics. Berlin, Heidelberg, New York Springer 1966

    Google Scholar 

  15. Abramowitz, M., Stegun, I.A.: Handbook of Mathematical Functions, p. 799. New York: Dover Publications Inc. 1965

    Google Scholar 

  16. Risken, H.: Z. Physik191, 302 (1966)

    Google Scholar 

  17. Hempstead, R.D., Lax, M.: Phys. Rev.161, 350 (1967)

    Google Scholar 

  18. Grossmann, S.: Phys. Rev. A17, 1123 (1978)

    Google Scholar 

  19. King, H., Deker, U., Haake, F.: Z. Physik B36, 205 (1979)

    Google Scholar 

  20. Ziegler, K., Horner, H.: RPA for the Linewidth of the Van der Pol oscillator. Z. Physik B37, 339 (1980)

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Abteilung für Theoretische Physik der Universität Ulm, Oberer Eselsberg, D-7900, Ulm, Germany

    H. Risken & H. D. Vollmer

Authors
  1. H. Risken
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. H. D. Vollmer
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

About this article

Cite this article

Risken, H., Vollmer, H.D. A polynomial expansion method for solving the laser Fokker-Planck equation. Z. Physik B - Condensed Matter 39, 89–93 (1980). https://doi.org/10.1007/BF01292643

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01292643

Keywords

Search

Navigation