Skip to main content
Log in

Problems for the elimination of atomic variables and the single-mode dye laser equations

  • Original Contributions
  • Published:
Zeitschrift für Physik B Condensed Matter

Abstract

The stochastic generalization of the adiabatic approximation has been developed earlier by Wunderlin and Haken [6] and recently by Schöner and Haken [7] and the authors [8]. Using these theories, a complex field amplitude equation for the single-mode dye laser is derived based on a set of semiclassical single-mode laser equations. An effective Fokker-Planck equation in which the laser intensity is decoupled from the phase variable is obtained. The relations between our theory and the phenomenological single-mode dye laser equation are discussed.

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

Access this article

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

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. Horsthemke, W., Lefever, R.: Noise-induced transitions. Berlin, Heidelberg, New York: Springer 1984; Schenzle, A., Brand, H.: Phys. Rev. A20, 1628 (1979)

    Google Scholar 

  2. Kaminishi, K., Roy, R., Short, R., Mandel, L.: Phys. Rev. A24, 370 (1981); Short, R., Mandel, L., Roy, R.: Phys. Rev. Lett.49, 647 (1982); Lett, P., Short, R., Mandel, L.: Phys. Rev. Lett.52, 341 (1984); Fox, R.F., Roy, R.: Phys. Rev. A35, 1838 (1987); Jung, P., Lieber, T., Risken, H.: Z. Phys. B — Condensed Matter66, 397 (1987)

    Google Scholar 

  3. Roy, R., Yu, A.W., Zhu, S.: Phys. Lett.55, 2794 (1985); Zhu, S., Yu, A.W., Roy, R.: Phys. Rev. A34, 4333 (1986); Graham, R., Hohnerbach, M., Schenzle, A.: Phys. Rev. Lett.48, 1396 (1982); De Pasquale, F., Sancho, J.M., San Miguel, M., Tartaglia, P.: Phys. Rev. Lett.,56, 2473 (1986) and References therein

    Google Scholar 

  4. Fox, R.F., Janes, C.E., Roy, R.: Phys. Rev. A30, 2482 (1984); Hong, F., Haken, H.: Phys. Rev. A36, 4028 (1987); Young, M.R., Singh, S.: Opt. Lett.13, 21 (1988)

    Google Scholar 

  5. Roy, R., Yu, A.W., Zhu, S.: In: Noise in nonlinear dynamical systems, Moss, F., McClintock, P. (eds.). Cambridge University Press 1988

  6. Morita, T., Mori, H., Mashiyama, K.T.: Prog. Theor. Phys.64, 500 (1980)

    Google Scholar 

  7. Wunderlin, A., Haken, H.: Z. Phys. B — Condensed Matter44, 135 (1981); Haken, H., Wunderlin, A.: Z. Phys. B — Condensed Matter47, 179 (1982)

    Google Scholar 

  8. Schöner, G., Haken, H.: Z. Phys. B — Condensed Matter63, 493 (1986);68, 89 (1987)

    Google Scholar 

  9. Wu, D.J., Cao, L.: Z. Phys. B — Condensed Matter81, 131 (1990);81, 451 (1990)

    Google Scholar 

  10. Takayama, H. (ed.): Cooperative dynamics in complex physical systems. Berlin, Heidelberg, New York: Springer 1989

    Google Scholar 

  11. Arnold, L.: Stochastic differential equations: theory and applications. New York: Wiley-Interscience 1974

    Google Scholar 

  12. Novikov, E.A.: Zh. Eksp. Teor. Fiz.47, 1919 (1964)

    Google Scholar 

  13. Hong, F., Haken, H.: Phys. Rev. A36, 4802 (1987); Opt. Commun.64, 454 (1987); Opt. Soc. Am. B5, 899 (1988); Phys. Rev. Lett.60, 2614 (1988)

    Google Scholar 

  14. Peacock-Lopez, E., De la Rubia, F.J., West, B.J., Lindenberg, K.: Phys. Rev. A39, 4026 (1989)

    Google Scholar 

  15. Haken, H.: Laser theory. New York: Springer 1984

    Google Scholar 

  16. Risken, H.: The Fokker-Planck equation. Berlin, Heidelberg, New York: Springer 1984

    Google Scholar 

  17. Svelto, O.: Principles of laser, 2nd edn. New York: Plenum 1982; Schaefer, F.P. (ed.): Dye lasers. Berlin, Heidelberg, New York: Springer 1973

    Google Scholar 

  18. Cao, L., Wu, D.J., Wang, H.X.: Phys. Lett. A133, 476 (1988)

    Google Scholar 

  19. Wu, D.J., Cao, L., Yang, B.: Commun. Theor. Phys.11, 379 (1989)

    Google Scholar 

  20. Hänggi, P., Mroczkowski, T.J., Moss, F., McClintock, P.V.E.: Phys. Rev. A32, 695 (1985)

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Rights and permissions

Reprints and permissions

About this article

Cite this article

Wu, Dj., Cao, L. Problems for the elimination of atomic variables and the single-mode dye laser equations. Z. Physik B - Condensed Matter 85, 111–116 (1991). https://doi.org/10.1007/BF01387795

Download citation

  • Received:

  • Revised:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01387795

Keywords

Navigation