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.
Similar content being viewed by others
References
Horsthemke, W., Lefever, R.: Noise-induced transitions. Berlin, Heidelberg, New York: Springer 1984; Schenzle, A., Brand, H.: Phys. Rev. A20, 1628 (1979)
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)
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
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)
Roy, R., Yu, A.W., Zhu, S.: In: Noise in nonlinear dynamical systems, Moss, F., McClintock, P. (eds.). Cambridge University Press 1988
Morita, T., Mori, H., Mashiyama, K.T.: Prog. Theor. Phys.64, 500 (1980)
Wunderlin, A., Haken, H.: Z. Phys. B — Condensed Matter44, 135 (1981); Haken, H., Wunderlin, A.: Z. Phys. B — Condensed Matter47, 179 (1982)
Schöner, G., Haken, H.: Z. Phys. B — Condensed Matter63, 493 (1986);68, 89 (1987)
Wu, D.J., Cao, L.: Z. Phys. B — Condensed Matter81, 131 (1990);81, 451 (1990)
Takayama, H. (ed.): Cooperative dynamics in complex physical systems. Berlin, Heidelberg, New York: Springer 1989
Arnold, L.: Stochastic differential equations: theory and applications. New York: Wiley-Interscience 1974
Novikov, E.A.: Zh. Eksp. Teor. Fiz.47, 1919 (1964)
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)
Peacock-Lopez, E., De la Rubia, F.J., West, B.J., Lindenberg, K.: Phys. Rev. A39, 4026 (1989)
Haken, H.: Laser theory. New York: Springer 1984
Risken, H.: The Fokker-Planck equation. Berlin, Heidelberg, New York: Springer 1984
Svelto, O.: Principles of laser, 2nd edn. New York: Plenum 1982; Schaefer, F.P. (ed.): Dye lasers. Berlin, Heidelberg, New York: Springer 1973
Cao, L., Wu, D.J., Wang, H.X.: Phys. Lett. A133, 476 (1988)
Wu, D.J., Cao, L., Yang, B.: Commun. Theor. Phys.11, 379 (1989)
Hänggi, P., Mroczkowski, T.J., Moss, F., McClintock, P.V.E.: Phys. Rev. A32, 695 (1985)
Author information
Authors and Affiliations
Rights 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
Received:
Revised:
Issue Date:
DOI: https://doi.org/10.1007/BF01387795