Zeitschrift für Physik B Condensed Matter

, Volume 59, Issue 1, pp 111–115 | Cite as

Toda potential in laser equations

  • G. L. Oppo
  • A. Politi


We show that the well known laser rate equations are fully equivalent to the motion in a Toda potential with intensity dependent losses. The dissipative terms are proportional to the square root ε of the ratio between the damping rate of the atomic population inversion and that of the field intensity. The limit case ε≪1 is extensively studied, finding analytical approximations for the period of the oscillations and the energy losses. Feasibility of adiabatic eliminations is also discussed.


Spectroscopy Neural Network State Physics Complex System Energy Loss 
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  1. 1.
    Arecchi, F.T., Lippi, G.L., Puccioni, G.P., Tredicce, J.R.: Opt. Comm.51, 308 (1984); J. Opt. Soc. Am. B (to appear)Google Scholar
  2. 2.
    Morsch, M., Risken, H., Vollmer, H.D.: Z. Phys. B.—Condensed Matter49, 47 (1982)Google Scholar
  3. 3.
    Lotka, A.: Proc. Natl. Acad. Sci.6, 420 (1920)Google Scholar
  4. 4a.
    Volterra, V.: Leçons sur la Theorie Mathematique de la Lutte pour la Vie. Paris: Gauthier-Villars 1936Google Scholar
  5. 4b.
    Nicolis, G., Prigogine, I.: Self Organization in nonequilibrium systems. New York: John Wiley 1977Google Scholar
  6. 5.
    Toda, M.: Phys. Rep.18, 1 (1975)Google Scholar
  7. 6.
    Haken, H.: Z. Phys.181, 96 (1964)Google Scholar
  8. 7.
    This result was already obtained following an alternative method (see Pantell, R.H., Puthoff, H.E.: Fundamentals in quantum electronics. New York: John Wiley 1969). The meaning ofE as a constant of motion, however, had not been clarifiedGoogle Scholar
  9. 8.
    Arecchi, F.T., Meucci, R., Puccioni, G., Tredicce, J.: Phys. Rev. Lett.49, 1217 (1982)Google Scholar
  10. 9.
    Arecchi, F.T., Lippi, G.L., Puccioni, G., Tredicce, J.: Coherence in quantum optics. Vol. V, p. 1227. New York: Plenum Press 1984Google Scholar
  11. 10.
    Rabinovich, M.I.: Usp. Fiz. Nauk125, 123 (1978) (Sov. Phys. Usp.21, 443 (1979))Google Scholar

Copyright information

© Springer-Verlag 1985

Authors and Affiliations

  • G. L. Oppo
    • 1
  • A. Politi
    • 1
  1. 1.Istituto Nazionale di OtticaFirenzeItaly

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