Toda potential in laser equations
- 45 Downloads
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.
Unable to display preview. Download preview PDF.
- 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.Morsch, M., Risken, H., Vollmer, H.D.: Z. Phys. B.—Condensed Matter49, 47 (1982)Google Scholar
- 3.Lotka, A.: Proc. Natl. Acad. Sci.6, 420 (1920)Google Scholar
- 4a.Volterra, V.: Leçons sur la Theorie Mathematique de la Lutte pour la Vie. Paris: Gauthier-Villars 1936Google Scholar
- 4b.Nicolis, G., Prigogine, I.: Self Organization in nonequilibrium systems. New York: John Wiley 1977Google Scholar
- 5.Toda, M.: Phys. Rep.18, 1 (1975)Google Scholar
- 6.Haken, H.: Z. Phys.181, 96 (1964)Google Scholar
- 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
- 8.Arecchi, F.T., Meucci, R., Puccioni, G., Tredicce, J.: Phys. Rev. Lett.49, 1217 (1982)Google Scholar
- 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
- 10.Rabinovich, M.I.: Usp. Fiz. Nauk125, 123 (1978) (Sov. Phys. Usp.21, 443 (1979))Google Scholar