Global bifurcations in a Laser with injected signal: beyond Adler's approximation

ZIMMERMANN M. G., NATIELLO M. A., SOLARI H. G.

CHAOS AN INTERDISCIPLINARY JR OF NONLINEAR SCIENCE

Año: 2001 vol. 11 p. 500 - 513

1054-1500

We discuss the dynamics in the laser with an injected signal from a perturbative point of viewshowing how different aspects of the dynamics get their definitive character at different orders in theperturbation scheme. At the lowest order Adler´s equation Proc. IRE 34, 351 1946 is recovered.More features emerge at first order including some bifurcations sets and the global reinjectionconjectured in Physica D 109, 293 1997 . The type of codimension-2 bifurcations present can onlybe resolved at second order. We show that of the two averaging approximations proposed Opt.Commun. 111, 173 1994 ; Quantum Semiclassic. Opt. 9, 797 1997 ; Quantum Semiclassic. Opt.8, 805 1996 differing in the second order terms, only one is accurate to the order required, hence,solving the apparent contradiction among these results. We also show in numerical studies how a                        homoclinic orbit of the Sil´nikov type, bifurcates into a homoclinic tangency of a periodic orbit ofvanishing amplitude. The local vector field at the transition point contains a Hopf-saddle-nodesingularity, which becomes degenerate and changes type. The overall global bifurcation is ofcodimension-3. The parameter governing this transition is , the cavity detuning with respect to theatomic frequency of the laser. © 2001 American Institute of Physics. DOI: 10.1063/1.1397757