Global bifurcations in a laser with injected signal: Beyond Adler's approximation.
We discuss the dynamics in the laser with an injected signal from a perturbative point of view showing how different aspects of the dynamics get their definitive character at different orders in the perturbation 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 reinjection conjectured in Physica D 109, 293 (1997). The type of codimension-2 bifurcations present can only be 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 of vanishing amplitude. The local vector field at the transition point contains a Hopf-saddle-node singularity, which becomes degenerate and changes type. The overall global bifurcation is of codimension-3. The parameter governing this transition is theta, the cavity detuning (with respect to the atomic frequency) of the laser. (c) 2001 American Institute of Physics.
Zimmermann
Martin G.
MG
Departamento de Fisica, Facultad Ciencias Exactas y Naturales, Universidad de Buenos Aires, Ciudad Universitaria, 1428 Buenos Aires, Argentina.
Natiello
Mario A.
MA
Solari
Hernan G.
HG