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Abstract:

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 6, the cavity detuning (with respect to the atomic frequency) of the laser. © 2007 American Institute of Physics.

Registro:

Documento: Artículo
Título:Global bifurcations in a laser with injected signal: Beyond Adler's approximation
Autor:Zimmermann, M.G.; Natiello, M.A.; Solari, H.G.
Filiación:Departamento de Física, Fac. Ciencias Exactas y Naturales, Universidad de Buenos Aires, 1428 Buenos Aires, Argentina
Ctr. for Mathematical Sciences (LTH), Lund University, S-221 00 Lund, Sweden
Año:2001
Volumen:11
Número:3
Página de inicio:500
Página de fin:513
DOI: http://dx.doi.org/10.1063/1.1397757
Título revista:Chaos
Título revista abreviado:Chaos
ISSN:10541500
Registro:https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_10541500_v11_n3_p500_Zimmermann

Referencias:

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  • Krauskopf, B., Van Der Graaf, W.A., Lenstra, D., (1997) Quantum Semiclassic. Opt., 9, p. 797
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Citas:

---------- APA ----------
Zimmermann, M.G., Natiello, M.A. & Solari, H.G. (2001) . Global bifurcations in a laser with injected signal: Beyond Adler's approximation. Chaos, 11(3), 500-513.
http://dx.doi.org/10.1063/1.1397757
---------- CHICAGO ----------
Zimmermann, M.G., Natiello, M.A., Solari, H.G. "Global bifurcations in a laser with injected signal: Beyond Adler's approximation" . Chaos 11, no. 3 (2001) : 500-513.
http://dx.doi.org/10.1063/1.1397757
---------- MLA ----------
Zimmermann, M.G., Natiello, M.A., Solari, H.G. "Global bifurcations in a laser with injected signal: Beyond Adler's approximation" . Chaos, vol. 11, no. 3, 2001, pp. 500-513.
http://dx.doi.org/10.1063/1.1397757
---------- VANCOUVER ----------
Zimmermann, M.G., Natiello, M.A., Solari, H.G. Global bifurcations in a laser with injected signal: Beyond Adler's approximation. Chaos. 2001;11(3):500-513.
http://dx.doi.org/10.1063/1.1397757