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 recovere...

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Autores principales: Zimmermann, Martín G., Natiello, Mario Alberto, Solari, Hernán Gustavo
Publicado: 2001
Acceso en línea:https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_10541500_v11_n3_p500_Zimmermann
http://hdl.handle.net/20.500.12110/paper_10541500_v11_n3_p500_Zimmermann
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Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA) de Universidad de Buenos Aires
id paper:paper_10541500_v11_n3_p500_Zimmermann
record_format dspace
spelling paper:paper_10541500_v11_n3_p500_Zimmermann2023-06-08T16:03:05Z Global bifurcations in a laser with injected signal: Beyond Adler's approximation Zimmermann, Martín G. Natiello, Mario Alberto Solari, Hernán Gustavo 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. Fil:Zimmermann, M.G. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina. Fil:Natiello, M.A. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina. Fil:Solari, H.G. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina. 2001 https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_10541500_v11_n3_p500_Zimmermann http://hdl.handle.net/20.500.12110/paper_10541500_v11_n3_p500_Zimmermann
institution Universidad de Buenos Aires
institution_str I-28
repository_str R-134
collection Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA)
description 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.
author Zimmermann, Martín G.
Natiello, Mario Alberto
Solari, Hernán Gustavo
spellingShingle Zimmermann, Martín G.
Natiello, Mario Alberto
Solari, Hernán Gustavo
Global bifurcations in a laser with injected signal: Beyond Adler's approximation
author_facet Zimmermann, Martín G.
Natiello, Mario Alberto
Solari, Hernán Gustavo
author_sort Zimmermann, Martín G.
title Global bifurcations in a laser with injected signal: Beyond Adler's approximation
title_short Global bifurcations in a laser with injected signal: Beyond Adler's approximation
title_full Global bifurcations in a laser with injected signal: Beyond Adler's approximation
title_fullStr Global bifurcations in a laser with injected signal: Beyond Adler's approximation
title_full_unstemmed Global bifurcations in a laser with injected signal: Beyond Adler's approximation
title_sort global bifurcations in a laser with injected signal: beyond adler's approximation
publishDate 2001
url https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_10541500_v11_n3_p500_Zimmermann
http://hdl.handle.net/20.500.12110/paper_10541500_v11_n3_p500_Zimmermann
work_keys_str_mv AT zimmermannmarting globalbifurcationsinalaserwithinjectedsignalbeyondadlersapproximation
AT natiellomarioalberto globalbifurcationsinalaserwithinjectedsignalbeyondadlersapproximation
AT solarihernangustavo globalbifurcationsinalaserwithinjectedsignalbeyondadlersapproximation
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