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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todo:paper_10541500_v11_n3_p500_Zimmermann2023-10-03T16:00:39Z Global bifurcations in a laser with injected signal: Beyond Adler's approximation Zimmermann, M.G. Natiello, M.A. Solari, H.G. 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. JOUR info:eu-repo/semantics/openAccess http://creativecommons.org/licenses/by/2.5/ar 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. |
| format |
JOUR |
| author |
Zimmermann, M.G. Natiello, M.A. Solari, H.G. |
| spellingShingle |
Zimmermann, M.G. Natiello, M.A. Solari, H.G. Global bifurcations in a laser with injected signal: Beyond Adler's approximation |
| author_facet |
Zimmermann, M.G. Natiello, M.A. Solari, H.G. |
| author_sort |
Zimmermann, M.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 |
| url |
http://hdl.handle.net/20.500.12110/paper_10541500_v11_n3_p500_Zimmermann |
| work_keys_str_mv |
AT zimmermannmg globalbifurcationsinalaserwithinjectedsignalbeyondadlersapproximation AT natielloma globalbifurcationsinalaserwithinjectedsignalbeyondadlersapproximation AT solarihg globalbifurcationsinalaserwithinjectedsignalbeyondadlersapproximation |
| _version_ |
1807316860141568000 |