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Hopf Bifurcation in Symmetrically Coupled Lasers

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Dynamics, Bifurcation and Symmetry

Part of the book series: NATO ASI Series ((ASIC,volume 437))

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Abstract

The theory of equivariant Hopf bifurcation with D m × O(2)-symmetry is used to determine the possible periodic patterns of polarized light produced in a ring of lasers with saturable absorber. For three coupled lasers the coupled Maxwell-Bloch equations are integrated numerically, displaying many of the theoretically classified periodic solutions with maximal and submaximal symmetry.

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References

  1. G. Dangelmayr, W. Güttinger, J. Oppenländer, J. Tomes, and M. Wegelin. Coupled neural oscillators with D 3 × D 3-symmetry. Preprint, 1992.

    Google Scholar 

  2. G. Dangelmayr, W. Güttinger, and M. Wegelin. Hopf bifurcation with D 3 × D 3-symmetry. Journal of Applied Mathematics and Physics (ZAMP), 44:595–638, 1993.

    Article  MATH  Google Scholar 

  3. G. Dangelmayr and M. Neveling. Codimension-two bifurcations and interactions between differently polarised fields for laser with saturable absorber. Journal of Physics A: Mathematical and General, 22:1291–1301, 1989.

    Article  MathSciNet  Google Scholar 

  4. E. J. D’Angelo, E. Izaguirre, G. B. Mindlin, G. Huyet, L. Gil, and J. R. Tredicce. Spatiotemporal dynamics of lasers in the presence of an imperfect O(2) symmetry. Physical Review Letters, 68(25):3702–2705, 1992.

    Article  Google Scholar 

  5. B. Dionne, M. Golubitsky, and I. Stewart. Arrays of oscillators with internal and global symmetries. In preparation.

    Google Scholar 

  6. C. Elphick, E. Tirapegui, M. E. Brachet, P. Coullet, and G. Iooss. A simple global characterization for normal forms of singular vector fields. Physica D, 29:95–127, 1987.

    Article  MathSciNet  MATH  Google Scholar 

  7. T. Erneux and P. Mandel. Stationary, harmonic, and pulsed operations of an optically bistable laser with saturable absorber. II. Physical Review A, 30(4): 1901–1909, 1984.

    Article  MathSciNet  Google Scholar 

  8. M. Golubitsky, B. Dionne, and I. Stewart. Coupled cells: Wreath products and direct products. These proceedings.

    Google Scholar 

  9. M. Golubitsky and I. Stewart. Hopf bifurcation in the presence of symmetry. Archive of Rational Mechanics and Analysis, 87:107–165, 1985.

    Article  MathSciNet  MATH  Google Scholar 

  10. M. Golubitsky, I. Stewart, and D. G. Schaeffer. Singularities and Groups in Bifurcation Theory. Volume II, volume 69 of Applied Mathematical Sciences. Springer, 1988.

    Google Scholar 

  11. R.-D. Li and T. Erneux. Preferential instability in arrays of coupled lasers. Physical Review A, 46(7):4252–4260, 1992.

    Article  Google Scholar 

  12. R.-D. Li, P. Mandel, and T. Erneux. Periodic and quasiperiodic regimes in self-coupled lasers. Physical Review A, 41(9):5117–5126, 1990.

    Article  Google Scholar 

  13. P. Mandel and T. Erneux. Stationary, harmonic, and pulsed operations of an optically bistable laser with saturable absorber. I. Physical Review A, 30(4):1893–1901, 1984.

    Article  MathSciNet  Google Scholar 

  14. P. Mandel, R.-D. Li, and T. Erneux. Pulsating self-coupled lasers. Physical Review A, 39(5):2502–2508, 1989.

    Article  Google Scholar 

  15. J. Oppenländer. Zur Dynamik hierarchischer Oszillatorennetze. Diplomarbeit, Universität Tübingen, Fakultät für Physik, Institut für Informationsverarbeitung, 1992.

    Google Scholar 

  16. K. Otsuka. Self-induced turbulence and chaotic itinerancy in coupled laser systems. Physical Review Letters, 65(3):329–332, 1990.

    Article  Google Scholar 

  17. K. Otsuka and J.-L. Chern. Synchronization, attractor fission, and attractor fusion in a globally coupled laser system. Physical Review A, 45(7):5052–5055, 1992.

    Article  Google Scholar 

  18. K. Otsuka and J.-L. Chern. Dynamical spatial-pattern memory in globally coupled lasers. Physical Review A, 45(11):8288–8291, 1992.

    Article  Google Scholar 

  19. R. L. Ruiz, G. B. Mindlin, and C. P. Garcia. Mode-mode interaction for a CO2 laser with imperfect O(2) symmetry. Physical Review A, 47(l):500–509, 1993.

    Article  Google Scholar 

  20. M. Wegelin. Patterns of polarized light in symmetrically coupled lasers. In preparation.

    Google Scholar 

  21. M. Wegelin. Nichtlineare Dynamik raumzeitlicher Muster in hierarchischen Systemen. Dissertation, Universität Tübingen, Fakultät für Physik, Institut für Informationsverarbeitung, 1993.

    Google Scholar 

  22. C. O. Weiss and R. Vilaseca. Dynamics of Lasers. VCH Verlagsgesellschaft, 1991.

    Google Scholar 

  23. H. Zeghlache and V. Zehnlé. Theoretical study of a laser with injected signal. I. Analytical results on the dynamics. Physical Review A, 46(9):6015–6027, 1992.

    Article  Google Scholar 

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© 1994 Springer Science+Business Media Dordrecht

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Wegelin, M. (1994). Hopf Bifurcation in Symmetrically Coupled Lasers. In: Chossat, P. (eds) Dynamics, Bifurcation and Symmetry. NATO ASI Series, vol 437. Springer, Dordrecht. https://doi.org/10.1007/978-94-011-0956-7_28

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  • DOI: https://doi.org/10.1007/978-94-011-0956-7_28

  • Publisher Name: Springer, Dordrecht

  • Print ISBN: 978-94-010-4413-4

  • Online ISBN: 978-94-011-0956-7

  • eBook Packages: Springer Book Archive

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