SpringerLink
Log in

Synchronized attractors and phase entrained with cavity loss of the coupled laser’s map

  • Regular Article – Nonlinear Dynamics
  • Published:
The European Physical Journal D Aims and scope Submit manuscript

Abstract

The laser differential equations are transformed into identical coupled maps. The laser cavity losses are studied analytically and numerically which provide important results. Phase and spatiotemporal synchronized attractors are observed via quasi-chaos under a certain range of control parameters, and symmetry breaking of chaotic attractors occur due to collisions with their basin boundaries, and transpire differently from the previous attractors. During the numerical simulations it is found that the sequence of strange attractors repeats with further increase in the coupling strength, which are orthogonal mirror images (the dynamics of the system are the same at different values of control parameters). Moreover, this article provides a technique to develop the lasing system which can be stable for not only large values of controlling parameters but also when there exists thermal fluctuation.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Subscribe and save

Springer+ Basic
EUR 32.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or Ebook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Price includes VAT (Germany)

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5

Similar content being viewed by others

Data Availability Statement

his manuscript has no associated data or the data will not be deposited. [Authors’ comment: This is a theoretical study and no experimental data. So data sharing is not applicable to this article.]

References

  1. A. Pikovsky, M. Rosenblum, J. Kurths, Synchronization, A Universal Concept in Nonlinear Sciences (Cambridge University Press, Cambridge, 2001)

    Book  Google Scholar 

  2. C. Feillet, P. Krusche, F. Tamanini, R.C. Janssns, M.J. Downey, P. Martin, M. Teboul, S. Saito, F.A. Levi, T. Bretscheirder, G.T.J. van der Horst, F. Delaunay, PANS 11, 9828–9833 (2014)

    Article  Google Scholar 

  3. W. Kinzel, A. Englert, M. Zigzag, I. Kanter, Phys. Rev. E. 97, 056207 (2009)

    Article  ADS  Google Scholar 

  4. M. Abdul, F. Saif, 6th chaotic Modeling and Simulation International conference 11–14 June 2013 Istanbul (Synchronized Attractors and Phase Entrained Chaos, Turkey, 2013)

  5. C. Miguel, Sorian, J. Garcia-Ojalvo, C.R. Mirasso, I. Fisher, Complex photons: dynamics and applications of delay-coupled semiconductors lasers. Rev. Mod. Phys. 85, 421 (2013)

    Article  ADS  Google Scholar 

  6. S. Guan, G.W. Wei, C.H. Lai, Phys. Rev. E 69, 066214 (2004)

    Article  ADS  Google Scholar 

  7. S. Sinha, Phys. Rev. E 66, 016209 (2008)

    Article  ADS  Google Scholar 

  8. H.G. Winful, L. Rahman, Phys. Rev. Lett. 65, 13 (1990)

    Article  ADS  MathSciNet  Google Scholar 

  9. A. Englert, S. Heiligenthal, W. Kinzel, I. Kanter, Phys. Rev. E 83, 046222 (2011)

    Article  ADS  Google Scholar 

  10. W.T. Silfast, Laser Fundamentals, 2nd edn. (Cambridge University Press, Cambridge, 2004)

    Book  Google Scholar 

  11. M. Mandel, E. Wolf, Optical Coherence and Quantum Optics (Cambridge University Press, Cambridge, 1995)

    Book  Google Scholar 

  12. M. Abdul, U. Farooq, J. Akbar, F. Saif, Discrete Dynamical Laser Equation for Critical Onset of Bistability, Entanglement and Disappearance, Laser Physics 28, 6 (2018)

    Google Scholar 

  13. W.E. Lamb, Phys. Rev. 134, 1429 (1964)

    Article  ADS  Google Scholar 

  14. M.M. Tehrani, L. Mandel, Mode competition in a ring laser at line center. Opt. Commun. 16, 16 (1976)

    Article  ADS  Google Scholar 

  15. R. Blumel, W.P. Reinhardt, Chaos in Atomic Physics (Cambridge University Press, Cambridge, 1997)

    Book  Google Scholar 

  16. K. Kaneko, Progress Theor. Phys. 69, 1427 (1983)

    Article  ADS  Google Scholar 

  17. G. Tanaka, M.A.F. Sanjuán, K. Aihara, Phys. Rev. E 71, 016219 (2005)

    Article  ADS  Google Scholar 

  18. M. Ghorbani, M. Mehta, R. Bruinsma, A.J. Levine, Phys. Rev. E 85, 021908 (2012)

    Article  ADS  Google Scholar 

  19. C. Grebogi, E. Ott, J.A. Yorke, Phys. Rev. Lett. 48, 1507 (1982)

    Article  ADS  MathSciNet  Google Scholar 

  20. X. Wang, C. Luo, Int. J. Mode. Phys. B. 22, 427 (2008)

    ADS  Google Scholar 

  21. V. Astakhov, A. Shabunin, T. Kapitaniak, V. Anishchenko, Phys. Rev. L. 79, 6 (1997)

    Article  ADS  Google Scholar 

  22. V. Astakhov, A. Shabunin, Phys. Rev. E 63, 056212 (2001)

    Article  ADS  Google Scholar 

  23. K. Falconer, The Geometry of Fractal Sets (Cambridge University Press, Cambridge, 1985)

    Book  Google Scholar 

  24. A. Jakobsen, Physica D 237, 3382 (2008)

    Article  ADS  MathSciNet  Google Scholar 

  25. M. Rosenblum, A. Pikovsky, J. Kurths, Phys. Rev. Lett. 76, 1804 (1996)

    Article  ADS  Google Scholar 

  26. G. Yan, M. Tung, J.-M. Yuan, D.H. Feng, L.M. Narducci, Phys. Rev. Lett. 52, 9 (1984)

    Article  MathSciNet  Google Scholar 

  27. I. Franovic, K. Todorovic, N. Vasovic, N. Buric, Phys. Rev. Lett. 108, 094101 (2012)

    Article  ADS  Google Scholar 

  28. M. Rosenblum, A. Pikovsky, J. Kurths, Europhys. Lett. 34, 165 (1996)

    Article  ADS  Google Scholar 

  29. H. Fujisaka, T. Yamada, Prog. Theor. Phys. 69, 32 (1983)

    Article  ADS  Google Scholar 

  30. L.M. Pecora, T.L. Carroll, Phys. Rev. Lett. 64, 821 (1990)

    Article  ADS  MathSciNet  Google Scholar 

  31. M. de Sousa Vieira, A.J. Lichtenberg, M.A. Lieberman, Int. J. Bifurc. Chaos Appl. Sci. Eng. 1, 691 (1991)

  32. A. Garfinkel, Self-organizing Systems (Plenum Press, New York, 1987)

    Google Scholar 

  33. J.M. Yuan, M.W. Tung, D.H. Feng, L.M. Narducci, Phys. Rev. A 28, 1662 (1983)

    Article  ADS  MathSciNet  Google Scholar 

  34. Z.T. Zhusubaliyev, E. Mosekilde, Phys. Lett. A 373, 946 (2011)

    Article  ADS  Google Scholar 

  35. T.S. Parker, L.O. Chua, Practical Numerical Algorithms for Chaotic System (Springer, New York, 1989)

    Book  Google Scholar 

  36. K. Ikeda, K. Matsumoto, Physica Amstredam 29D, 223 (1987)

    Article  ADS  Google Scholar 

  37. K. Ikeda, K. Otsuka, K. Matsumoto, Prog. Theor. Phys. Suppl. 30, 295 (1989)

    Article  ADS  Google Scholar 

  38. J. Briggs, F.D. Peat, The Turbulent Mirror (Harper and Row Press, New York, 1989)

    Google Scholar 

  39. J.P. Goedgebuer, L. Larger, H. Porte, Phys. Rev. Lett. 80, 2249 (1998)

    Article  ADS  Google Scholar 

  40. J.P. Goedgebuer, L. Larger, H. Porte, F. Delorme, Phys. Rev. E. 57, 2795 (1998)

    Article  ADS  Google Scholar 

  41. O.E. Rossler, The Chaotic Hierarchy. In A Chaotic Hierarchy (Singapore World Scientific, Singapore, 1991)

    MATH  Google Scholar 

  42. S. Wiggins, Global Bifurcations and Chaos: Analytical Methods (Springer-Verlag, New York, New York, 1988)

    Book  Google Scholar 

Download references

Acknowledgements

This project is supported by CAS-TWAS and The Fundamental Research Fund for the Central Universities. I am grateful to Professor Bao for his support and useful discussions.

Author information

Authors and Affiliations

  1. School of Electronic Science and Engineering, University of Electronic Science and Technology of China, Chengdu, China

    M. Abdul

  2. Department of Physical Science and Technology, Sichuan University, Chengdu, Sichuan, China

    M. Abdul & Zhiyou Zhang

  3. Department of Physics, Riphah International University Lahore, Punjab, Pakistan

    Altaf Ur Rahman

  4. Institute of Nano Science and Technology, University of Science and Technology of China, Hefei, China

    Min**g Chen

  5. The Abdus Salam International Centre for Theoretical Physics (ICTP), Trieste, Italy

    Jehan Akbar

  6. Department of Physics, Hazara University Mansehra, Mansehra, Pakistan

    Jehan Akbar

Authors
  1. M. Abdul
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Altaf Ur Rahman
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Min**g Chen
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Jehan Akbar
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. Zhiyou Zhang
    View author publications

    You can also search for this author in PubMed Google Scholar

Contributions

All authors contributed equally to the paper.

Corresponding author

Correspondence to M. Abdul.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Abdul, M., Rahman, A.U., Chen, M. et al. Synchronized attractors and phase entrained with cavity loss of the coupled laser’s map. Eur. Phys. J. D 76, 51 (2022). https://doi.org/10.1140/epjd/s10053-022-00370-1

Download citation

  • Received:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1140/epjd/s10053-022-00370-1

Search

Navigation