Skip to main content
SpringerLink
Log in

A Quasi Separable Dissipative Maxwell–Bloch System for Laser Dynamics

  • Published:
Qualitative Theory of Dynamical Systems Aims and scope Submit manuscript

Abstract

The Maxwell–Bloch dissipative equations describe laser dynamics. Under a simple condition on the parameters there exist two time-dependent first integrals, that allow a nonstandard separation of variables in the equations. That condition has a precise physical meaning. The separated differential equations lead naturally to simple conjectures on the asymptotic behavior of the physical variables.

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

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

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

References

  1. Arecchi, F.T., Bonifacio, R.: Theory of optical maser amplifiers IEEE. J. Quantum Electron. 1, 169–178 (1965)

    Article  Google Scholar 

  2. Arecchi, F.T., Meucci, R.: Chaos in lasers. Scholarpedia 3(9), 7066 (2008)

    Article  Google Scholar 

  3. Gorni, G., Zampieri, G.: Revisiting Noether’s theorem on constants of motion. J. Nonlinear Math. Phys. 21(1), 43–73 (2014)

    Article  MathSciNet  MATH  Google Scholar 

  4. Gorni, G., Zampieri, G.: Nonlocal variational constants of motion in dissipative dynamics (Submitted by Jean Mawhin). Differ. Integral Equ. 30, 631–640 (2017)

    MATH  Google Scholar 

  5. Gorni, G., Zampieri, G.: Nonstandard separation of variables for the Maxwell–Bloch conservative system. São Paulo J. Math. Sci. 12(1), 146–169 (2018)

    Article  MathSciNet  MATH  Google Scholar 

  6. Gorni, G., Zampieri, G.: Nonlocal and nonvariational extensions of Killing-type equations. Discrete Contin. Dyn. Syst. Ser. S 11(4), 675–689 (2018)

    MathSciNet  MATH  Google Scholar 

  7. Haken, H.: Analogy between higher instabilities in fluids and lasers. Phys. Lett. 53A(1), 77–78 (1975)

    Article  Google Scholar 

  8. Haken, H.: Light, Laser Light Dynamics, vol. 2. North-Holland Physics Publishing (1985)

  9. Johnson, L.E.: Optically pumped pulsed crystal lasers other than ruby. In: Levine, A.K. (ed.) Lasers, A Series of Advances, vol. 1. Dekker, New York (1996)

    Google Scholar 

  10. McNeil, B.: Due credit for Maxwell–Bloch equations. Nat Photonics 9, 2017 (2015)

    Article  Google Scholar 

  11. Newell, A.C., Moloney, J.: Nonlinear Optics. Addison Wesley, Boston (1992)

    MATH  Google Scholar 

  12. Pucacco, G., Rosquist, K.: Energy dependent integrability. J. Geom. Phys. 115, 16–27 (2017)

    Article  MathSciNet  MATH  Google Scholar 

  13. Tredicce, J.R., Arecchi, F.T., Puccioni, G.P., Poggi, A., Gadomski, W.: Dynamic behavior and onset of low-dimensional chaos in a modulated homogeneously broadened single-node laser: experiments and theory. Phys. Rev. A 34(3), 2073–2081 (1986)

    Article  Google Scholar 

  14. Tredicce, J.R., Arecchi, F.T., Lippi, G.L., Puccioni, G.P.: Instabilities in lasers with an injected signal. J. Opt. Soc. Am. B 2(1), 173–183 (1985)

    Article  Google Scholar 

Download references

Acknowledgements

The research was done under the auspices of INdAM (Istituto Nazionale di Alta Matematica). G.Z. thanks Antonio Marigonda for his help in the affiliation to the Department.

Author information

Authors and Affiliations

  1. Dipartimento di Matematica e Informatica, Università di Udine, via delle Scienze 208, 33100, Udine, Italy

    Gianluca Gorni

  2. Institut de Physique de Nice, UMR7010, Université de Nice - Sophia Antipolis, CNRS, 1361 route des Lucioles, 06560, Valbonne, France

    Stefania Residori

  3. Dipartimento di Informatica, Università di Verona, strada Le Grazie 15, 37134, Verona, Italy

    Gaetano Zampieri

Authors
  1. Gianluca Gorni
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Stefania Residori
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Gaetano Zampieri
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Gaetano Zampieri.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Gorni, G., Residori, S. & Zampieri, G. A Quasi Separable Dissipative Maxwell–Bloch System for Laser Dynamics. Qual. Theory Dyn. Syst. 18, 371–381 (2019). https://doi.org/10.1007/s12346-018-0290-3

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s12346-018-0290-3

Keywords

Mathematics Subject Classification

Search

Navigation