Advertisement

Regular and Chaotic Dynamics

, Volume 20, Issue 2, pp 173–183 | Cite as

Stability of continuous wave solutions of one laser model with large delay

Article
  • 54 Downloads

Abstract

Analysis of a delay differential laser model with large delay is presented. Sufficient conditions for existence of continuous wave solutions are found. It is shown that parameters determining the main part of asymptotics of these solutions lie on a bell-like curve. Sufficient conditions for stability of continuos wave solutions are found. The number of stability regions on bell-like curves is studied. It is proved that more than one region of stability may exist on these curves. It is shown that solutions with the same main part of asymptotics may have different stability properties if we change the value of linewidth enhancement factor. A mechanism for the destabilization of continuous wave solutions is found.

Keywords

large delay stability laser dynamics asymptotic methods 

MSC2010 numbers

34K13 34K20 37N20 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Slepneva, S., Kelleher, B., O’Shaughnessy, B., Hegarty, S.P., Vladimirov, A.G., and Huyet, G., Dynamics of Fourier Domain Mode-Locked Lasers, Optics Express, 2013, vol. 21, no. 16, pp. 19240–19251.CrossRefGoogle Scholar
  2. 2.
    Vladimirov, A.G. and Turaev, D.V., Model for Passive Mode-Locking in Semiconductor Lasers, Phys. Rev. A, 2005, vol. 72, no. 3, 033808, 13 pp.CrossRefGoogle Scholar
  3. 3.
    Vladimirov, A.G., Turaev, D., and Kozyreff, G., Delay Differential Equations for Mode-Locked Semiconductor Lasers, Opt. Lett., 2004, vol. 29, no. 11, pp. 1221–1223.CrossRefGoogle Scholar
  4. 4.
    Vladimirov, A.G. and Turaev, D.V., A New Model for a Mode-Locked Semiconductor Laser, Radiophys. Quantum El., 2004, vol. 47, nos. 10–11, pp. 769–776.CrossRefGoogle Scholar
  5. 5.
    Kashchenko, A.A., Stability of the Simplest Periodic Solutions in the Stuart — Landau Equation with Large Delay, Automatic Control Comput. Sci., 2013, vol. 47, no. 7, pp. 566–570; see also: Modelirovanie i Analiz Informatsionnykh Sistem, 2012, no. 3, pp. 136–141.CrossRefGoogle Scholar
  6. 6.
    Wu, J., Theory and Applications of Partial Functional-Differential Equations, Appl. Math. Sci., vol. 119, New York: Springer, 1996.CrossRefMATHGoogle Scholar
  7. 7.
    Kashchenko, S.A., Application of Method of Normalization for Studying of Differential-Difference Equations with Small Multiplier for Derivative, Differ. Uravn., 1989, vol. 25, no. 8, pp. 1448–1451 (Russian).MATHMathSciNetGoogle Scholar

Copyright information

© Pleiades Publishing, Ltd. 2015

Authors and Affiliations

  1. 1.Mathematical DepartmentP.G. Demidov Yaroslavl State UniversityYaroslavlRussia

Personalised recommendations