WIAS Preprint No. 975, (2004)

Q-switching instability in a mode-locked semiconductor laser


  • Rachinskii, Dmitri
  • Vladimirov, Andrei G.
    ORCID: 0000-0002-7540-8380

2010 Mathematics Subject Classification

  • 78A60 34C23

2008 Physics and Astronomy Classification Scheme

  • 42.60.Fc 42.55.Px 42.60.Mi 42.65.Pc 42.60.Gd


  • Semiconductor laser, mode-locking, Q-switching, delay differential equations, Neimark-Sacker bifurcation




We suggest analytic estimates for the Q-switching instability boundary of the continuous-wave mode-locking regime domain for a ring cavity semiconductor laser. We use a differential delay laser model that allows to assume large gain and loss in the cavity, which is a typical situation for this laser class. The slow saturable absorber approximation is applied to derive a map that describes the transformation of the pulse parameters after a round trip in the cavity. The Q-switching instability boundary is then obtained as a Neimark-Sacker bifurcation curve of this map. We study the dependence of this boundary on laser parameters and compare it with the boundaries obtained by the New stability criterion and by direct numerical analysis of the original differential model. Further modification of our approach, based on the hyperbolic secant ansatz for the pulse shape, is used to estimate the width and repetition rate of the mode locking pulses.

Appeared in

  • J. Opt. Soc. Amer. B Opt. Phys., 23 (2006) pp. 663-670.

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