Theoretical Studies of Active, Synchronous, and Hybrid Mode-Locking

  • J. M. Catherall
  • G. H. C. New
Conference paper
Part of the Springer Series in Chemical Physics book series (CHEMICAL, volume 38)


In previous work, we have shown how self-consistent solutions for both active mode-locking (AML) and mode-locking by synchronous pumping (MLSP) may be derived from simple difference equations [1–2]. Using a rate-equation model for the gain and a unidirectional ring cavity with the bandwidth controlled by a Fabry-Perot etalon, we demonstrated in the case of MLSP that for positive values of the cavity mismatch ... (= pump period — cavity period), steady-state profiles can be generated from a first-order difference equation (the “stepping algorithm). The simplicity of this solution arises from the fact that for ... > 0, the mismatch (like the filter) introduces delay, and both processes therefore transfer information across the pulse profile from front to back. For ... < 0 however, the information flows are opposed; the profile is then governed by a second-order difference equation and recourse to numerical methods is unavoidable. The set of steady-state solutions presented in Fig. 1 indicates that as ... is decreased, the profiles are forced into the region ahead of threshold, until a point is reached where they broaden abruptly; this effect has frequently been observed experimentally (e.g. [3]).


Spontaneous Emission Saturable Absorber Pulse Profile Stochastic Source Cavity Period 
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  1. [1]
    J.M. Catherall, G.H.C. New and P.M. Radmore, Opt. Lett., 7, 319 (1982).ADSCrossRefGoogle Scholar
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    G.H.C. New, L.A. Zenteno and P.M. Radmore, Opt. Commun., 48, 149 (1983).ADSCrossRefGoogle Scholar
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    C.P. Ausschnitt, R.K. Jain and J.P. Heritage, IEEE J. Quantum Electron., QE-15, 912 (1979).Google Scholar
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    J.A. Fleck, Phys. Rev. B, 1, 84 (1970).Google Scholar
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    F.A. van Goor, Opt. Commun., 45, 404 (1983).ADSCrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1984

Authors and Affiliations

  • J. M. Catherall
    • 1
  • G. H. C. New
    • 1
  1. 1.Department of PhysicsImperial College of Science and TechnologyLondonUK

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