WIAS Preprint No. 1737, (2012)

Spontaneous motion of cavity solitons induced by a delayed feedback


  • Tlidi, Mustapha
    ORCID: 0000-0003-3660-2524
  • Averlant, Etienne
  • Vladimirov, Andrei G.
    ORCID: 0000-0002-7540-8380
  • Panajotov, Krassimir

2010 Mathematics Subject Classification

  • 78A60 37L10

2008 Physics and Astronomy Classification Scheme

  • 05.45.-a 02.30.Ks 42.65.-k


  • semiconductor lasers, delayed feedback, Swift-Hohenberg equation, localized structures, bifurcations




We consider a broad area Vertical-Cavity Surface Emitting Laser (VCSEL) operating below the lasing threshold and subject to optical injection and time-delayed feedback. We derive a generalized delayed Swift-Hohenberg equation for the VCSEL system which is valid close to the nascent optical bistability. We first characterize the stationary cavity solitons by constructing their snaking bifurcation diagram and by showing clustering behavior within the pinning region of parameters. Then we show that the delayed feedback induces a spontaneous motion of two-dimensional cavity solitons in an arbitrary direction in the transverse plane. We characterize moving cavity solitons by estimating their threshold and calculating their velocity. Numerical 2D solutions of the governing semiconductor laser equations are in close agreement with those obtained from the delayed generalized Swift- Hohenberg equation.

Download Documents