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Solitons in Femtosecond Lasers

  • Michel Piché
  • Jean-François Cormier
  • Allaoua Belahlou
  • Isabelle Richard
  • Xiaonong Zhu
  • Simon Deblois

Abstract

We have developed an analytical model to describe the steady-state operation of self-mode-locked lasers emitting pulses of very short duration. The model is based on the generalized nonlinear Schrödinger equation with dispersive terms up to fourth-order; we argue that a rigorous derivation of that equation cannot proceed through the slowly-varying envelope approximation. We show that the generalized nonlinear Schrödinger equation that includes second- and fourth-order dispersion has an analytical solution that takes the form of a bright soliton; the temporal profile of the field envelope of that solution is given as the square of a hyperbolic secant. The solution is stable in presence of a weak third-order dispersion. We have extended the analysis to include the effects of spectral filtering by the gain medium and laser mirrors, and the nonlinear gain associated to Kerr lensing; we then predict the existence of chirped solitary waves for which we have found an analytical expression. The predictions of the model are in a satisfactory agreement with the measurements reported by different groups on lasers emitting pulses of duration below 20 fs. We then describe our own experimental results obtained when second-order dispersion was progressively eliminated in a self-mode-locked Tirsapphire laser; we observed that, due to the residual third-order dispersion, the laser tended to produce short pulses with asymmetric spectral distributions.

Keywords

Optical Soliton Bright Soliton Pulse Spectrum Nonlinear Schrodinger Equation Nonlinear Gain 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer Science+Business Media New York 1997

Authors and Affiliations

  • Michel Piché
    • 1
  • Jean-François Cormier
    • 1
  • Allaoua Belahlou
    • 1
  • Isabelle Richard
    • 1
  • Xiaonong Zhu
    • 1
  • Simon Deblois
    • 1
  1. 1.Département de physique, Centre d’optique, photonique et laserUniversité LavalCité UniversitaireCanada

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