Solitons in Femtosecond Lasers

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.