Dynamics of Nonlinear and Dispersion Managed Solitons

Abstract

The relation between the fundamental parameters of energy and temporal duration of ultrashort pulses, under the condition of varying the average dispersion, are demonstrated both theoretically and experimentally in a solid-state femtosecond mode-locked laser. An asymptotic theory for nonlinear and dispersion managed solitons agrees well with the experimental data and demonstrates that the dominant factor in the pulse dynamics arises from the equilibrium established between the nonlinear Kerr effect and linear dispersion. Solitons are fascinating nonlinear phenomena that arise widely in physics. Solitons have a finite, localized energy and propagate unchanged. They form from the competition between linear dispersion and the nonlinear index of refraction. Surprisingly, when the sign of the linear dispersion periodically varies, as in long distance fiber communications, a new breed of soliton forms. The change in the sign of the dispersion causes these so-called dispersion managed (DM) solitons to temporally broaden and recompress or ‘‘breathe’’ as they propagate [1]. The prevalence of DM solitons has generated significant research toward understanding their behavior [2‐5]. To experimentally characterize the propagation dynamics of DM solitons, a medium amenable to systematic changes in the linear dispersion is required. Such characterization has proven difficult partly because of the complexity in systematically varying the linear dispersion. The ultrashort optical pulses propagating in solid-state modelocked lasers are also dispersion managed. However, the method by which these pulses are dispersion managed allows for systematic control over the cavity dispersion and thus, provides a near ideal environment to undertake such studies. In addition, these pulses experience a periodicity in the nonlinear refractive index, known as nonlinear management. Recent theoretical work in understanding their dynamics has shown novel behavior that is distinct from that of classical solitons [4]. Here, we report the first experimental demonstration of the systematic varying of the group velocity dispersion for a nonlinear and dispersion managed soliton. We show remarkable agreement between experiments and the DM theory of solitons for the scaling of the fundamental pulse properties of energy and temporal duration for the ultrashort pulses in a mode-locked laser. This study advances the understanding of the dynamics of the DM system in ultrashort pulsed mode-locked lasers, which have numerous important applications that rely upon pulse stability [6 ‐10]. In the classical theory of solitons, the nonlinear � ^ � ^