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The complex Ginzburg-Landau equation has been used extensively to describevarious non-equilibrium phenomena. In the context of lasers, it models thedynamics of a pulse by averaging over the effects that take place inside thecavity. Ti:sapphire femtosecond lasers, however, produce pulses that undergosignificant changes in different parts of the cavity during each round-trip.The dynamics of such pulses is therefore not adequately described by an averagemodel that does not take such changes into account. The purpose of this work isseveralfold. First we introduce the dispersion-managed Ginzburg-Landau equation(DMGLE) as an average model that describes the long-term dynamics of systemscharacterized by rapid variations of dispersion, nonlinearity and gain in ageneral setting, and we study the properties of the equation. We then explainhow in particular the DMGLE arises for Ti:sapphire femtosecond lasers and wecharacterize its solutions. In particular, we show that, for moderate values ofthe gain/loss parameters, the solutions of the DMGLE are well approximated bythose of the dispersion-managed nonlinear Schrodinger equation (DMNLSE), andthe main effect of gain and loss dynamics is simply to select one among theone-parameter family of solutions of the DMNLSE.

The dispersion-managed Ginzburg-Landau equation and its application to femtosecond lasers