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The dynamics and stability of continuous-wave and multi-pulse structures arestudied theoretically, for a generalized model of passively mode-locked fiberlaser with an arbitrary nonlinearity. The model is characterized by a complexGinzburg-Landau equation with saturable nonlinearity of a general form($I^m/(1+\Gamma I)^n$), where $I$ is the field intensity, $m$ and $n$ are twopositive real numbers and $\Gamma$ is the optical field saturation power. Theanalysis of fixed-point solutions of the governing equations, reveals aninteresting loci of singular points in the amplitude-frequency plane consistingof zero, one or two fixed points depending upon the values of $m$ and $n$. Thestability of continuous waves is analyzed within the framework of themodulational-instability theory, results demonstrate a bifurcation in thecontinuous-wave amplitude growth rate and propagation constant characteristicof multi-periodic wave structures. In the full nonlinear regime thesemulti-periodic wave structures turn out to be multi-pulse trains, unveiled vianumerical simulations of the model nonlinear equation the rich variety of whichis highlighted by considering different combinations of values for the pair($m$,$n$). Results are consistent with previous analyses of the dynamics ofmulti-pulse structures in several contexts of passively mode-locked lasers withsaturable absorber, as well as with predictions about the existence ofmulti-pulse structures and bound-state solitons in optical fibers with strongoptical nonlinearity such as cubic-quintic and saturable nonlinearities.

journal of the optical society of america. b, optical physics/journal of the optical society of america. b, online

Continuous-wave stability and multi-pulse structures in a universal  Complex Ginzburg-Landau model for passively mode-locked lasers with saturable  absorber