Continuous-wave stability and multipulse structures in a universal complex Ginzburg–Landau model for passively mode-locked lasers with a saturable absorber

Abstract

The stability of continuous waves and the dynamics of multipulse structures are studied theoretically for a generic model of passively mode-locked fiber lasers with arbitrary nonlinearity. The model is characterized by a complex Ginzburg–Landau equation with a nonlinear term I m / ( 1 + Γ I ) n , where I is the field intensity, m and n are real numbers, and Γ is the saturation power. Fixed-point solutions of the governing equations reveal an interesting loci of singular points in the amplitude-frequency plane consisting of zero, one, or two fixed points, depending on the values of m and n . The continuous-wave stability is analyzed within the framework of the modulational-instability theory, and the results demonstrate a bifurcation in the continuous-wave amplitude growth rate and propagation constant characteristic of multiperiodic wave structures. In the full nonlinear regime, these multiperiodic wave structures turn out to be multipulse trains, unveiled via numerical simulations of the model nonlinear equation, the rich variety of which is highlighted by considering different combinations of values for the pair ( m , n ). The results are consistent with previous analyses of the dynamics of multipulse structures in several contexts of passively mode-locked lasers with a saturable absorber, as well as with predictions about the existence of multipulse structures and bound-state solitons in optical fibers with strong optical nonlinearity, such as cubic-quintic and saturable nonlinearities.