Femtosecond solitons and double-kink solitons in passively mode-locked lasers

A cubic-quintic complex Ginzburg-Landau equation that describes the dynamics of the field in passively mode-locked lasers is considered. For passively mode-locked lasers with spectral filtering, we show analytically that the competing cubic-quintic nonlinearity induces propagating dissipative chirp-free solitonlike dark/bright solitons and double-kink solitons in our physical model. In the case of model without spectral filtering, the phase-engineering technique is employed to produce approximate bright and dark soliton solutions for investigating the dynamics of chirped femtosecond dissipative solitons in passively mode-locked lasers under consideration. Parameter domains are delineated in which the chirp-free and chirped pulses exist. We show that the nonlinear chirp associated with each pulse in the case of absence of spectral filtering is directly proportional to the intensity of the wave. Also, we show that the amplitude and the width of pulses and those of the corresponding chirping can be controlled by varying various parameters such as, for example, the linear parabolic gain dispersion, the nonlinear gain, the linear gain/loss, the nonlinear chirping parameter. Our theoretical results are confirmed by direct numerical simulations on the model equations.