Narrow Results

Based on the extended scalar nonlinear Schrödinger equation, the influences of pumping schemes on the properties of dissipative soliton are investigated theoretically in passively mode-locked ytterbium-doped fiber laser with positive dispersion cavity. Results show that, under the conditions of the same initial total gain, the dissipative solitons obtained in the backward pumping fiber laser have the narrowest spectral width, shortest pulse duration and highest pulse peak power for the forward, backward and bidirectional pumping schemes, moreover, the linear fitting degree of pulse chirp is lowest. With the same gain saturation energy, the pulse energies of the dissipative solitons are equal for three pumping schemes, but the differences of output spectra and temporal waveforms increase as the gain saturation energy increases.

The dynamics of a chain of interacting active particles of Rayleigh-type is studied. Particles are interconnected via Morse potential forces. The steady-state modes (attractors) of the chain with periodic boundary conditions look like cnoidal waves with a uniform distribution of the particles’ density maxima along the chain. However, if the system starts from random initial conditions, a metastable state with nonuniform distribution of density maxima is formed. Characteristics of metastable states, excitation probability of different modes and their lifetimes are studied by numerical simulation.

We review recent results on periodic pulsations of the soliton parameters in a passively mode-locked fiber laser. Solitons change their shape, amplitude, width and velocity periodically in time. These pulsations are limit cycles of a dissipative nonlinear system in an infinite-dimensional phase space. Pulsation periods can vary from a few to hundreds of round trips. We present a continuous model of a laser as well as a model with parameter management. The results of the modeling are supported with experimental results obtained using a fiber laser.

The perturbations of chirped dissipative solitons are analyzed in the spectral domain. It is shown, that the structure of the perturbed chirped dissipative soliton is highly nontrivial and has a tendency to an enhancement of the spectral perturbations especially at the spectrum edges, where the irregularities develop. Even spectrally localized perturbations spread over a whole soliton spectrum. As a result of spectral irregularity, the chaotic dynamics develops due to the spectral loss action. In particular, the dissipative soliton can become fragmented though remains localized.