Discrete family of soliton pairs in mode-locked fiber laser

The interaction of solitary-pulses (SPs) in optical systems attracts great attention since the experimental observation of stable SPs. The formation of different types of two-peak solutions or so called bound states (BSs) in dissipative systems was theoretically proposed and experimentally confirmed. One prominent dissipative optical system, where BSs have been experimentally proven, is the mode-locked fiber laser. The present work is devoted to the discrete family of stationary BS solutions derived from the complex cubic-quintic Ginzburg-Landau equation (CQGLE). In the numerical simulations a discrete family of stationary two-soliton solutions with different peak-to-peak separation is observed, which is identified as different BS levels. These levels are obtained by means of two numerical schemes, viz. the solution of the evolution or the stationary problem. Based on the results from the stationary analysis, a linear stability analysis is carried out. The obtained growth rates perfectly coincide with the results of the propagation model.