Discrete family of dissipative soliton pairs in mode-locked fiber lasers

We numerically investigate the formation of soliton pairs (bound states) in mode-locked fiber ring lasers. In the distributed model (complex cubic-quintic Ginzburg-Landau equation) we observe a discrete family of soliton pairs with equidistantly increasing peak separation. This family was identified by two alternative numerical schemes and the bound state instability was disclosed by a linear stability analysis. Moreover, similar families of unstable bound state solutions have been found in a more realistic lumped laser model with an idealized saturable absorber (instantaneous response). We show that a stabilization of these bound states can be achieved when the finite relaxation time of the saturable absorber is taken into account. The domain of stability can be controlled by varying this relaxation time.