Observation of bound states of solitons in a passively mode-locked fiber laser

Abstract

We report on an experimental observation of bound states of solitons in a passively mode-locked fiber soliton ring laser. The observed bound solitons are stable and have discrete, fixed soliton separations that are independent of the experimental conditions. DOI: 10.1103/PhysRevA.64. 033814 PACS number͑s͒: 42.55.Wd, 42.81.Dp, 42.60.Fc, 42.65.Re Bound states of solitons known as high-order soliton solutions of the nonlinear Schrödinger equation ͑NLSE͒ have been extensively studied ͓1-5͔. A bound state of solitons of the NLSE is formed because two or more fundamental solitons coexist, and they have the same velocity and locate at the same position. Recently, another form of bound solitons has also been theoretically predicted ͓6͔ to exist in nonlinear dynamical systems such as the Ginzburg-Landau equation ͓7,8͔, and the coupled nonlinear Schrödinger equations ͓9͔. In contrast, the formation of these bound solitons is due to a direct interaction between the solitons, and the propagation of them is characterized by the fact that the solitons have discrete, fixed separations.It is well known that the dynamics of passively modelocked fiber soliton lasers can be well modeled by the complex Ginzburg-Landau equation ͓10,11͔. The same equation also describes the soliton propagation in the long-distance optical transmission lines ͓12-13͔. It would be expected that the predicted bound states of solitons could be observed in these systems. However, to the best of our knowledge, so far no bound states of solitons of this form have been experimentally confirmed in the systems.Two effects in optical fibers are detrimental to the formation of the predicted bound states of solitons. One is the Raman effect. Theoretical studies have shown that a strong Raman effect destroys the bound solitons ͓6͔. Another one is the random-phase variations of the solitons, which causes random soliton interactions. Although in fiber soliton lasers, the influence of the Raman effect can be significantly reduced by the effect of laser gain dispersion ͓14͔, no efficient way has been found to suppress the random relative phase variations between solitons. In this paper, we report on an experimental observation of bound states of solitons in a passively mode-locked fiber soliton laser. We confirm experimentally the existence of stable bound states of solitons with discrete, fixed soliton separations.Our experiment is conducted on a passively mode-locked fiber soliton ring laser. A schematic of the laser configuration is shown in Fig. 1. The laser cavity is about 10 m long, which comprises of a 4-m long 2000 ppm erbium-doped fiber with a group velocity dispersion of about Ϫ10 ps/nm km and two pieces of 3-m-long single-mode dispersion-shifted fiber, whose group velocity dispersion is Ϫ1 ps/nm km. The nonlinear polarization rotation technique ͓15͔ is used to achieve the self-started mode locking in the laser. To this end, a polarization-dependent isolator together with two polarization controllers is used to adjust the polarization of light in the cavi...

Soliton Molecules and Multisoliton States in Ultrafast Fibre Lasers: Intrinsic Complexes in Dissipative Systems

“…Afanasjev et al and Akhmediev et al also investigated analytically and numerically the existence and stability of bound states with π, 0 and ±π/2 phase differences [13][14][15]. So far bound states have been studied by simulated and/or experimental methods in types of fibre laser cavities, i.e., in soliton [16,17], stretched-pulse [18], gain-guided [19] and self-similar [20] regimes, as well as dissipative soliton regime associating with large net-normal dispersion and spectral filtering [21]. A lot of experimental observations of bound solitons have been reported in fibre lasers mode-locked by nonlinear polarization evolution (NPE) [22][23][24], nonlinear amplifying loop mirror (NALM) [8,25] and some real saturable absorbers (e.g., semiconductor saturable absorber mirror (SESAM) [26], carbon nanotubes (CNT) [27][28][29], graphene [30,31], topological insulator [32], molybdenum disulphide (MoS 2 ) [33] and black phosphorus [34]).…”

Dissipative soliton fiber lasers with higher-order nonlinearity, multiphoton absorption and emission, and random dispersion

“…Interaction of two DSs in a fiber laser may lead to the formation of a stable bound state with the group velocity different from that of a single soliton [26][27][28][29][30][31]. Further, collisions between bunched complexes of two or several DSs and a free one may lead to the absorption of the incident free soliton by the bound state [32,33].…”

Bound states of dispersion-managed solitons in a fiber laser at near zero dispersion

“…For the soliton-bunching mode, there are two submodes: loosely bound solitons, where the binding force between the solitons is weak. Therefore, the pulse separations can be easily altered by the environmental perturbations; and the multipulse solitons [6], where the solitons tightly bind together with discrete, fixed pulse separations. The multipulse solitons can even function as a unit and form states of bound multipulse solitons [7].…”