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...

We have experimentally observed continuous-wavelength tuning in a passively mode-locked fiber ring laser. Depending on the polarization setting, two separated tuning ranges are observed. We show that the wavelength tuning is a result of the existence of birefringence in the laser cavity. We have also shown that the same mechanism is responsible for the power asymmetry of sidebands appearing in the soliton spectrum.

Experimental study of the soliton dynamics of a passively mode-locked fiber ring laser revealed a state of bound-soliton operation in the laser, where two solitons bind together tightly with fixed pulse separation. We further report on the properties of the bound-soliton emission of the laser. In particular, we demonstrate both experimentally and numerically that, like the single-pulse soliton operation of the laser, the bound soliton emission is another intrinsic feature of the laser. DOI: 10.1103/PhysRevA.66.033806 PACS number͑s͒: 42.55.Wd, 42.81.Dp, 42.60.Fc, 42.65.Sf Self-started, passively mode-locked fiber lasers as a potential source of ultrashort optical pulses have been intensively investigated ͓1-7͔. A generic feature of the lasers found is that under suitable operation conditions, they can emit the so-called soliton pulses-optical pulses that are sech-form shaped and have nearly transform-limited bandwidth-duration product. Under a soliton operation, not only the output pulses of the lasers become ultrashort, but also the pulse-to-pulse energy and peak power become ultrastable, which was found to be quantum noise limited ͓8͔.Soliton emission of the lasers is a natural consequence of the nonlinear pulse propagation in the fiber cavity, where due to the balanced action between the fiber-optical Kerr effect and the cavity dispersion on a pulse, the shape and duration remain unchanged with the propagation. Although in a passively mode-locked fiber laser, apart from the optical fiber other optical components such as the gain medium and output coupler coexist in the cavity, which affect the detailed dynamics of the formed pulses. It is nevertheless demonstrated that under weak influence of them, the average dynamics of the solitons could be well described by the nonlinear Schrödinger equation ͓9͔. In this paper we report on the states of bound-soliton emission and their properties in a passively mode-locked fiber ring laser. We show both experimentally and numerically that apart from the single-pulse soliton emission, the laser can also emit stable, closely spaced soliton pairs. In particular, when operating in the regime, the bound-soliton pair is the only stable structure of the solitary wave in the laser, as a unit, it has exactly the same features as those of a single-pulse soliton. For this reason, we refer the fiber laser as a bound-soliton fiber laser.Bound states of solitons have recently been predicted in the coupled nonlinear Schrödinger equations ͓10͔ and the quintic complex Ginzburg-Landau equation ͓11,12͔. Formation of bound solitons was explained as a result of direct soliton interaction. Solitons formed in these systems have an oscillating tail; when they interact, their effective interaction potential has spatial local minima, which give rise to stable, bound solitons. Bound solitons thus formed are characterized as having fixed, discrete pulse separations independent of soliton propagation. For a passively mode-locked fiber laser, when the influences of laser gain and cavity losses ͑and...

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We report on the existence of a different form of solitary waves in a passively mode-locked fiber ring laser. Studying the interaction between bound solitons observed in a passively mode-locked fiber laser revealed that the bound-soliton pair behaves as a unit, and the properties of their interaction have exactly the same features as those of the single-pulse soliton in the laser, which suggests that the observed bound solitons are in fact another form of solitary waves in the laser. Numerical simulation confirmed the existence of a different form of solitons in the laser. DOI: 10.1103/PhysRevA.68.013816 PACS number͑s͒: 42.81.Dp, 42.55.Wd, 42.60.Fc, 42.65.Re Solitary wave generation is a generic property of many nonlinear dynamic systems and has been widely investigated ͓1-3͔. Optical solitons due to their theoretical importance and potential practical applications in optical communication and signal processing systems have attracted special attention ͓4 -7͔. An optical soliton generally refers to an optical pulse that can propagate in media without changing its shape and pulse width even under weak perturbations. A typical example of optical soliton generation is the nonlinear pulse propagation in optical fiber, where due to the balanced interaction between the optical Kerr effect and the fiber chromatic dispersion on a pulse, whose shape and pulse width become constant with propagation. Optical pulse propagation in fiber is governed by the nonlinear Schrödinger equation ͑NLSE͒.Optical solitons have also been observed in the passively mode-locked fiber lasers ͓8-10͔. However, as in a laser, apart from the optical fiber, there exist other cavity components, such as the gain medium and the output coupler, whose existence affects the detailed dynamics of the formed solitons. It was found that solitons observed in fiber lasers exhibited special features. These include the soliton energy quantization ͓11͔, the soliton bunching ͓12͔, and the quasiharmonic and harmonic mode locking ͓13͔. Only under weak perturbations caused by the gain, loss, and saturable absorption, the average soliton dynamics of a laser could be described by the NLSE; generally, it is described by the complex Ginzburg-Landau equation or the coupled complex Ginzburg-Landau equations ͓14͔.So far, all solitons observed in the optical fiber and/or the fiber laser systems are characterized as having a single peak, sech-form pulse profile. Although the higher-order NLSE solitons have more complicated pulse profiles, these solitons are intrinsically unstable ͓15͔. They are difficult to be observed in a practical system. In this paper, we report on the experimental evidence of a different form of double-pulse solitary waves in a passively mode-locked fiber ring laser. In a previous paper, we have reported on the experimental observation of bound solitons in a passively mode-locked fiber laser ͓16͔. Further studies on the interaction between the bound solitons revealed that the two bound pulses always behave as a unit. They could not break up. In parti...