Soliton operation of passively mode-locked erbium-doped fiber lasers has been extensively investigated [1–3]. It was shown that the soliton formation in the lasers is a result of the balanced interaction between the cavity dispersion and the nonlinear Kerr effect of the optical fibers. Although existence of the erbium gain alone could also support soliton formation in the fiber lasers [4], as the spectrum of the soliton formed in the lasers is generally narrower than the spectral bandwidth of the erbium gain, practically the impact of the erbium gain on the property of the formed soliton is limited. A special situation occurs when the pulse width of the formed soliton becomes so narrow that its spectral bandwidth is comparable with that of the erbium gain profile. However, in the fiber lasers due to the existence of saturable absorber effect in cavity, which is necessary for the self-started mode locking, such a situation is unstable. A soliton in this case will collapse [5] and consequently a so-called noise-like pulse emission state will be formed [6–12]. In a noise-like pulse emission state although the mode-locked pulse still repeats at the fundamental cavity repetition rate, there exist complicated fine-structures within it. As the mode-locked pulse moving in the cavity the details of the fine-structures vary randomly. Therefore, it was called as a “noise-like pulse”. It was shown that through specially designing the laser cavity certain unique properties of the noise-like pulse could be achieved. These include the generation of intense noise-like pulses with a few picoseconds pulse duration [8], broadband noise-like pulse generation through controlling the cavity dispersion [9], and high energy broadband noise-like pulse generation [10]. Taking advantage of the large pulse energy and broadband spectrum features of the laser emission, it was also used for demodulation of fiber Bragg grating sensor array [11] and as a seed to generate super continuum [12].

M. Hororwitz et al. [6] firstly reported the noise-like pulse mode-locking in the erbiumdoped fiber lasers. They explained it as caused by the large birefringence of the laser cavity in combination with the nonlinear cavity transmission. According to their explanation significant cavity birefringence would be necessary for the noise-like pulse generation. Recently we have experimentally observed similar noise-like pulse operation in erbium-doped fiber lasers whose cavity has only weak birefringence [7]. Our experimental results rules out the possibility that it is generated by the large cavity birefringence of the lasers. Further numerical simulations and experimental investigations showed that the formation of the noise-like pulse is caused by the soliton collapse effect in the lasers [5, 7], and it is a generic feature of the passively mode-locked soliton fiber lasers. Previous studies on the noise-like pulse emission fiber lasers have focused on lasers with net negative cavity group velocity dispersion (GVD). We have recently demonstrated soliton operation of a mode-locked erbium-doped fiber laser made of purely positive dispersion fibers [13]. The fibers used in the laser cannot support optical solitons. Therefore, the soliton formed is purely supported by the erbium gain. It is a gain-guided soliton. As the soliton shaping mechanism of the gain-guided soliton is different to that of the solitons formed in fiber lasers with net negative cavity GVD, despite of the fact that the spectral bandwidth of the formed gain-guided solitons is comparable to the effective gain bandwidth of the laser, no soliton collapse was observed. Nevertheless, in our experiment a stable noise-like pulse operation was still observed in the fiber laser. Obviously, the mechanism of the noise-like pulse generation in the current laser is different from those reported previously [6–12]. In this letter, we report on features of the observed noise-like pulse emission in the gain-guided soliton fiber lasers. Based on numerical simulations we further show that the noise-like pulse emission is caused by the peak power clamping effect of the laser cavity on the gain-guided soliton.

Details of the fiber laser such as the cavity configuration and the parameters of the optical fibers used were reported previously [13]. Briefly it is a typical single mode passively mode-locked fiber ring laser mode-locked with the nonlinear polarization rotation (NPR) technique [1]. The essential difference of the laser to the conventional soliton fiber lasers is that all the fibers used to construct the laser cavity have positive GVD. Therefore, the fibers themselves cannot support optical soliton generation. Nevertheless, we found experimentally that through appropriately selecting the linear cavity phase delay bias, self-started mode-locking could still be achieved in the laser. In particular, the features of the mode-locked pulse could be well described by the coupled laser Ginzburg-Landau equations (GLEs) [14]. The same coupled-GLEs were also used to describe the soliton operation of fiber lasers under the negative cavity GVD. This result suggests that the pulse formed in the laser is in fact an optical solitary wave, namely a gain-guided soliton.

 

Fig. 1. (a) Optical spectrum and (b) autocorrelation trace of the noise-like pulse.

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Starting from a state of the gain-guided soliton operation, if the linear cavity phase delay bias is changed or the pump strength is significantly increased, another stable state of socalled noise-like pulse emission could always be obtained. Figure 1 shows for example a well-developed such state with pump power of about 700 mW. The optical spectrum of the state as shown in Fig. 1(a) is broad and smooth, indicating that it is still a mode-locked state. Indeed from the oscilloscope trace of the state it is confirmed that only one mode-locked pulse circulates in the cavity with the cavity repetition rate. Figure 1(b) shows the autocorrelation trace of the pulse, which has a profile indicating that random fine structures exist on the mode-locked pulse profile. Similar laser emission feature known as noise-like pulse emission has also been observed in the conventional soliton fiber lasers with negative GVD [6–12]. However, different from the noise-like pulse generation in the conventional soliton fiber lasers where the noise-like pulse state always occurs suddenly as the control parameter is smoothly changed, the noise-like pulse emission of the current laser appears gradually. Fig. 2 shows the optical spectrum change as the laser emission transits from a gain-guided soliton state to the fully developed noise-like pulse state. Initially the spectrum of the pulse has a characteristic of steep edges. The bottom of the steep edges then gradually broadens. Eventually the spectrum becomes that shown in Fig. 1(a). In obtaining Fig. 2 we have fixed all other laser parameters but increased the pump power strength, which is about 394.0 mW for the gain-guided soliton state, 518.2 mW and 602.6 mW, respectively, for the intermediate states shown. The same process occurred when the pump power is fixed for example at the 700 mW while the orientations of the wave plate were tuned. We emphasize that each of the intermediate states is a stable state of the laser. Under the current cavity setting, the maximum achievable peak power of the gain-guided solitons is about 26 W.

 

Fig. 2. Variation of the optical spectrum with pump power under fixed orientations of the wave plates (array direction indicating pump power increasing).

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In order to understand the feature of the laser, we numerically simulated the gain-guided soliton operation under various laser parameters using the same coupled laser GLEs reported previously [13]. Again in our simulations we have taken into account the effects of the laser cavity components and the cavity. To make our simulation comparable to the experiment, we have used the following parameters: nonlinear fiber coefficient λ=3 W^-1km^-1, erbium fiber gain bandwidth Ω _g = 25 nm, fiber dispersions k″_EDF =-40 (ps/nm)/km, k″_DCF =-0.2 (ps/nm)/km, and k‴ =0.1 (ps²/nm)/km, beat length Lb=L/2, orientation of the intracavity polarizer to the fiber fast birefringent axis ψ=0.152π, cavity length L= 5.5m and gain saturation energy P_sat=1000 pJ. Fig. 3 shows for example the calculated pulse profiles and optical spectra when the linear cavity phase delay bias is set as Ph=1.3π and the pump power is changed. Stable gain-guided soliton can always be obtained, and the soliton spectrum has the characteristic steep spectral edges and an effective gain bandwidth limited edge-to-edge width. Increasing the pump power, initially the peak power, pulse width and spectral bandwidth of the gain-guided soliton increase. When the peak power of the soliton reaches to a certain fixed level, which under our current linear cavity phase delay bias setting is about 9.1 W, the bottom of the soliton spectrum starts to broaden as shown in Fig. 3(b). Eventually the soliton spectrum becomes smooth and broadband. We note the evolution of the calculated pulse profiles with the pump power change, once the bottom of the soliton spectrum broadens, the pulse profile becomes quickly randomly modulated, indeed like a “noise-like” pulse. However, the noise-like pulse is clearly different to that obtained in the conventional soliton fiber lasers reported [7, 10]. Numerically it was found that the pump threshold of the noiselike pulse formation is determined by the setting of the linear cavity phase delay bias. With our current laser cavity parameter selection, the larger the Ph value, the higher is the pump threshold, and furthermore, the higher peak power of the stable gain-guided soliton achievable. Finally, it is to point out that the calculated spectral broadening exhibits nearly symmetric evolution with respect to the soliton central wavelength, while the experimentally observed spectral broadening is obviously asymmetric. This difference is caused by that in the simulations a symmetric parabolic gain profile is used, however, the real gain profile of the EDF is asymmetric and not parabolic shaped.

 

Fig. 3. Numerically calculated variation of the pulse profile and optical spectrum with pump strength. The linear cavity phase delay bias is fixed at Ph=1.3π. (a) Pulse profiles (noise-like pulse profile is shifted to avoid confusion); (b) optical spectra;

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Fixing the pump strength but shifting the linear cavity phase delay bias towards the polarization switching point, the same pulse profile and soliton spectral evolution were numerically obtained, which is well in agreement with the experimental observations. Based on the numerical simulation we found that the generation of the observed noise-like pulse could be caused by the cavity peak power clamping effect of the laser [15]. To understand it, we point out that although the laser cavity now has positive GVD, as the NPR technique is used for achieving mode-locking, the cavity peak power clamping effect still exists. When the peak power of the gain-guided soliton is clamped, further increase of the laser gain will not increase the soliton energy but amplify the dispersive waves and the background noise. We have analyzed the effect of soliton peak clamping on the soliton operation in the conventional soliton fiber lasers. The solitons formed in the conventional soliton fiber lasers have narrow and almost transform-limited pulse width. It is determined by the balanced interaction between the GVD and the optical Kerr effect. The linear and nonlinear waves in the lasers have very different group velocities, once generated the dispersive waves will quickly separate from the soliton pulse. Therefore, the amplified dispersive wave can be reshaped into a new soliton and the soliton peak clamping leads to multiple soliton formation in the lasers. In the case of a gain-guided soliton fiber laser, the soliton has broad pulse width and large frequency chirp. The positive GVD of the cavity further makes the linear wave and the nonlinear wave having only small group velocity difference. Therefore, in the time domain the dispersive waves almost co-propagate with the soliton wave. The dispersive waves are linear wave. They have different phase velocity to the soliton wave. When dispersive waves become strong enough, they interfere with the soliton wave and result in the noise-like soliton pulse profile. Numerically we have confirmed that the noise-like pulse formation is always related to the soliton peak clamping, if the clamping is removed, e.g. either through shifting the linear cavity phase delay bias or reducing the pump strength, a noise-like pulse can be always returned to a gain-guided soliton. Furthermore, no multiple gain-guided solitons could be generated in the laser.

In conclusion, we have experimentally observed a noise-like pulse emission in the gainguided soliton fiber laser and numerically simulated the effect. We found that the noise-like pulse generation is caused by the cavity peak power clamping effect, an intrinsic feature of the soliton fiber lasers mode-locked with the NPR technique. Our studies further confirm that the laser cavity effect plays an important role on the soliton features of a mode-locked soliton fiber laser.