1. Introduction

Passively mode-locked fiber lasers as ultra-short optical sources have attracted considerable interest due to their various practical applications such as optical communication, optical sensing, nonlinear optics, industry and medicine. Generally, several passively mode-locked techniques, such as semiconductor saturable absorber (SESAM) [1,2], nonlinear polarization rotation (NPR) [3,4], nonlinear optical loop mirror (NOLM) [5], and nonlinear amplifier loop mirror (NALM) [6], have been used to achieve passively mode-locked pulses in fiber lasers. Since the passively mode-locked pulse possesses high peak power, the passively mode-locked fiber lasers are regarded as useful platforms for observing nonlinear dynamics of mode-locked pulses. Thus, there is always a strong motivation to study nonlinear phenomena by designing the cavity configuration and selecting the cavity parameters. Up to date, different soliton dynamics and formation have been observed in fiber lasers, i.e., conventional soliton [7,8], noise-like soliton [9], vector soliton [10], similariton pulse evolution [11,12], bound soliton [13,14], dissipative soliton [15,16] and so on. However, a common characteristic of the solitons mentioned above is that the multi-pulse oscillation (or wave breaking) would occur as the increasing energy of mode-locked pulse due to the overdriven nonlinear effect [17]. Therefore, the application requirement of high energy pulses in fiber lasers could not be satisfied. As a solution of reducing the nonlinear effect, the microstructure large mode area (LMA) gain fiber was employed in the fiber laser, and thus, to obtain high energy pulses [18,19]. Nevertheless, the LMA fiber was not able to be directly fused with the conventional single mode fiber, making the fiber lasers non-all-fiber configuration design. Therefore, from the achievement of high-energy pulse and all-fiber cavity design view of point, new soliton operation regimes without wave breaking is needed to be exploited.

Very recently, following by the certain parameter selections in the frame of complex Ginzburg-Landau equation, a new concept of soliton formation known as dissipative soliton resonance (DSR) has been theoretically proposed to achieve high energy pulse without wave-breaking from a fiber laser [16, 20–24]. The DSR phenomenon features that the width and energy of wave-breaking-free mode-locked pulse increase with the increasing pump power while maintaining their amplitude constant, indicating that the pulse shape operating in DSR region is rectangular. Thus, the pulse energy could be increased greatly compared with other soliton operation regimes. So far, by using NPR mode-locking technique, the DSR phenomenon has been observed in fiber ring lasers operating both in positive and negative dispersion regimes [25–28]. However, according to theoretical prediction of DSR phenomenon, the observation of DSR in mode-locked fiber lasers is independent of the mode-locking technique. Therefore, it would be interesting to know whether the DSR phenomenon could be observed in fiber lasers by using other mode-locking techniques, i.e., NALM-based figure-eight fiber lasers.

In this work, we report on the experimental observation of rectangular pulses operating in DSR region in an erbium-doped figure-eight fiber laser with net anomalous dispersion which is mode locked using the NALM technique. In our experiment, the duration of the wave-breaking-free rectangular pulse can be increased from 46.29 to 73.73 ns by simply increasing the pump power while keeping almost constant amplitude of pulses. At a maximum pump power of 341 mW, the pulse energy can be up to 3.25 nJ with a fundamental repetition rate of 3.54 MHz. In particular, the spectrum of the rectangular pulses exhibits conventional soliton sidebands. The obtained results demonstrated that the observation of DSR phenomenon is independent of mode-locking technique, which could be an intrinsic feature of fiber laser under proper settings of cavity parameters.

2. Experimental setup

The schematic of all-fiber figure-eight fiber laser is shown in Fig. 1 . The unidirectional ring (UR) and NALM are depicted at the left and the right, respectively, which are joined by a 2 × 2 3-dB fiber coupler. The UR part is composed of a polarization controller (PC) which we use to adjust the polarization state of the pulse, a polarization insensitive isolator (PI-ISO) and a 10% fiber output coupler (OC). The NALM consists of a 1.8-m long erbium doped fiber (EDF) with group velocity dispersion (GVD) parameter of D = −15 ps/nm/km, a 30-m single mode fiber (SMF-28) with GVD of 17 ps/nm/km, a PC, two 980/1550 nm wavelength-division-multiplexer (WDM) and two 980-nm laser diodes providing bidirectional pumping with the total power of approximately 341 mW. It is a dispersion-managed (DM) fiber laser and the net cavity dispersion is −1.194 ps2 at 1550 nm. The 30-m long SMF in the NALM cavity is introduced into the fiber laser to increase the nonlinearity. The fundamental repetition rate and cavity length are estimated as 3.54 MHz and 58.4 m, respectively. An optical spectrum analyzer (OSA, Anritsu MS9710C) and an oscilloscope are employed to monitor the laser output simultaneously.

 

Fig. 1 Schematic of the figure-eight fiber laser. WDM: wavelength division multiplexer; EDF: erbium-doped fiber; SMF: single mode fiber; PC: polarization controller; PI-ISO: polarization insensitive isolator; UR: unidirectional ring; NALM: nonlinear amplifying loop mirror.

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3. Experimental results and discussions

The NALM technique was utilized for obtaining the passive mode-locking state of the fiber laser. In our fiber laser, the mode-locking threshold is about 78mw. After achieving the passive mode-locking state, different operation regimes of fiber laser could be observed, including conventional soliton and bright-dark soliton pair [29]. A typical spectrum of conventional mode-locking with sech-pulse profile is shown in Fig. 2(a) . The 3-dB spectral bandwidth is 1.49 nm. The corresponding pulse-train is presented in Fig. 2(b). The repetition rate, as determined by the cavity length, is 3.54 MHz. We have also shown the autocorrelation trace in the inset of Fig. 2(b). The pulse duration, if a sech pulse shape is assumed, is 1.85 ps.

 

Fig. 2 Conventional mode-locking operation of the fiber laser. (a) Pulse spectrum; (b) pulse-train and autocorrelation trace.

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Then the pump power was further increased, after properly adjusting the PCs, a notable pulse formation with rectangular shape was presented on the oscilloscope. Generally, the rectangular pulse train can be achieved at a pump power of about 197 mW. Figure 3 shows the typical rectangular pulse emission of the laser at the pump power of about 341 mW. As can be seen in Fig. 3(a), the output pulse has a rectangular shape, and the measured pulse width is 73.7 ns. The output rectangular pulse with large scan range is also presented in the inset of Fig. 3(a), showing that the repetition rate of the rectangular pulse is 3.54 MHz. In the experiment, no fine structure of the rectangular pulse and pulse bunching were observed, demonstrating that the rectangular pulse is not structured by superimposing a bunch of pulses but a single pulse. Fig. 3(b) shows the corresponding mode-locked spectrum of the rectangular pulse. Being different from the reported results in Ref [25–27], it should be noted that the spectrum of rectangular pulse exhibits the conventional soliton sidebands [28]. Here, the central wavelength of the spectrum is 1559.8 nm and the 3-dB bandwidth is 3.32 nm. In this case, the average output power is 11.5 mW, corresponding to the pulse energy of 3.25 nJ.

 

Fig. 3 A typical rectangular pulse emission of the laser at the fundamental cavity frequency of 3.54 MHz. (a) Mode-locked rectangular pulse train; (b) corresponding optical spectrum.

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As demonstrated by the DSR theory, the duration of rectangular pulse will broaden with the increasing pump power while the peak of the pulse almost keeps constant. To investigate this characteristic, we increased the pump power and observed the pulse evolution when the PC was fixed in the experiment. The measured results are shown in Fig. 4 . Obviously, the width of mode-locked rectangular pulse increased with the pump power, as shown in Fig. 4(a). Here, the width of mode-locked rectangular pulse broadens from 46.29 ns to 66.27 ns while the pump power increases from 197.6 mW to 303.2 mW. It is worth noting that there is no multi-pulse oscillation was observed during the pulse broadening process. Meanwhile, we have shown the corresponding evolution of the pulse spectrum in Fig. 4(b). As can be seen in Fig. 4(b), despite of the slightly increasing spectral intensity, the 3-dB bandwidths of mode-locked spectra were almost invariable, which is in agreement with the theoretical prediction in [21]. Thus, based on the experimental observations above, we believe that we have observed the DSR phenomenon in the figure-eight fiber laser.

 

Fig. 4 Rectangular pulses under different pump power. (a) Output pulses; (b) corresponding optical spectra.

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In our experiment, with proper adjustment of the PCs and pump power, we can always observe wave-breaking-free rectangular pulse operating in DSR region. In order to better investigate the characteristics of the pulse operating in DSR region, Fig. 5 shows the evolution of pulse width and output power versus pump power under different adjustments of PCs compared with that of Fig. 4. In Fig. 5, it can be seen that the pulse width change from 43.1 ns to 72.2 ns when the pump power was increased from 197.6 to 341 mW. At a maximum pump power of 341 mW, the average output power is 10.86 mW. Thus, considering the 3.54 MHz repetition rate of the mode-locked pulse, in this case the pulse energy is 3.07 nJ. Note that the pulse energy obtained here is different from that of Fig. 4. It is mainly because the cavity loss for a specific wavelength varied with the rotation of PCs [30]. Therefore, with the same value of pump power, the obtained pulse energy could be changed with different orientations of PCs.

 

Fig. 5 Pulse width and average output power varies with the pump power.

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In the experiment, we have observed the soliton sidebands when the fiber laser operated in DSR region. The generation of soliton sidebands is an intrinsic feature of the passively mode-locked fiber laser operating in net anomalous dispersion regime, which is formed due to the constructive interference between the soliton pulse and dispersive waves [31]. It should be also noted that the maximum energy of pulse we have obtained is limited to be 3.25 nJ. However, according to theory of DSR phenomenon, the maximum pulse energy associates with a set of parameters of the laser cavity and the available pump power [24]. Therefore, it is expected that the higher-energy pulse can be achieved when the parameters of the laser cavity are appropriately adjusted and the higher pump power is employed.

4. Conclusion

In conclusion, we have demonstrated the generation of mode-locked rectangular pulses operating in DSR region in an erbium-doped figure-eight fiber laser with net anomalous dispersion. With the increase of pump power, the duration of the wave-breaking-free pulse broadens and the pulse energy can be up to 3.25 nJ at a maximum pump power of 341 mW. Meanwhile, the spectrum of mode-locked pulse operating in DSR exhibits conventional soliton sidebands. The obtained results demonstrated that the pulse formation operating in DSR region is independent of mode-locking techniques, which may be useful for better understanding the DSR phenomenon in fiber lasers.