1. Introduction

Temporal solitons in optical fibers, which were first observed by Mollenauer et al. in 1980 [1], have been the fascinating subject of considerable theoretical and experimental studies over the past decades. The passively mode-locked fiber lasers are deemed as the powerful tools to generate optical solitons, as well as the excellent platforms for investigating nonlinear dynamics of optical solitons. So far, depending on the cavity design and parameter selections, different soliton formation and dynamics have been observed in fiber lasers, such as dissipative soliton [2,3], bound soliton [4], similariton pulse evolution [5,6] and so on. The investigations of soliton generation and propagation in fiber lasers were always motivated by skillfully selecting the cavity parameters.

Recently, a new soliton formation mechanism, namely dissipative soliton resonance (DSR), was theoretically proposed through selecting certain parameters in the frame of complex Ginzburg-Landau equation [7–12]. The pulse in DSR region features the wave-breaking-free phenomenon and the flat-top pulse profile. The pulse width broadens with the increasing pump power while maintaining its amplitude constant, indicating that the pulse energy operating in DSR region can be greatly enlarged despite of the overdriven intracavity nonlinear effect. However, the above-mentioned DSR pulses are only addressed with a scalar theory.

In fact, since single mode fiber (SMF) actually supports two orthogonal polarization modes, the vector nature is also interesting to be considered when the soliton pulse propagates in fiber lasers [13,14], as we called vector soliton. By designing a polarization-insensitive laser cavity and detecting two orthogonal polarization components of the pulse, different pulse dynamics have been observed in vector soliton fiber lasers, i.e., polarization-locked vector soliton (PLVS) [15–17], polarization-rotation vector soliton (PRVS) [18,19], soliton trapping [20], and coherent energy exchange [21]. On the other hand, regarding to the experimental demonstrations of DSR phenomenon, so far most of them were observed in nonlinear polarization rotation (NPR) based fiber lasers [22–25]. However, since a polarizer is required in the fiber ring laser based on NPR technique, it is not suitable for the generation of vector solitons. According to the theoretical prediction, the DSR phenomenon in mode-locked fiber lasers is independent of the mode locking technique. Therefore, a question naturally arises as to whether the DSR phenomenon could be obtained in fiber lasers based on other mode-locking techniques. And more importantly, taking the significance of DSR phenomenon in the field of laser physics into account, it would be worthy of investigating the vector nature of mode-locked pulse operating in DSR region in a polarization-insensitive laser cavity.

Very recently, we have observed the DSR phenomenon in a nonlinear amplifier loop mirror (NALM) based mode-locked figure-eight fiber laser [26]. It should be noted that there is no polarization discrimination component (i.e., polarizer) in the laser cavity. Therefore, the laser setup could be suitable for observing vector nature of mode-locked pulse. However, in the previous work [26] the DSR pulse with duration only from 46.29 ns to 73.73 ns was obtained and the pulse profile transition from sech-like to rectangular was not observed, making that the vector nature of DSR pulse could not be fully investigated. Enlightened by these results, in this work we further optimized the cavity parameter settings to investigate the vector nature of DSR phenomenon. By properly rotating the polarization controllers (PCs), we achieved the mode-locked pulse with the pulse profile transition from sech-like to rectangular in DSR region. The rectangular pulse trapping of two orthogonal polarization components centered at different wavelengths was observed. We also investigated the vector pulse characteristics of two polarization components with both the narrow (picosecond) and long (nanosecond) durations under the condition of different pump power level. It was found that the two polarization components propagated as a group-velocity locked vector soliton despite of the cavity birefringence. In addition, different spectral distributions were obtained in the measured polarization resolved spectra.

2. Experimental setup

Figure 1 shows the schematic of the figure-eight fiber laser for investigating the vector nature of mode-locked pulse in DSR region. It is based on a nonlinear amplifying loop mirror (NALM) that is coupled to a unidirectional ring cavity through a 50/50 fiber coupler. A piece of 1.8 m long erbium-doped fiber (EDF) with group velocity dispersion (GVD) parameter of −15 ps/nm/km is used as the gain medium, which is pumped by a 980 nm laser diode. The other fibers are all standard SMFs with length of 57.5 m. Thus, the total cavity length is 59.3 m, corresponding to 3.44 MHz fundamental repetition rate. Two polarization controllers (PCs) are introduced to adjust the cavity birefringence. A polarization-independent isolator (ISO) ensures the unidirectional operation. A 10% fiber coupler is used to output laser. For the purpose of resolving the two orthogonal polarization components, a polarization beam splitter (PBS) is connected to the output coupler. An optical spectrum analyzer (OSA, Anritsu MS9710C) and an oscilloscope (LeCroy WaveRunner 104MXi, 1GHz) with a photodetector (Tektronix P6703B, 1.2GHz) were used to record the output laser, respectively.

 

Fig. 1 Schematic of the polarization-insensitive figure-eight fiber laser.

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3. Experimental results and discussions

The NALM acts as the saturable absorber in our fiber laser. The mode-locking threshold is about 150 mW. By simply rotating the PCs, the conventional soliton operation could be achieved [27]. However, in this case the multi-pulse would be observed if the pump power was high enough. With further proper adjustment of the PCs, the pulse became breaking-free and the pulse width broadened with the increasing pump power, which is the typical signature of DSR phenomenon. Figure 2(a) shows the pulse spectrum operating in DSR region at the pump power of 250 mW. As can be seen here, the soliton sidebands are observed due to the net anomalous dispersion of the laser cavity [28]. Figure 2(b) presents the mode-locking pulse-trains recorded by the oscilloscope at the pump power of 190 mW (red curve) and 250 mW (blue dotted curve). Here, the pulse profiles are rectangular. Moreover, the pulse width increased from 41.7 ns to 58.1 ns when the pump power was adjusted from 190 mW to 250 mW. These observations demonstrate that the pulse obtained in our fiber laser operates in DSR region.

 

Fig. 2 (a) Typical spectrum of DSR pulse; (b) pulse trains under the pump power of 190 mW and 250 mW.

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Although the self-starting mode-locking threshold is 150 mW, the fiber laser could sustain mode-locking state when the pump power was decreased to ~70 mW due to the pump hysteresis [29]. In this case, we could detect the pulse profile evolution with the decreasing pump power, as shown in Fig. 3(a) . The pulse profile transition from rectangular to sech-like shape was observed with the pump power from 90 mW to 70 mW, which was in agreement with the previous reports [10,25]. Correspondingly, the measured pulse duration was decreased from 5.1 ps to 0.97 ps. In order to further study the characteristics of DSR phenomenon, we have shown the measured pulse width and output power versus the pump power in Fig. 3(b). The largest output power of rectangular pulse is 9.01 mW. In addition, the pulse width could be varied from 0.97 ps to 100.63 ns by increasing the pump power from 70 to 350 mW.

 

Fig. 3 (a) Pulse profile evolution with decreasing pump power; (b) pulse width and output power versus pump power.

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As mentioned above, the laser cavity is polarization-insensitive. Thus, vector soliton generation is an intrinsic feature in our figure-eight fiber laser. To investigate the vector nature of the DSR pulse, a PBS was employed to analyze the characteristics of two polarization components in both spectral domain and time domain. Firstly we selected a proper pump power of 100 mW. Figure 4(a) illustrates the spectrum of vector soliton as well as the corresponding two orthogonal polarization components under the 100 mW pump power. It can be seen that the two orthogonal polarization components located at different wavelengths with a separation of 0.26 nm, whose intensity difference is ~6.1 dB. Consequently, although the fiber birefringence exists in the laser cavity, the two polarization components could compensate the fiber birefringence-induced polarization dispersion by shifting the center frequencies. Then they could trap each other as a group-velocity locked vector soliton. Based on the experimental observation, it is worthy of noting that the rectangular pulse trapping in DSR region is similar to that of conventional vector soliton [20], demonstrating that the pulse trapping is a universal phenomenon of vector soliton despite of the soliton formation mechanism. In addition, the wavelength locations of soliton sidebands shown in the spectra of two polarization components are also different due to the center wavelength shift. Meanwhile, the vector nature of DSR in time domain was also investigated corresponding to the case of Fig. 4(a). By employing a commercial autocorrelator, it was found that the pulse profiles of two polarization components were both rectangular shapes, as shown in Fig. 4(b). The horizontal and vertical pulse widths are both about 9.3 ps.

 

Fig. 4 Vector nature of DSR pulse at the pump power of 100 mW. (a) Polarization-resolved spectra; (b) Autocorrelation traces.

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For the purpose of comparison, the vector nature of the pulse in DSR region at different pump power level was further investigated. We found that the pulse profiles of the two polarization components have the same evolution trend, namely the pulse widths both increased with the pump power. Typically, Fig. 5 shows the vector nature of DSR pulse at the pump power of 300 mW. In this case, the spectral intensity difference of two polarization components is larger than that at 100 mW pump power, which is ~17.2 dB, as shown in Fig. 5(a). And the center wavelength shift is not so evident, which is ~0.1 nm. Since the polarization state of the vector DSR pulse evolved along the fiber, the spectral intensities of two polarization components at the output port are related to polarization state at the input port of PBS. Therefore, we think that the difference of vector spectra between the cases of 100 mW and 300 mW is mainly due to the change of polarization state at the input port of PBS caused by the increased pump power. Then the pulse vector feature in the time domain was investigated. As expected, the pulse profiles of two polarization components are both rectangular, which possess almost the same duration of ~75 ns (full width at half maximum), as shown Fig. 5(b). These results demonstrate that the pulses of two orthogonal polarization components could both operate in DSR region with the increasing pump power.

 

Fig. 5 Vector characteristics of DSR pulse at the pump power of 300 mW. (a) Polarization-resolved spectra; (b) Oscilloscope traces.

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Note that only the pulse trapping and group-velocity locked vector soliton operating in DSR region was observed in this experiment. However, by further adjusting the cavity parameters, it is expected that other vector soliton dynamics of DSR such as PLVS, PRVS and coherent energy exchange may be obtained. These observations would be beneficial for complementing the understanding of soliton characteristics in DSR region. Furthermore, the vector nature of DSR phenomenon could be also investigated in passively mode-locked fiber lasers based on other polarization-insensitive saturable absorbers, such as graphene, carbon nanotube and semiconductor saturable absorber mirror (SESAM).

4. Conclusion

In summary, we have investigated the vector characteristics of the pulse operating in DSR region in a polarization-insensitive figure-eight fiber laser. With proper adjustment of the PCs, the DSR phenomenon could be observed in our fiber laser. The mode-locked pulse presents typical signatures of DSR. The frequency shift of two orthogonal polarized components of DSR pulse was observed to achieve the pulse trapping and propagating as a group-velocity locked vector soliton. It was also found that the spectral distributions of two polarization components were different from each other. The observed results demonstrate that the vector nature of DSR pulse also shows similar characteristics to the conventional vector soliton, which would increase the understanding of fundamental physics of DSR phenomenon.