We report on the experimental observation of a novel form of vector soliton interaction in a fiber laser mode-locked with SESAM. Several vector solitons bunch in the cavity and move as a unit with the cavity repetition rate. However, inside the bunch the vector solitons make repeatedly contractive and repulsive motions, resembling the contraction and extension of a spring. The number of vector solitons in the bunch is controllable by changing the pump power. In addition, polarization rotation locking and period doubling bifurcation of the vector soliton bunch are also experimentally observed.
©2009 Optical Society of America
Solitons, as a special nonlinear localized wave, have been extensively investigated [1–3]. It has been shown that not only in the lossless (i.e. Hamiltonian) nonlinear systems but also in the nonlinear dissipative systems solitons can be formed. A soliton formed in a dissipative system with intrinsic gain-loss mechanism is also known as a dissipative soliton [2, 3].
Optical solitons formed in a fiber laser are typical dissipative solitons. Both experimental and numerical studies have shown that in a fiber laser multiple solitons could be generated, and moreover interaction between the solitons could lead to formation of states of bound solitons [4–6] or bunches of solitons . Several research groups have studied the interaction between the dissipative solitons formed in a mode locked fiber laser [8–10]. Tang et al. have shown that there are three types of soliton interaction mechanisms dominating in the system: a global type of soliton interaction caused by the unstable cw lasing, a local type of soliton interaction caused by the resonant dispersive waves, and the direct soliton-soliton interaction . Olivier et al.  and Grelu et al.  have also reported a form of group soliton interaction in a fiber laser. It was shown that due to the different group velocities between a single soliton and a state of bound solitons, periodic collisions between them occurred in the laser cavity. However, the collision didn’t destroy the state of bound solitons.
Due to asymmetric fiber core and/or fiber bending, a practical fiber always exhibits birefringence. Considering fiber birefringence and the vector nature of light, vector solitons can also be formed in birefringence fibers. Indeed, both the polarization locked vector solitons (PLVSs) and the group velocity locked vector solitons (GVLVSs) have been observed in the fiber lasers with weakly birefringence cavity mode locked by SESAM [13–15]. In a recent experiment we have also observed the effect of polarization rotation locking of the vector solitons to the cavity repetition rate of a fiber ring laser .
Previous studies on the laser soliton interaction were mainly focused on the scalar type of solitons. In this paper, we report on the vector soliton interaction in a fiber laser. A novel form of vector soliton bunch was experimentally observed. It was found that, like the conventional soliton bunches reported previously, the vector soliton bunch moved as a unit with the fundamental cavity repetition rate in the cavity. However, different from the conventional soliton bunches the vector solitons in the bunch constantly moved with respect to each other, coming close and then spreading out, resembling the contraction and extension of a spring. Based on the observed features of the multiple vector solitons in our laser, we speculate that the saturable absorption of SESAM could generate a kind of attractive force between the vector solitons that are not too far apart in the cavity, and the observed vector soliton evolution in a bunch could be caused by the mutual actions of the resonant dispersive wave mediated long range soliton interaction and the attractive force. In addition, we also show that the polarization of the vector soliton bunch could rotate and be locked to the multiple of the cavity repetition rate, and under certain condition a vector soliton bunch could also exhibit period doubling bifurcation.
2. Experimental setup and results
The fiber laser is schematically shown in Fig. 1. We used 6 m erbium-doped fiber (StockerYale EDF-1480-T6) as the gain medium, the other fibers used were all the standard single mode fibers (SMFs). A fiber coupled semiconductor saturable absorber (SESAM) was used as the mode locker. A 3-port polarization-independent circulator was used to force the unidirectional operation of the laser and simultaneously incorporate the SESAM into the cavity. A fiber-based polarization controller was placed between the incoming branch of the circulator and the wavelength division multiplexer to control the net birefringence of the cavity. We note that there is no polarizing component in the laser cavity. The laser was pumped by a 1480 nm Raman fiber laser with maximum output of 700 mW, and the backward pump theme was adopted to avoid overdriving the SESAM by the residual pump power. The laser beam was coupled out of the cavity through a 10% fiber coupler. The SESAM has a saturable absorption of about 8% and a fast recovery time of 2 ps. A 2 GHz photodetector (Thorlab DET01CFC) and a 350 MHz oscilloscope (Agilent 54641A) were used to monitor the properties of the output pulse train.
Self-started mode locking is always obtained in the laser. With appropriate PC setting stable vector solitons either as the PLVSs or the GVLVSs could be observed. Figure 2(a) and Fig. 2(c) show a state of multiple vector solitons (State A) of the laser. The optical spectrum of the state has clear and sharp spectral sidebands. It shows that the mode locked pulses are solitons . Figure 2(c) shows that there are 5 solitons coexisting in the cavity, and they are far apart. The separations among the solitons are fixed, which means that all the solitons have exactly the same group velocity in the cavity. With the help of an external cavity polarization beam splitter (PBS), the polarization components of the solitons along two orthogonal polarization directions are experimentally resolved. It is found that independent of the birefringence change of the external cavity fibers used to guide the soliton into the PBS, two orthogonal polarization components are always obtained, and the maximum intensity ratio of them measured is about 75:1. The polarization resolved measurement further confirms that the observed solitons are the vector solitons.
In our experiment the State A is difficult to obtain. Generally once the laser is mode-locked, a state as shown in Fig. 2(b) and Fig. 2(d) (State B) is obtained. To obtain State A, we need to further carefully select the linear cavity birefringence (through tuning the orientations of the paddles of the PC) and / or decrease the pump power simultaneously. Compared with State A, clear spectrum deformation could be identified, e.g. the spectral sidebands shown in Fig. 2(b) are clearly blurred. Figure 2(d) shows the oscilloscope trace of the laser emission in State B. It looks like a single-pulse soliton circulating in the cavity. Increasing or decreasing pump power could not destroy the state, but increase or decrease the intensity of the pulse. The State B could be easily confused as a large energy single pulse soliton state. We point out that it is actually a bunch of vector solitons circulating in the cavity. Measured with a high-resolution detection system (a 45 GHz photodetector, New Focus 1014, and a 50 GHz sampling oscilloscope, Agilent 86100A), the “single pulse” shown in Fig. 2(d) could be resolved and it is shown in Fig. 3 and the corresponding video. There are eight vector solitons in the bunch. Monitored with the high resolution detection system details of the relative vector soliton evolution inside the bunch is further revealed. It was found that different from the conventional soliton bunches, where the solitons are static in a bunch, the vector solitons moved constantly inside the bunch and repeated the same process: coming close and then pushing away. No soliton merging was observed. The restless relative evolution of the vector solitons inside the bunch straightforwardly explains why the observed optical spectrum is blurred. Obviously, the relative evolution of the vector solitons is caused by their group velocity differences, which is a result of their carrier frequency fluctuations under mutual interactions. Their carrier frequency jittering is reflected on the measured soliton spectrum.
Experimentally we tried to isolate the fiber laser from possible environment perturbations, such as placing it on an air-supported optical table, putting it into a box, fixing the fiber segments. However, State B is always obtained, indicating that the vector soliton evolution in the bunch is caused by the mutual soliton interaction, rather than the environmental disturbance. Carefully changing the pump power the number of vector solitons in a bunch can be controlled. With less vector solitons in a bunch the moving speed of the vector solitons becomes slower. However, no bunch with only two vector solitons has been experimentally obtained. Further experimental studies on the vector soliton bunch also revealed that the polarization of the bunch either rotates or not. Especially, the polarization rotation could also exhibits the polarization rotation locking feature of the single vector soliton . Figure 4 shows the polarization resolved measurement of a vector soliton bunch. Rotation of the bunch polarization is obvious. The polarization rotation frequency is locked to the half of the cavity repetition rate in the case of Fig. 4. The weak interactions among the vector solitons seem have no effect on the polarization rotation of each individual vector soliton. However, the polarization resolved spectra of the vector soliton bunch do not show the “peak-dip” form of coherent exchange sidebands. As the carrier frequency of each individual vector soliton within a bunch jitters, and the measured optical spectrum is an averaged result, a “smear out” of the FWM type of sidebands is understandable. However, it is to note that this does not mean that there is no coherent energy exchange between the two orthogonal polarization components of a vector soliton.
Experimentally in order to confirm that the restless vector soliton bunch is not a special case of a specific fiber laser, we reduced the cavity length of the fiber laser and found that the restless vector soliton bunch could always be generated. Recently we have reported the period doubling of vector solitons in fiber lasers . Similar phenomenon has also been observed on the bunch of restless vector solitons in some reduced cavity length fiber lasers. Figure 5(a) shows for example a typically measured oscilloscope trace of a restless vector soliton bunch. We note that the cavity length of the fiber laser now is about 7.5 m. The total energy of the bunch varies obviously with the cavity roundtrips and exhibits period doubling. To confirm the result we have also shown the RF power spectrum of the laser emission in Fig. 5(b). A new frequency component appeared at the half cavity fundamental repetition frequency position, showing that the energy of the bunch varies with twice of the cavity roundtrip times. A period doubled vector soliton bunch state cannot self-start. It is obtained from a period one state through tuning the paddles of the PC.
The restless vector soliton evolution inside the bunch as shown in the video clearly suggests that there exist complicated interactions among the vector solitons. The pulse width of the vector soliton shown in State A is measured as about 724 fs if a Sech2 pulse profile is assumed. The soliton pulse width in a fiber laser varies slightly with the cavity birefringence and pump strength. We estimate that in all cases the soliton pulse width in our laser should be shorter than 1ps. As the time resolution of our detection system is about 25ps, and with the system we could still resolve the individual soliton in a bunch, it suggests that the soliton separation in the bunch is larger than 5 times of their pulse width. Therefore, the direct soliton-soliton interaction effect could be excluded. Obviously, there is an attractive force between the vector solitons in a bunch. Moreover, the attractive force no longer exists once the vector solitons become far apart, as shown in Fig. 2(c). We believe that this kind of attractive force could be generated by the saturable absorption effect of the SESAM. It is easy to understand that if two pulses come to a saturable absorber within the absorber recovery time, the leading edge of the first pulse would experience stronger absorption. Considering a saturable absorber in a soliton fiber laser, as solitons are stable, the energy loss caused by the saturable absorber would eventually be balanced by the gain medium within one cavity roundtrip. However, the effective soliton separation would be reduced. Therefore, the saturable absorption in a soliton fiber laser could effectively generate an attractive force between the solitons with separation within the absorber recovery time. It is known that determined by the properties of the semiconductor materials, the saturable absorption of a SESAM exhibits two recovery times, a fast one with strong absorption and a slow weak absorption with a recovery time extending to ~100 ps . Our experimental results also suggest the existence of such a weak slow saturable absorption in our SESAM. Under effect of the attractive force the solitons in a bunch will always be pulled together. However, when the solitons become too close, the resonant dispersive waves mediated long-range soliton-soliton interaction also becomes strong, which eventually pushes the solitons away. As no balance between the two types of soliton interaction could be established, the solitons are forced to oscillate in a bunch. Obviously, both of the interactions are weak as compared with the coupling between the two orthogonal components of the vector solitons. Therefore, the vector nature of the solitons as well as the other vector soliton features such as the polarization rotation is maintained despite of the oscillations of the solitons.
In conclusion, we have experimentally observed a novel form of vector soliton bunch in a passively mode locked fiber laser. Associated with the circulation of the soliton bunch in the cavity with the fundamental cavity repetition rate, the vector solitons inside the bunch exhibited repeatedly mutual attraction and repulsion movement. However, except resulting in that the measured soliton spectrum becomes blurred, the soliton evolution has no effect on the vector soliton features. We speculate that the saturable absorption of the SESAM could produce a kind of attractive force between the solitons. And the observed soliton bunch is formed under effect of the attractive force and the long-range type of soliton-soliton interaction in a fiber laser.
L. M. Zhao acknowledges the Singapore Millennium Foundation for providing him a postdoctoral fellowship. This research is supported by the National Research Foundation Singapore under the contract NRF-G-CRP 2007-01.
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