Multiple polarization dynamic patterns of vector solitons, including fundamental solitons, bunched solitons, loosely or tightly bound states and harmonic mode locking have been observed experimentally in an erbium-doped fiber ring laser with graphene as a saturable absorber. By carefully adjusting the pump power and the orientation of the intra-cavity polarization controller, either polarization rotation or polarization locked operation have all been achieved for the above vector solitons. This is the first time that high order harmonic mode locking of polarization rotation vector solitons has been achieved. The signal to noise ratio of our system was ~51 dB, which indicates that the laser operated with high stability.
© 2015 Optical Society of America
Since Hasegawa and Tappert theoretically showed the existence of solitons  and then Mollenauer et al. experimentally observed temporal solitons in a single mode fiber (SMF) , soliton pulses have been widely applied in optical communication, materials processing, metrology, fiber optical sensing and many other domains. When the pumping power exceeds a certain value, more than one pulse will emerge in an anomalously dispersive mode-locked fiber laser because of quantization of the soliton energy . Because of the quite different possible manifestations of soliton interaction dynamics, various multiple-solitons dynamic patterns, such as soliton bound states (BSs) [4–7], bunched solitons [8, 9], coexistence of strong and weak pulses , harmonic mode locking [8, 11–15], soliton rain [16, 17], soliton gas and soliton crystal  can appear. On the other hand, SMFs always show birefringence because of imperfections in their circular core, random mechanical strains and bends etc. Consequently, SMFs typically support two orthogonally polarized components, so that the solitons are said to have a vector nature. In general, the orthogonal polarization components propagate at different group and phase velocities. However, Menyuk has shown numerically that orthogonally polarized solitons can trap one another through cross-phase modulation, thus enabling solitons to propagate as a single entity . Such vector solitons are known as group velocity locked vector solitons (GVLVSs). Soon afterwards, Islam et al. experimentally observed GVLVSs in a birefringent optical fiber . Besides the locking of group velocities, for low-birefringence conditions in which the linear birefringence is comparable with potential nonlinear birefringence, the group velocity difference is assumed to be negligible. Within this regime polarized vector soliton will maintain both their temporal and polarization state profiles during propagation within a birefringent environment, Such solitons are referred to as phase- or polarization-locked vector solitons (PLVSs) [21–23]. Finally, some vector soliton polarization states can rotate and be locked to the cavity roundtrip or to multiples of it. These vector solitons are referred to as polarization rotation vector solitons (PRVSs) .
If the fiber laser mode locking is based on the nonlinear polarization rotation technique, the intra-cavity polarizer will fix the soliton polarization, so these fiber lasers can only form scalar solitons. On the other hand, if the fiber laser is mode locked with polarization independent saturable absorbers (SA), such as semiconductor saturable absorption mirrors (SESAMs), carbon nanotubes (CNTs), etc, vector solitons can be formed. Since vector solitons can be widely used in secure communication , trapping and manipulation of atoms or nanoparticles , and control of magnetization , polarization vector solitons in fiber lasers have attracted much attention. In 1995, Afanasjev first theoretically proposed the idea of the vector soliton fiber laser . Subsequently, researchers have experimentally observed multiple phase-locked high-order harmonic mode-locked vector solitons , fundamental dissipative vector solitons (DVSs) and multiple DVSs and DVS harmonic mode-locking , fundamental PLVSs  and GVLVSs , and vector soliton bunching  in SESAM mode locked fiber lasers. Other researchers have also experimentally obtained fundamental PRVSs , fundamental PLVSs , polarization locked fundamental BSs, and multipulse soliton operation [36, 37], and vector pulse trapping and scalar dissipative solitons in mode-locked fiber lasers with CNTs as SA.
Compared with CNTs and SESAM, graphene has a controllable saturable absorption strength, super broadband saturable absorption and ultrafast saturation recovery time. Consequently, it can be used as another polarization independent SA for generating vector solitons in a fiber laser. In 2010, Zhang et al. experimentally obtained both polarization rotation and polarization locked vector dissipative solitons with either one or two soliton pulses in the cavity in a dispersion-managed graphene fiber laser with large net cavity dispersion . Song et al. have experimentally observed stable PLVSs emission in a graphene mode-locked fiber laser, and have found that under certain conditions, this laser could also emit vector solitons with quasi-periodic variations in the pulse energy and polarization rotation during the cavity roundtrips . Subsequently, this research group has also observed multiple PRVSs , stable bunches of vector solitons, restless oscillations of vector solitons, vector soliton rain, and giant vector solitons . However, apart from above modes of soliton operation, there also exist other polarization dynamic patterns for vector solitons, such as BSs, harmonic or quasi-harmonic mode locking. In our previous work, we experimentally observed multiple-soliton dynamic patterns in a graphene erbium-doped fiber ring laser [5, 8]. The question therefore arises as to whether or not these patterns all have vector characteristics. It is also important to know whether their vector characters can be switched from a polarization locked state to a polarization rotation state in a graphene erbium-doped fiber ring laser. The present work addresses these questions.
In this paper, we have experimentally observed multiple polarization dynamic patterns of vector solitons in a graphene mode-locked fiber laser, and have found that not only do fundamental solitons, and bunched solitons have associated vector solitons as found in [40, 41], either tightly BSs or loosely BSs. Harmonic mode locking has also been experimentally observed. In addition, by carefully adjusting the orientation of the intra-cavity polarization controller, we have observed the switch from the polarization rotation to polarization locked for vector-soliton polarization dynamic patterns. The signal to noise ratio of our system was ~51 dB, which indicates that the laser operated in a high stability condition.
2. Experimental setup
The experimental setup of the laser discussed in this paper is shown in Fig. 1. The total cavity length of the ring laser was 14.4 m, corresponding to a fundamental repetition rate of ~14.34 MHz. This includes the gain medium, which was a 2-m length of high doping concentration erbium doped fiber (HDCEDF) with a group velocity dispersion (GVD) of 66.3 ps2/km, and a 12.4-m standard single mode fiber (SMF) with a GVD of −22ps2/km. The total cavity dispersion of the laser was −0.14 ps2. A 1480 nm laser diode with a maximum output power of 300 mW injected the pump light into the laser cavity through a 1480/1550 nm wavelength division multiplexer (WDM). A graphene absorber with the modulation depth of 3.41% was used as the SA. A polarization insensitive isolator (PI-ISO) operating at 1550 nm with an isolation of 45 dB ensured that the signal light propagated along the cavity in a unidirectional manner. An intra-cavity polarization controller (PC1) was used to change the polarization state of the cavity. A 90:10 output coupler (OC1) was used to output 10% of the cavity light. In order to observe the vector characteristics of the solitons, another extra-cavity polarization controller, PC2 and a fiber-based polarization beam splitter (PBS) were connected to the OC2. An optical spectrum analyzer (Yokogawa AQ6317C) with a maximum resolution of 0.01 nm, a 1-GHz digital sampling oscilloscope (Yokogawa DL9140) with three photodetectors with a 1 GHz bandwidth, and a radio frequency (RF) spectrum analyzer (Agilent N9020A) with a maximum measurable RF frequency of 26.5 GHz were used to observe the optical spectrum, temporal pulse shape, and the stability of operation.
3. Experimental results and discussion
3.1 Fundamental vector soliton
The laser used in this work had a very low mode locking threshold of about 10.5 mW. Once the pump power exceeded this threshold, self-starting mode-locked single pulse operation could be easily achieved. With carefully adjustment of the PC1, typical fundamental PLVSs could be obtained in the cavity. Figure 2(a) shows the optical spectra before and after passing through the PBS. The central wavelength is 1557.6 nm. From the spectra we can clearly see the Kelly sidebands which confirm that the pulses are optical solitons in the negative dispersion regime . The insert shows pulse train. Assuming a sech2 pulse profile, the full width at half maximum (FWHM) of a single pulse is about 1.38 ps as shown in Fig. 2(b). Figure 2(c) shows the wideband RF spectrum up to 300 MHz. The fundamental repetition rate of the pulse traces may be seen to be 14.34 MHz, corresponding to the cavity length of 14.4 m. The signal to noise ratio was up to 51 dB, which indicates that the laser operated in a highly stable regime. Figure 2(c) also shows the absence of sidebands and harmonics. The temporal pulse traces of the two orthogonal polarization components are shown in Fig. 2(d). They have uniform and equal pulse amplitudes, and the same central wavelength (Fig. 2(a)), as expected for PLVSs.
By slightly adjusting PC1, our laser operation state could be switched from fundamental PLVSs to the PRVSs. The time-domain characteristics of the PRVSs are presented in Fig. 3(a). The pulse strengths of the two polarization components shown in orange and green complement each other and alternate in amplitude with a period equal to twice the cavity round trip time, which indicates that the polarization state of the soliton is rotating. The corresponding optical spectra with the same central wavelength of 1558.8 nm are shown in Fig. 3(b). The spectrum shown by blue line is for pulses before passing through the PBS and is the standard soliton spectrum. From Fig. 3(b) we can see that the intensities of the two orthogonal polarization components spectra obtained after passing through the PBS change in a complementary way that can be attributed to coherent energy exchange between the two orthogonal polarization components [40, 43].
3.2 Vector bound state solitons
3.2.1 Tightly bound vector solitons
By increasing the pump power to 11 mW and carefully tuning the orientation of PC1, polarization locked and rotation bound vector solitons were also obtained. Note that since there exist different balances of attraction and repulsive force between adjacent solitons caused by Kelly nonlinearity and dispersion, both tightly (soliton interval is less than five pulse widths)  and loosely (soliton interval is greater than five pulse widths) bound vector solitons have been observed. Figure 4 shows the features of tightly bound polarization locked vector solitons. The optical spectra before (blue line) and after (orange and green lines) passing through the PBS are shown in Fig. 4(a). The central wavelengths are all 1558.75 nm. The period of the spectral modulation is related to the soliton separation through c·ΔT·Δλ = -λ2. The period, Δλ, of the spectral modulation is 2.42 nm, which corresponds to a soliton separation, ΔT, of about 3.1 ps as shown in Fig. 4(b). The FWHM of the pulse is 1.62 ps. The pulse separation is less than five pulse widths, confirming that it is a tightly bound vector solitons. Figures 4(c) and 4(d) show the temporal waveforms of the total pulse trace and the two orthogonal polarization states, all of which have the same pulse amplitude.
Fixed pump power and only slight tuning of the orientation of the paddles of the PC1, the operation state can be switched to polarization rotation tightly bound vector solitons as shown in Fig. 5. Figure 5(a) shows the optical spectra before (blue line) and after (orange and green lines) passing through the PBS with the same central wavelength of 1559.25 nm, from which we can see the spectral intensity difference between the two orthogonal polarization components is far less than 15 dB. The pulse amplitude of the total pulse before passing through the PBS is constant, while those of the two polarization states alternate with a period of twice cavity roundtrip time (see Fig. 5(b)). These observations indicate the BSs are polarization rotation bound vector solitons. The insert of Fig. 5(a) shows the autocorrelation trace of the total pulse with a pulse width of 1.25 ps and soliton separation of 4.83 ps, corresponding to a spectral modulation of 1.48 nm. It may also be seen that the soliton separation is less than five pulse widths, again suggesting that the solitons are tightly bound.
3.2.2 Loosely bound vector solitons
Further rotating the PC1 while holding the pump power at 11 mW, allowed us also to obtain loosely bound polarization locked and rotation vector solitons. Figure 6 shows the bound vector solitons in the polarization locked state. The spectra have a dense modulation of 0.58 nm (see Fig. 6(a)), which corresponds to a soliton separation of 14.1 ps as illustrated in the insert. Compared with the spectra of Fig. 4(a), there is a pair of Kelly sidebands appearing in the loosely BSs spectrum. The central wavelength is 1559.5 nm and the FWHM of the pulse is 1.43 ps. The soliton separation is more than five times the pulse width, indicating that the solitons should be categorized as loosely bound solitons of the type observed in soliton fiber lasers. Figure 6(b) shows an oscillogram of the pulse trains. The pulse trains are uniform in both amplitude and spacing both before and after passing through the PBS.
On this basis, with further slightly tuning of the PC1, polarization rotation loosely bound vector solitons were also observed as shown in Fig. 7. The spectra with a central wavelength of 1559.3 nm are shown in Fig. 7(a). The density modulation of 0.24 nm shown in the right insert of Fig. 7(a) is much denser than the spectral modulation of the polarization locked bound vector solitons shown in Fig. 4, and corresponds to a soliton separation of 33.7 ps as shown in the left insert which refers to the autocorrelation trace of the total pulse. By comparing the spectra and those in Fig. 5(a), we find that in addition to the usual Kelly sidebands, a pair of additional sidebands once again appears in the spectra. Figure 7(b) shows the total pulse traces and the pulse sequences of the two polarization rotation components, as in Fig. 5, which show that the pulse amplitudes are complementary. The pulse width is 1.94 ps.
3.3 Vector soliton bunching
On increasing the pump power to 29 mW, multiple solitons appeared in the cavity. By carefully rotating the PC1, these pulses were found to group themselves into tight packets in the bunched soliton mode. With further rotating of the PC1, both polarization locked and rotation bunched solitons were obtained. Figures 8(a) and 8(c) show the oscilloscope traces and the optical spectra of polarization locked vector bunched solitons. The separations between adjacent solitons were not equal, and decreased with time along a given bunch (See Fig. 8(b)). These characteristics can be seen in the PLV bunched solitons both before and after passing through the PBS. The central wavelengths were all 1559.2 nm. It is obvious that two sets of weak sidebands and a pair of peak-dip sidebands coexist with the Kelly sidebands. We attribute the weak sidebands to soliton interactions and the peak-dip sidebands to cavity birefringence.
Further adjusting of the PC1 caused the PLVSs bunching to become unstable and start to flow, until the laser switched to the PRVSs state, at which point stable PRV bunched solitons were formed. Figure 9(a) shows typical pulse traces for PRVSs bunching before (blue line) and after (orange and green lines) passing through the PBS. The amplitude of the pulses in bunches were periodic with a period of twice the cavity round trip time. In this case, the amplitudes of bunches were complementary to each other. Note that there are only two types of pulse bunches distinguished by their amplitudes. The optical spectra with a central wavelength of 1559.3 nm are shown in Fig. 9(b). Both the Kelly sidebands and peak-dip sidebands appear in the spectra. In addition, the CW on the spectrum is high that it contains a significant part of the total pulse energy.
3.4 Harmonic mode locking vector solitons
With further adjusting of the PC1, the bunched vector solitons became unstable, and multiple soliton groups were disrupted. The multiple vector solitons then occupied all the available space along the cavity but the soliton amplitudes did not show any significant correlations with each other. In this case, if we further adjusted the pump power and PC1 until the CW lasing became unstable, all vector solitons could be caused to distribute along the cavity with equal spacing. That is to say, vector soliton harmonic mode locking occurred. When the pump power was increased to 53 mW, we obtained 11th order harmonic PLVSs with a repetition rate of 157.8 MHz as shown in Fig. 10. The pulse traces before (Fig. 10(a)) and after (Fig. 10(b)) passing through the PBS all had uniform pulse amplitudes. The RF spectrum with a resolution bandwidth of 100 kHz is shown in Fig. 10(c). The signal to noise ratio of the harmonic mode locking vector solitons is about 31 dB. Figure 10(d) shows the corresponding optical spectra with a central wavelength of 1557.8 nm. Based the experimental results, it is believed that, apart from the gain recovery and the acoustic effect [45, 46], unstable CW lasing in the cavity may play an indispensable role in the formation of harmonic mode locking. We understand the above explanation as follows. As the laser operates in the anomalous dispersion region, a CW component is intrinsically unstable due to the modulation instability . This unstable CW component can introduce a kind of global soliton interaction mechanism between all the solitons, so that all the solitons in the cavity start to move. Only when they are equally distributed over the whole cavity, does the movement of the solitons cease, and steady harmonic mode-locking is formed . Recently, researchers have also experimentally [8, 11, 48–50] and theoretically [51, 52] demonstrated the role of the CW component in determining harmonic mode-locking properties.
Aside from the polarization locked harmonic mode locking vector solitons, we also achieved polarization rotation harmonic mode locking vector solitons by rotating PC1 at a fixed pump power of 53 mW. Figure 11 shows the vector characteristics of the 7th harmonic with a repetition rate of 100.2 MHz (see Fig. 11(c)). The pulse trains before (blue line) and after (orange and green lines) passing through the PBS are shown in Fig. 11(a). The pulse amplitudes of the two polarization components after passing through the PBS are complementary based on the total pulse before passing through the PBS. The corresponding optical spectra have the same central wavelength of 1558.3 nm. There are two types of sidebands (Kelly sidebands and peak-dip sidebands) in the spectra. The unstable CW underlying the optical spectrum stabilizes the harmonic mode locking.
Through analysis of the above experimental results, based on the soliton energy quantization effect and the birefringence of the cavity we obtained various patterns of vector solitons. Once a certain type of soliton pattern had been formed, carefully adjusting the PC1 but maintaining the pump power at a constant value, allowed the laser operation to convert back and forth between the locked polarization mode and rotation polarization mode. If we compare the spectra of the two polarization states of vector solitons, it is clear that there is a pair of peak-dip optical sidebands in addition to the conventional Kelly sidebands on the spectrum of the PRVSs, which is based on coherent energy exchange between the two orthogonal polarization components. In addition, we found that the new sidebands are not completely symmetric with respect to the peak wavelength in the polarization spectra. They are also not in the same place in different polarization rotation spectra obtained with different orientations of the intra-cavity PC. From this, it is obvious that the position of the peak-dip sidebands depends on the cavity birefringence [40, 43]. It is worth mentioning that we do not observe the extra peak-dip sidebands in the optical spectrum of the polarization rotation tightly bound vector solitons. We suspect this may be caused by the deep modulation of the spectrum burying the little peaks and dips due to the low vector spectral intensities.
In addition, unlike in [38, 40, 53], all the presented spectra in our experiment exhibit a CW lasing component close to the center wavelength, we think this may be due to the shallow modulation depth of the saturable absorber, as mentioned in , a shallow modulation depth corresponds to a large defect-induced nonsaturable loss. Zhao et al.  have pointed out that the linear cavity loss is in fact a sinusoidal function of the wavelength, and the strength of the CW component is determined by the linear cavity transmission of the laser. By optimizing the modulation depth of the saturable absorber, therefore, or changing the birefringence, these CW components can be suppressed.
In conclusion, we have experimentally investigated the polarization dynamics of vector soliton patterns in a graphene mode-locked erbium-doped fiber laser. The vector characteristics for locked and rotation polarization of the fundamental soliton, bunched solitons, loosely and tightly bound solitons and high order harmonic mode locking solitons were all obtained by carefully adjusting the pump power and the orientations of the intra-cavity PC.
This research was supported by grants from the National Natural Science Foundation of China (Grant nos. 11074065, 11374089 and 61308016), the Hebei Natural Science Foundation (Grant nos. F2012205076 and A2012205023), the Specialized Research Fund for the Doctoral Program of Higher Education of China (Grant no. 20101303110003) and the Technology Key Project of Colleges and Universities Hebei Province (Grant nos. ZH2011107 and ZD20131014).
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