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Abstract
We investigate various patterns of vector solitons arising in a passively mode-locked fiber laser based on semiconductor saturable absorber mirror (SESAM). By properly adjusting the cavity parameters including the pump power and intra-cavity birefringence, the fundamental vector solitons, vector soliton molecules, and macroscopic vector solitons can be separately observed. In particular, both vector soliton molecule and macroscopic vector solitons exhibit multi-pulse structure along one polarization axis while there occurs single pulse profile at its orthogonal polarization component. Thus, they can be treated as “1 + 2” and “1+n” vector solitons. Moreover, the size of the macroscopic solitons can be manipulated from half of the cavity to even the whole cavity. The generation mechanisms of these vector soliton patterns are also investigated.
© 2020 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
Passively mode-locked fiber laser as a flexible source of ultrafast optical pulses has always been a hotspot over past decades, due to its advantages of compact size, high stability, and simple configuration [1]. In addition, such lasers provide periodic boundary conditions, which can act as a convenient experimental platform for studying the formation and dynamics of temporal optical solitons [2]. Soliton molecule, also known as bound-state soliton, is an attractive phenomenon caused by interactions between individual solitons. Recently, stable and dynamically evolving soliton molecules have been found to arise from a variety of mode-locked mechanisms [3–7], resulting in distinct relationships between mutual amplitudes, phases and separations [8]. Particularly, apart from stable soliton molecules with fix separations and phases, they can also operate at metastable state characterized by oscillating separ ation and phase [9,10].
The first theoretical analysis of soliton molecule was performed by N. N. Akhmediev et al. based on complex Ginzburg-Landau equation (CGLE) [11,12]. Experimentally, nonlinear polarization rotation (NPR) effect is commonly used to generate various soliton patterns, due to its comprehensive phenomena and easy implementation. However, owing to the use of the polarization sensitive component within the mode-locked fiber cavity, theoretically a scalar soliton is often obtained from NPR-based fiber laser [13]. Alternatively, with the rapid development of 2D-material based saturable absorbers (SAs) which are normally polarization-independent, vector solitons are allowed to generate [14,15]. According to the strength of fiber birefringence, various vector solitons can be successfully obtained in 2D-material based fiber lasers, such as group velocity locked vector soliton (GVLVS) [16,17], polarization locked vector soliton (PLVS) [18,19], and polarization rotation locked vector soliton (PRLVS) [20,21].
Generally, the fundamental vector soliton can be regarded as “1 + 1” type, leading to the occurrence of fundamental solitons at two orthogonal components. In terms of vector soliton molecule (VSM), the common structure is “2 + 2” type, where soliton molecules happen at two orthogonal polarization axes. Over the past few years, such “2 + 2” type VSM has been widely investigated by taking into account of various mode-lockers including semiconductor saturable absorber mirror (SESAM) [22], carbon nanotube (CNT) [23,24], and graphene [7]. Recently, a new type “1 + 2” VSM has also been observed [25,26]. However, the authors mentioned that such “1 + 2” VSM is in fact a “pseudo-high-order” soliton because it is obtained by the extra-cavity polarization projection method [27], which means the vector soliton is still fundamental “1 + 1” type within the fiber laser. In this paper, we experimentally observe “1 + 2” type VSM directly generated from the fiber laser cavity, as well as particular “1+n” type multiple vector solitons (MVS), which refers to multi-solitons on one axis while single soliton on its orthogonal axis. These multi-solitons always emerge and evolve as a unit which can be treated as a macroscopic soliton. In our experiment, the soliton spacing of VSM and the size of macroscopic soliton can both be manipulated by the pump power and cavity birefringence. These interesting results further enrich the fundamental physics of vector soliton dynamic, and may have potentials of polarization-related optical applications, such as optical communications [28] and three-dimensional display [29], polarization multiplexing transmission [30] and free-running dual-comb generation [31]. Therefore, this study is supposed to play an important role in both theoretical researches and scientific applications.
2. Experimental setup
The proposed fiber laser is schematically shown in Figure 1. The self-starting mode-locked operation can be achieved by a commercial SESAM (BATOP, SAM-1550-15-7ps-x), which is attached at the end surface of a standard FC/PC fiber connector. The SESAM possesses low-intensity absorption of 15% at the wavelength of 1550 nm, modulation depth of 8%, and relaxation time of 7 ps. The circulator is used to incorporate the SESAM into the cavity, as well as guarantee the unidirectional propagation and suppress the detrimental reflections. A 1.2-m EDF (Nufern, SM-ESF-7/125) is used as the gain medium, which is pumped by a 976-nm laser diode (LD) with maximum output power of 400 mW. The absorption coefficient of the EDF is ∼55 dB/m near 1530 nm. The intra-cavity linear birefringence is adjusted by a polarization controller (PC). A 10:90 fiber optical coupler (OC) is utilized as the output port of the fiber laser. The total optical cavity length is estimated around 14.2 m.
Fig. 1. Schematic diagram of the fiber laser cavity. WDM: wavelength division multiplexer, EDF: Erbium-doped fiber, LD: laser diode, SESAM: semiconductor saturable absorber, PC: polarization controller, OC: optical coupler, PBS: polarization beam splitter.
As for the polarization resolved measurement at the fiber laser output, an in-line polarization beam splitter (PBS) is used to separate two orthogonal polarization components, and to simultaneously measure the polarization characteristics of generated solitons. In order to mitigate the fiber pigtail induced polarization rotation, we insert another PC between the laser output port and the PBS. Finally, an optical spectrum analyzer (OSA, Yokogawa AQ6370C) with a resolution of 0.02 nm and a 5-GHz oscilloscope (OSC, Tektronix DPO 4104) together with a 400-MHz photodetector (PD) are applied to monitor the optical spectrum and the output pulse-train, respectively. The radio frequency (RF) spectrum is measured by a 20-Hz∼6-GHz electrical spectrum analyzer (R&S, FSQ). Additionally, the pulse profile is measured by a commercial autocorrelator (Femtochrome, FR-103XL).
3. Experimental results
3.1 Fundamental PLVS state
The continuous wave (CW) lasing starts under the condition of 60 mW pump power. When the pump power is above the threshold of 80 mW, self-started mode-locking is achieved with proper setting of PC1, as shown in Figure 2. The pulse-train, as shown in Figure 2(a), presents a consistent peak intensity with a repetition rate of 14.5 MHz, which corresponds to the 14.2-m cavity length. The average output power is around 1.2 mW, so that we can estimate the single pulse energy to be 83 pJ. Figure 2(b) shows the typical spectrum of conventional soliton with 3-dB spectral bandwidth of 2.8 nm. This relatively narrow wavelength range is mainly limited by operation bandwidth of SESAM and newly-discovered mode-lockers can be used to extend the spectrum, such as topological insulators [32] and transition metal sulfides [33–36]. By using these wide bandwidth materials, sub-picosecond or femtosecond pulses can also be expectable. Figure 2(c) illustrates the fundamental frequency with a signal-to-noise ratio (SNR) of more than 70 dB. No extra RF component is observed around the RF spectrum peak, indicating of the good quality of single pulse mode-locking. The inset shows the RF spectrum with 400-MHz frequency range, which shows uniform peak intensity. The anomalous dispersion cavity generates typical ultrafast pulses with a full-width at half maximum (FWHM) of 2.7 ps if a sech2 pulse profile is fixed, as shown in the autocorrelation trace of Figure 2(d). Therefore, the output pulses are nearly transform-limited. Since all the optical components are polarization-independent, the cavity can be regarded as a vector module leading to the generation of vector solitons. After polarization resolving measurement, we obtain the two orthogonal polarization components of the vector soliton. Two resolved pulse-trains have the same repetition rate as the total one without polarization rotation phenomenon [20,21]. The optical spectra from two axes only have about 3-dB intensity difference, as shown in inset of Figure 2(b). Therefore, we have successfully obtained a typical PLVS output.
Fig. 2. Mode-locking at 80-mW pump power: (a) oscilloscope trace of the pulse-train, inset: pulse-trains after PBS; (b) optical spectrum; (c) RF spectrum; (d) autocorrelation trace.
3.2 Single-axis VSM state
By increasing the pump power to 100 mW and adjusting the polarization state, the laser operation turns into the soliton molecule mode locking. As shown in Figure 3, The output spectrum shown in Figure 3(a) with black line clearly demonstrates a regular modulation with a period of 0.6 nm, which is a typical characteristic of the soliton molecule. After polarization resolving measurement, the spectrum from vertical axis maintains the modulated profile while the one from horizontal axis becomes standard sech2 shape, indicating the single soliton state. The autocorrelation traces in the inset further confirm the “1 + 2” soliton state. The total and vertical pulses show typical double-humped autocorrelation trajectory, exhibiting three peaks with an intensity ratio of 1:2:1. This indicates that the two solitons of soliton molecule have the same intensity. Base on Fourier analysis, the 0.6-nm (around 75-GHz) spectral fringe spacing corresponds to 13.3-ps soliton separation, which agrees well with the experimental observation. Along the horizontal axis, there is no such double-humped profile, which verifies the generation of typical single soliton state. Figure 3(b) shows the total and resolved pulse-trains trapping each other, which co-propagate as a non-dispersive unit.
Fig. 3. Experimental observation of “1 + 2” soliton molecule: (a) optical spectra before and after PBS, inset: autocorrelation traces; (b) oscilloscope trace of the pulse-trains before and after PBS.
It is noteworthy that this typical “1 + 2” soliton molecule is directly generated from fiber laser cavity, instead of using polarization projection method to manipulate two single soliton along the output port, which obtains “pseudo-high-order” solitons as discussed in [25–27]. In our case, two orthogonal components are locked as a single unit and can be regarded as a real high-order vector soliton. Figure 4 shows the different transmission process through polarization resolving measurement between the two cases. A general vector soliton which has two orthogonal components goes through a PC then a PBS. The PC functions as a phase retarder to adjust the phase difference between two components. The PBS can manipulate the projection of the vector soliton, as well as separate the orthogonal polarizations for measurement. In our case, by adjusting the PC, two orthogonal components of the “1 + 2” type VSM can be completely separated along two axes of PBS, as shown in Figure 4(a). In terms of “1 + 1” type vector soliton, as shown in Figure 4(b), it can also transform into a soliton molecule with appropriate phase retard by PC adjustment together with the projection of PBS. Moreover, “2 + 2” type VSM could also be obtained if the time separation between the two orthogonal components is efficiently large [25]. In this case, during the PC adjustment, both intensity and phase difference of two projection-acquired solitons may change, leading to the obvious spectral interference fringe movement [27]. However, in our case, the position and spacing of fringe always keep unchanged which further confirms that the “1 + 2” type VSM is obtained within the cavity by a fixed intensity and phase difference. On the other hand, in the experiment, the shape of spectral profile can only be varied by adjusting PC within cavity (PC1 in Figure 1). Figure 5 shows loosely bound states of soliton molecules obtained by slightly adjusting PC1. The purple and green line in Figure 5(a) show the optical spectra (with 5- and 10-dB offset) of two states of soliton molecules with denser fringes of 0.33 nm and 0.13 nm, respectively, corresponding to the pulse separation of 24 ps and 61.5 ps, which are about 9 and 23 times of the pulse width, as shown in Figure 5(b). Therefore, two solitons are loosely bound together. Our experimental observations signify that the soliton separation can be flexibly manipulated by finely adjusting the intra-cavity birefringence.
Fig. 4. Different transmission process of (a) intra-cavity and (b) extra-cavity generated soliton molecule
Fig. 5. Loosely bound states of soliton molecules: (a) modulated optical spectra; (b) corresponding autocorrelation traces
3.3 Single-axis MVS state
When the pump power is further increased to 120 mW, the pulses split into multiple, as shown in Figure 6(a) and 6(b) with black line. It is known that, for fiber laser operated in anomalous dispersion region under the condition of high pump power, excess nonlinear phase shift accumulation will result in the spectrum broadening, consequently pulse deformation and wave breaking occur [37]. In previous researches on the MVS, no matter PLVSs or PRLVSs, two orthogonal components both contain multiple solitons [38–41]. In our experiment, after the polarization resolving measurement, the vertical component has multi-soliton state, while the horizontal component is still fundamental state. Similar to “1 + 2” type VSM, the obtained state can be regarded as “1+n” type MVS.
Fig. 6. “1+n” type vector soliton: (a)(c) oscilloscope trace of the pulse-trains before and after PBS; (b)(d) corresponding optical spectra before and after PBS
In such case, along the vertical axis, there are seven pulses existing within every cavity period. These pulses with different separations and similar peak power occupy up to half of cavity length, which can be considered as a macroscopic soliton. Slightly adjusting the PC1, another stable state of “1+n” type MVS can also be generated, as shown in Figure 6(c) and 6(d). The number of pulses within one cavity period is seven, and this new macroscopic soliton occupies the whole cavity. If the PC1 is rotated to the former angle, the macroscopic soliton can also evolve to the previous state. Moreover, we observe that the pump power hysteresis phenomenon is related to the multi-soliton operation [21]. When we continually decrease the pump power, the multi-soliton state maintains until to 110 mW pump power, while the soliton molecule maintains until to 95 mW pump power and single soliton under the condition of 76 mW pump power, which are all lower than the thresholds when increasing pump power.
It is found that the states of MVS are sensitive to the pump power and orientation of PC. Theoretically, the multi-soliton operation is attributed to the soliton energy quantization effect [42]. Once multiple solitons appear in a cavity, they will evolve into various regimes based on the interactions among the solitons, continuous waves and dispersive waves [41]. As a result, changing the pump power and the birefringence will give rise to different multi-soliton dynamic patterns converting form one to another. What we have observed in Figure 6 is just some of those cases, it is anticipated that rich soliton dynamics may be further obtained. We have to admit that it would be more convincing and attractive if some real time spectral measurements like dispersion Fourier transform (DFT) technique can be recorded [43]. However, limited by existing experimental conditions, the DFT measurement cannot be conducted at present.
4. Discussion
In a scalar soliton fiber laser, there exists different types of soliton interaction among the unstable CW lasing, resonant dispersive waves, and direct soliton-soliton interaction [44]. However, for a vector model, four wave mixing (FWM) effect induced the inter-axis energy-exchange also needs to be taken into account [45]. Such kind of energy-exchange between two orthogonal components of vector solitons will form extra peak-dip sidebands in the optical domain and polarization rotation in the time domain. In our previous work [13], we have pointed out that large local birefringence may enhance the energy-exchange interaction between two orthogonal components, and stimulate the evolvement from scalar solitons to vector solitons. In this case, the intra-cavity birefringence is relatively low, thus the two orthogonal components propagate independently with weak energy-exchange. Therefore, the intensity difference on two polarization axes will give rise to distinct evolve processing of the nonlinear waves. As we can see from the above results, on the vertical axis with higher energy, the pulses are more easily to either bound or split due to the intra-axis soliton interactions. Therefore, various multiple soliton patterns, such as bound-state soliton, soliton bunch, and soliton rain, etc. can all be observed on the vertical axis under the condition of different pump power. Here, we mainly present and discuss two most typical and stable states, including VSM and MVS.
5. Conclusion
In summary, special vector soliton types of VSM and MVS arising in one single polarization axis are experimentally observed. The weak cavity birefringence limits the energy-exchange between two orthogonal components of generated vector soliton. Because of the light intensity difference between two orthogonal components, the pulses on the vertical axis having higher energy are more easily to evolve into the soliton molecule or macroscopic soliton state, due to the relatively stronger nonlinear effect. Particularly, the obtained single-axis soliton molecule can flexibly operate at both tightly and loosely bound states with different pulse separations from 13.3 ps to 61.5 ps. On the other hand, the size of macroscopic soliton can be manipulated up to half of cavity or even the whole cavity. Such phenomenon further proves that two components of a vector soliton can evolve independently and pave a new way for the practical use as flexible seed sources for high-power lasers or polarization-multiplexed light sources for optical communication system.
Funding
Natural Science Foundation of Hubei Province (2019CFB598); the Open Project Program of Wuhan National Laboratory for Optoelectronics (2019WNLOKF005); National Natural Science Foundation of China (61605179); Wuhan Municipal Science and Technology Bureau (2018010401011297); Fundamental Research Funds for the Central Universities, China University of Geosciences, Wuhan (162301192695, G1320311998, ZL201917).
Disclosures
The authors declare no conflicts of interest.
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