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Different polarization dynamic states in an unidirectional, vector, Yb-doped fiber ring laser have been observed. A rich variety of dynamic states, including group velocity locked polarization domains and their splitting into regularly distributed multiple domains, polarization locked square pulses and their harmonic mode locking counterparts, and dissipative soliton resonances have all been observed with different operating parameters. We have also shown experimentally details of the conditions under which polarization-domain-wall dark pulses and bright square pulses form.
© 2015 Optical Society of America
1. Introduction
Passively mode-locked fiber lasers (PMFLs) have attracted considerable attention during the past two decades because of their simple implementation, low cost and compactness. Apart from ultrashort pulses with femtosecond or picosecond pulse duration, PMFLs can also generate square-wave pulses on nanosecond timescales. In 1991, Richardson et al. first observed nanosecond square-wave pulses generated in a figure-8 PMFL, and pointed out that the peak power clamping effect could be used to generate square pulses [1]. Matsas et al. obtained square-wave pulses in a nonlinear polarization switching mode-locked fiber laser [2]. Subsequently, square pulses were frequently observed in long-cavity net-negative-dispersion erbium-doped fiber lasers (EDFLs) [3–6], figure-8 passively mode-locked normal dispersion ytterbium-doped fiber lasers (YDFLs) [7, 8], and YDFL with a microfiber-based graphene saturable absorber (GSA) [9]. Recently, the formation of another new square-wave state, named dissipative soliton resonance (DSR) has been demonstrated theoretically through careful selection of the laser parameters [10–15]. Since under DSR conditions, the pulse energy can, in principle, increase indefinitely with increasing pump power without wave breaking while the pulse amplitude remains constant, the DSR state has attracted significant attention over the past few years. The experimental observation of square-wave pulses in the DSR region has been realized both with normal-dispersion mode-locked EDFLs [16, 17], and anomalous-dispersion mode-locked EDFLs [18–20]. Very recently, both Liu et al. and our group have experimentally obtained DSR pulses in a nonlinear polarization rotation mode-locked YDFL [21, 22]. All the above experiments have confirmed that square pulse can be obtained in the DSR region in mode-locked fiber lasers [9, 16–22].
The above pulses were all generated in PMFLs, i.e. devices containing a fast saturable absorber. However, if the fast saturable absorber element is removed from the experiment, the fiber laser cavity can still show pulsations at the cavity round-trip frequency [23, 24]. In addition, since a single-mode fiber can support two degenerate modes that are polarized in orthogonal directions, the fiber laser output beam contains two linearly polarized components, so that the laser is said to have a vector nature, and if the laser cavity does not have a polarizer, the cross coupling between these two orthogonal polarization components can lead to different polarization dynamic states according to their different propagation velocities along the fiber. These dynamic states include group velocity locked (GVL) polarization domains (PDs), and polarization locked pulses. In 1987, Zakharov and Mikhaǐlov first theoretically predicted the existence of the PD in nonlinear optics [25]. In 1993, Wabnitz and Daino theoretically studied the possibility of generating PD solitary waves in nonlinear optical fibers [26], and in 1994, Haelterman and Sheppard theoretically revealed the existence of polarization-domain-wall (PDW) solitons in a dispersive Kerr medium [27, 28]. They also showed that the polarization modulation instability in the normal-dispersion regime of a single-mode fiber was associated with the existence of PDW dark vector solitons [29]. The formation of the PD and PDW solitons was also experimentally confirmed in optical fibers [30–33], and subsequently, researchers have observed PD and PDW solitons in EDFLs with net anomalous dispersion in the cavity [34–37].
As mentioned above, most experimental research to date has focused on EDFLs with net-anomalous-dispersion [34–37]. However, compared with net-anomalous-dispersion EDFLs, YDFLs with net-normal-dispersion are more suitable for generation of high-energy pulses. In 2013, Lecaplain et al. first theoretically demonstrated the formation of PD and PDW complexes in fiber ring lasers operating with a normal path-averaged dispersion [38]. However, to the best of our knowledge, no experimental observation of the PD in an all normal dispersion YDFL has been reported. Since the vector YDFL without an external, fast saturable absorber element in its cavity can still exhibit pulsations, the question arises as to whether this vector laser can emit PD, nanosecond square-wave pulses, or DSR pulse as in PMFLs. This was the initial motivation for our work.
In this paper, we report experimental observations performed with an all normal dispersion Yb-doped fiber ring laser cavity without polarization-selective elements, highlighting the GVL PDs and their splitting into regularly distributed multiple domains, polarization locked square pulses and their harmonic mode locking counterparts as well as DSR states. We also provide a comprehensive polarization-resolved study of the operation of the vector fiber laser. The results provide a guideline for identifying the formation of different types of square pulses as well as these new operation regimes for vector YDFLs.
2. Experimental setup
The laser used in this work, as shown in Fig. 1, was a ring fiber laser with a cavity configuration similar to that used in Ref [39]. A fiber-pigtailed 976 nm laser diode with a maximum pumping power of 300 mW was used to pump the Yb-doped fiber (YDF) through a 976/1060 nm wavelength-division multiplexer (WDM). A 1 m long segment of YDF with a peak core absorption of 1200 dB/m at 976 nm (Yb1200-4/125, LIEKKITM) was used as the gain medium. All the other fibers (126 m in total) were standard single-mode fibers (HI1060, Corning). A polarization controller (PC1) was used to control the polarization of the light in the resonant cavity. A polarization-independent isolator (PI-ISO) was employed to force unidirectional operation of the laser. The laser signal was monitored using one port of a 50:50 optical coupler (OC2) spliced at the 10% output port of the 10:90 OC1. To balance the phase delay caused by the pigtailed fibers of the OCs used outside the cavity, a second polarization controller, PC2, was inserted before the fiber pigtailed polarization beam splitter (PBS). The unresolved output of the laser and the polarization resolved beams could then be simultaneously detected. An optical spectrum analyzer (Yokogawa AQ6317C) with a maximum resolution of 0.01 nm, a 1 GHz real-time oscilloscope (Yokogawa DL9140) with three 1-GHz photodetectors, 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, pulse train, pulse repetition rate and the stability, respectively.
Fig. 1 Schematic setup of the all-normal-dispersion vector ring oscillator. WDM: wavelength division multiplexer, YDF: Yb-doped fiber, PC: polarization controller, SMF: single mode fiber, PI-ISO: polarization-independent isolator, OC: output coupler, PBS: fiber pigtailed polarization beam splitter.
3. Experimental results and discussion
3.1 Group velocity locked polarization domains and regularly distributed multiple domains
Since there were no polarization sensitive components in our laser, the laser always simultaneously oscillated with two orthogonal linear polarizations. Under various laser operation conditions, these two laser oscillations can have different central wavelengths, and there can then be different interactions between them, which would result in various operation states. As an example, Fig. 2(a) shows a typical optical spectrum of the laser emission when the pump power was about 253 mW. As may be seen, the total laser spectrum looks like the laser is operating in a dual-wavelength emission mode (Initial trace). The central wavelengths of the two orthogonal polarization components are 1069.8 nm (x axis trace) and 1073.1 nm (y axis trace), respectively. Due to the small cavity birefringence, there is only a small wavelength difference of 3.3 nm between the two orthogonally polarized laser oscillations.
Fig. 2 The total output of the laser (upper trace), laser emission along one polarization component x axis (middle trace) and along its orthogonal polarization component y axis (lower trace). (a) is the corresponding spectra of (b). PDW dark pulses at the total/initial laser output and the PDs at the two orthogonal polarization components, (b), (c) and (d), by adjusting PC1.
In general, these orthogonal polarization components propagate at different group velocities in the fiber. 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 [40]. Such vector solitons are known as GVL solitons. Figure 2(b) shows the total output and the polarization resolved outputs for the GVL PDs. We can see that within one cavity round-trip period (~625 ns), the laser emission switched from one polarization to the other, forming two PDs. One polarization component shows a quasi-square PD (middle trace), whereas the other displays a chaos-state PD (lower trace). Since the two laser oscillations have an obvious wavelength separation, they must have incoherent coupling. As a result, a dark pulse with a full width at half maximum (FWHM) of 40.5 ns and a contrast of 91.5%, was formed in the total laser intensity output (upper trace of Fig. 2(b)). Since the dark pulse is located at the region where the PDs switch, it can be viewed as a PDW dark pulse. Carefully tuning PC1 resulted in changing the widths of the PDs, Fig. 2(c) shows another manifestation of the PDs. With further adjustment of the pumping power and PC1, each PD would split into several PDs. With different cavity parameters, these new PDs could distribute either regularly or irregularly in the cavity. As an example, Fig. 2(d) shows regularly distributed multiple domains within one cavity round-trip period.
3.2 Polarization-locked square pulses
3.2.1 Generation of square pulses
By further careful adjustment of the paddle orientations of PC1, the net linear cavity birefringence as well as the wavelength separation between the two orthogonal linear polarization components could be changed. This separation could be tuned to zero, at which point the group velocity difference may be assumed to be negligible. Within this regime, polarized vector solitons maintain both their temporal and polarization profiles during propagation within the birefringent environment. Such solitons are referred to as phase- or polarization-locked vector solitons [41–43]. Figure 3(a) shows the temporal trace of square pulses. The tops of the square pulses were in the form of plateaus with a gradient in amplitude and fine-grained fluctuations across the plateau. The FWHM of the square pulses was 67.2 ns. The spectrum with three peak structures was due to a birefringence-induced filtering effect in the long cavity length and a relatively high pump strength [44, 45]. The polarization resolved spectrums shown in Fig. 3(b) indicate that the spectra of the two orthogonally polarized components had the same spectral structure and main-peak wavelength. In this case, the oscilloscope traces of the two polarization-resolved pulses were uniform without any antiphase modulation. This is a typical characteristic of polarization-locked vector pulses [41–43]. The RF spectrum of the square pulses, shown in Fig. 3(c), was measured using an RF spectrum analyzer. It was clear that the fiber laser could operate at the fundamental repetition rate of ~1.6 MHz, and under those conditions, the signal-to-noise ratio was larger than 55 dB. The inset of Fig. 3(c) shows the wideband RF spectrum up to 60 MHz, and confirms stable operation. The envelope of the RF spectrum was periodically modulated because the long duration of the square pulse introduced significant side frequencies [4]. It's important to note that the square pulse trains we have generated are different from those generated in quasi-isotropic cavity fiber lasers discussed elsewhere [23, 24, 36, 38].
Fig. 3 Square-pulse emission: Temporal traces of the initial intensity (upper trace) and the polarization resolved laser emission along the x axis (middle trace) and y axis (lower trace) (a). Optical spectrum (b). RF spectrum with a 3 MHz span and 10 kHz resolution bandwidth. Inset: RF spectrum over a 60 MHz span (c).
3.2.2 The collapse and harmonic mode locking of square pulses
From Fig. 4, one can see that once the square pulse was formed, its peak intensity and width both increased with the pump power. When the upper limit of peak intensity was reached, the square pulses split because of energy quantization effects. Figure 4(a) shows the temporal evolution of square pulses with pump power increasing from 142 mW to 250 mW. Media 1 also shows this process. When the square pulses split into two or more pulses, careful adjustment of the intra-cavity PC, allowed harmonic mode locking (HML) to take place. The harmonic mode locking resulted from the balance of attractive and repulsive forces between adjacent square pulses which arose from the interactions between nonlinearity, dispersion, nonlinear gain saturation and loss. Figure 4(b) and Media 2 record the evolution of square pulses with adjustment of the paddle orientation of PC1. Figures 4(c) and 4(d) show the pulse trains and corresponding spectra of the 2nd and 3rd order HML square pulses.
Fig. 4 Evolution of square pulses with changing pump power. (See Media 1) (a). Evolution of square pulses with adjustment of the paddle orientation of PC1 (See Media 2) (b). Oscilloscope traces of 2nd and 3rd order HML square pulses (c). The corresponding spectra (d).
3.2.3 DSR phenomenon
In this experiment, we also found that there existed a specific range of operating parameters in which the gradient plateaus of the tops of the square pulses would become flat plateaus. Figure 5(a) shows typical oscilloscope traces of this type of square pulse emission. In this case, the square pulse duration increased with the pump strength while the peak intensity remained almost constant. Media 3 records the evolution of the pulse width with gradually increasing pump power. Figure 5(b) shows the evolution of the optical spectrum of these square pulses. The short-wavelength overall spectral intensity obviously increased more than that of the long-wavelength range (See inset of Fig. 5(b)). This indicates that the shorter-wavelength side of the spectrum would have more effect on the trailing edge of the pulse. In fact, since the laser operated in an all-normal dispersion cavity, the longer-wavelength components travel faster than the shorter-wavelength components. The strong effect of the shorter-wavelength side would lead the pulse to become broader near its trailing edge in the time-domain (see Fig. 5(a)).
Fig. 5 The evolution of square pulses with increasing pump power: square pulses of widths 31.0, 36.6, 41.8, 46.8, 52.6, 58.6, 64.3, 70.3, 76.2, 81.6, and 87.8 ns at pump powers of 78, 83, 88, 93, 98, 103, 108, 113, 118, 123, and 128 mW, respectively (a) (See Media 3), and the corresponding spectra(b).
Figure 6 shows details of the pulse widths, output powers, peak powers and pulse energies versus the pump power. As shown in Fig. 6(a), the pulse width increases linearly with the pump power. The injected pump powers were selected as 78, 83, 88, 93, 98, 103, 108, 113, 118, 123, and 128 mW. The corresponding pulse durations were 31.0, 36.6, 41.8, 46.8, 52.6, 58.6, 64.3, 70.3, 76.2, 81.6, and 87.8 ns, respectively. Figure 6(b) shows the pulse energy and peak power as a function of the pump power. Note that the pulse energy increased linearly with the pump power without suffering pulse break-up, while the peak power of the square pulse inside the cavity remained almost constant. Square pulses with flat plateaus is a characteristic of DSR [9, 16–22]. Therefore, the square pulse could be regarded as a DSR pulse. In our experiment, the peak power of the square pulses was about 0.16 W in the cavity and the recorded maximum pulse energy was 1.33 nJ. Polarization resolved study of the operation of the flat-topped square pulse still showed polarization-locked vector square pulse trains without any antiphase modulation. Using numerical simulation, Chang et al. pointed out that the DSR pulse did not have linear chirp across the whole pulse but, nonetheless, good compression could still be achieved [11]. Further work using a pair of diffraction gratings to compress the square pulses and study their characteristics is ongoing.
Fig. 6 The measured average output power and pulse width variation with pump power (a). Peak power and pulse energy vs pump power (b).
3.3 Discussion
The above experimental results indicate that square pulses can be produced in an all-normal dispersion oscillator without polarization-selective elements. Typically, when a laser is operated in an all-normal-dispersion regime, an external bandwidth-limited filter and a saturable absorber are required in the resonant cavity to change the cavity loss and shape the pulse, respectively. However, since there were no explicit external bandpass filters or saturable absorbers in our laser cavity, the observed pulse forming must be based on other considerations. We infer that a giant bright pulse can result from self-mode locking as reported in Ref [39]. The interplay between the laser signal and the saturated population inversion can act as a weakly saturable absorber [46]. A birefringence-induced filtering effect can act as an artificial filter as frequently occurs in fiber lasers with long cavity lengths [44, 45, 47]. We therefore believe that the formation of square pulses is a consequence of the giant bright pulses resulting from a self-mode-locking effect in a longer cavity.
4. Conclusion
In conclusion, we have experimentally demonstrated a relatively simple example of the formation of group velocity locked polarization domains and polarization-locked square pulses in a ring cavity fiber laser that did not include polarization dependent loss elements, so that full vector propagation was allowed. With appropriate operating parameters, DSR pulses could also be generated in this long-cavity oscillator.
Acknowledgments
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 of Hebei Province (Grant Nos. ZH2011107 and ZD20131014).
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