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Abstract
We report the generation of both polarization-locked vector dissipative soliton and group velocity-locked vector conventional soliton in a nanotube-mode-locked fiber ring laser with large normal dispersion, for the first time to our best knowledge. Depending on the polarization-depended extinction ratio of the fiber-based Lyot filter, the two types of vector solitons can be switched by simply tuning the polarization controller. In the case of low filter extinction ratio, the output vector dissipative soliton exhibits steep spectral edges and strong frequency chirp, which presents a typical pulse duration of ~23.4 ps, and can be further compressed to ~0.9 ps. In the contrastive case of high filter extinction ratio, the vector conventional soliton has clear Kelly sidebands with transform-limited pulse duration of ~1.8 ps. Our study provides a new and simple method to achieve two different vector soliton sources, which is attractive for potential applications requiring different pulse profiles.
© 2017 Optical Society of America
1. Introduction
Solitons, as stable localized wave packets that can propagate undistorted over long distances, have been extensively investigated over the last decades [1–3]. Back in 1980, Mollenauer et al. have firstly reported the experimental observation of optical solitons in single mode fibers (SMFs) [4]. In fact, as SMFs are always weakly birefringent due to pressures and twists, the vector nature of solitons should be considered as they propagate in the fiber [5,6]. Considering the fiber birefringence, various vector solitons including the polarization-rotating vector solitons, group velocity-locked vector solitons, and polarization-locked vector solitons, can be formed in SMFs [7–9].
Optical solitons can be observed not only in SMFs but also in mode-locked fiber lasers. However, different from solitons formed in SMF, the laser is a typical nonlinear dissipative system where the gain and loss play key roles [10–14]. Depending on the net cavity dispersion of fiber lasers, several kinds of solitons, such as conventional solitons, dispersion-managed solitons, self-similar pulses, and dissipative solitons have been investigated [15–21]. Furthermore, vector solitons are also theoretically predicted in mode-locked fiber lasers and experimentally confirmed recently [22–28]. Zhao et al. have proposed an anomalous dispersion fiber laser that can generate the group velocity-locked vector conventional solitons (VCSs), and interpreted the formation as caused by the soliton frequency shift of the coupled solitons [29]. Tang et al. have shown the existence of high-order polarization-locked VCSs in a fiber laser mode-locked with a semiconductor saturable absorber mirror, indicating that the formation of the soliton requires not only that the group velocities of the two components are locked but also that their phase velocities are locked [30,31]. Both the polarization-locked and polarization-rotating vector dissipative solitons (VDSs) in normal dispersion regime have been experimentally obtained by Zhang et al [32]. On the other hand, versatile laser sources with different types of pulse profile are highly desirable for practical applications. Through carefully controlling the gain/loss of a normal dispersion laser cavity, switching among dispersion-managed solitons, similaritons, and dissipative solitons has been reported [33]. Recently, conventional soliton, dispersion-managed soliton, and dissipative soliton mode-locking regimes have been realized from a versatile erbium-doped fiber (EDF) laser by an in-cavity programmable filter [34]. However, to the best of our knowledge, no report that both VDS and VCS are delivered from a fiber ring laser with the same net cavity dispersion.
In this paper, we have demonstrated a nanotube-mode-locked EDF laser with a section of polarization-maintaining fiber (PMF) in normal dispersion regime, delivering two types of vector solitons: polarization-locked VDS and group velocity-locked VCS. The two types of vector solitons can be switched by simply varying the orientations of the intracavity polarization controller (PC). When the equivalent filter is under the condition of low extinction ratio, the VDS characterized by the steep spectral edges and strong frequency chirp, which is normally generated in positive dispersion regime, can be obtained. While in the case of high extinction ratio, the VCS characterized by the clear Kelly sidebands and transform-limited pulse, which is normally generated in negative dispersion regime, can be gotten in the same laser. This is a new and simple method to control and achieve different pulse profiles from a same fiber laser.
2. Experimental setup
Figure 1 shows the schematic diagram of the experimental setup. The fiber laser has a ring cavity that consists of a piece of 22-m EDF with a dispersion parameter D of –42 ps/nm/km, a total length of 4.3-m standard SMF with a dispersion parameter D of 17 ps/nm/km, and a section of 0.69-m PMF with a dispersion parameter D of 17 ps/nm/km at 1550 nm, respectively. The mode-locker is assembled by sandwiching the single wall carbon nanotubes (SWNTs) based saturable absorber (SA) film between two fiber connectors. The damage threshold peak intensity of the SWNTs film is ~570 MW/cm2. A polarization-independent isolator (PI-ISO) is employed to force the unidirectional operation of the ring cavity. A PC1 is used to fine-tune the birefringence of the cavity. The 10% port of an optical coupler (OC) provides the laser output. The laser is pumped by a 980 nm laser diode (LD) through a wavelength division multiplexer (WDM). A section of PMF is added between the WDM and SA to serve as a fiber-based Lyot filter if laser cavity also consists of elements with polarization dependent loss. In the laser cavity polarization dependent loss is inserted by fused WDM and fused OC [35]. The output pulse can be polarization-resolved along two birefringence axes with a polarization beam splitter (PBS) and a PC2 external to the cavity. An optical spectrum analyzer, a commercial autocorrelator (AC), a radio-frequency (RF) analyzer, and a 6-GHz digital oscilloscope with a photodiode detector are used to monitor the laser output simultaneously.
Fig. 1 Schematic diagram of the experimental setup. LD, laser diode; WDM, wavelength-division multiplexer; EDF, erbium-doped fiber; OC, optical coupler; PI-ISO, polarization- independent isolator; PC, polarization controller; SWNTs-SA, single wall carbon nanotubes saturable absorber; PMF, polarization-maintaining fiber; PBS, polarization beam splitter.
3. Experimental results
The net cavity dispersion of the fiber laser is estimated as ~1.1 ps2. With an appropriate PC state, self-started mode locking can be easily established by increasing the pump power P = 26 mW. Noting that once mode locking, the laser can operate stable at least for several hours, and this stable process is repeatable after the breakdown of the stability. Figure 2 shows a typical mode-locking state of the laser. The optical spectrum in Fig. 2(a) exhibits steep spectral edges, which is the typical feature of the dissipative solitons [36]. The central wavelength and 3-dB spectral bandwidth of the dissipative soliton are ~1565.8 nm and ~4.3 nm, respectively. Figure 2(b) is the corresponding AC traces of the experimental data and a Gaussian-shaped fit. Assuming a Gaussian temporal profile, the pulse duration of the dissipative soliton is ~23.4 ps. The time-bandwidth product (TBP) is 12.3, indicating that the pulse is strongly chirped. Furthermore, we investigate the dissipative soliton by injecting it into SMF external to the cavity. In the experiment, the length of SMF is gradually increased from 0 to 100 m. The dissipative soliton shows compression from 0 to 28 m, and is broadened from 28 to 100 m. The pulse duration of the dissipative soliton can be compressed to ~0.9 ps. The corresponding TBP is ~0.47, expected in the case of transform-limited Gaussian pulse. The average output power and peak power of the dissipative soliton are ~0.8 mW and ~118 W, respectively.
Fig. 2 (a) Optical spectra, (b) AC traces, (c) and (d) oscilloscope traces, (e) and (f) RF spectra of polarization-locked VDS. The blue and red curves denote horizontal and vertical components, respectively.
To verify the vector nature of the dissipative soliton, we use a PBS and a PC2 external the cavity to separate its two orthogonally-polarized components. It turns out that the dissipative soliton, shown in Fig. 2 is a polarization-locked VDS. The polarization feature of the dissipative soliton is clearly reflected in Figs. 2(c) and 2(d). After passing through a polarizer, the two polarization-resolved oscilloscope traces show uniform pulse height without any modulation, with ~132 ns interval between the two adjacent pulses, indicating that the polarization of the dissipative soliton is fixed along the cavity [32]. For a phase locked vector soliton, we can also measure its polarization-resolved spectra [30]. The two components shown in Fig. 2(a) have the same central wavelengths, and comparable spectral intensities, but clearly different spectral distributions. The AC traces in Fig. 2(b) show that the two orthogonally-polarized components exhibit nearly identical intensity. Figure 2(e) and 2(f) are RF spectra of polarization-resolved components. Both the fundamental repetition rates are ~7.545552 MHz with signal-to-noise ratios >55 dB. The fact that no polarization evolution frequency is observed further confirms that the two components are polarization-locked [30].
However, in addition to above polarization-locked VDS, another distinct solitary state can also be obtained by simply adjusting the PC1. Figure 3 shows such a soliton state of the laser. Rather than steep spectral edges shown in Fig. 2(a), the optical spectrum of the soliton is described by the appearance of clear Kelly sidebands, which is the typical feature of conventional solitons [37,38]. The central wavelength and 3-dB spectral bandwidth of the soliton are ~1565.8 nm and ~1.5 nm, respectively. The AC trace has a good sech2 temporal profile with a pulse duration of ~1.8 ps, which is much narrower than the former one. The corresponding TBP is 0.33, expected for transform-limited chirp-free pulse. According to the phase-matching condition, the spectral separation between first-order Kelly sidebands is expressed by [39], and then Δλ is calculated as ~8.7 nm, which is in agreement with the experimental result. Based on the above analysis, we can conclude that the soliton should be a conventional soliton. To our knowledge, this is the first experimental observation of conventional soliton obtained at large normal dispersion regime. The average output power and peak power of the conventional soliton are ~0.7 mW and ~52 W, respectively.
Fig. 3 (a) Optical spectra, (b) AC traces, (c) and (d) oscilloscope traces, (e) and (f) RF spectra of group velocity-locked VCS.
Through separating the two orthogonally-polarized components of the conventional soliton, it turns out that the conventional soliton is a group velocity-locked VCS. As can be clearly seen from the polarization-resolved spectra shown in Fig. 3(a), the two orthogonal polarization components have clearly different spectral distribution and ~0.7 nm central wavelength difference. The center of the horizontal polarization component is ~1565.3 nm, while that of the vertical polarization component is ~1566 nm. The AC traces in Fig. 3(b) show that the pulse durations of the horizontal and vertical components are estimated as 1.95 and 1.85 ps, respectively. Figures 3(c) and 3(d) illustrate that the two polarization-resolved oscilloscope traces exhibit the equally-spaced uniform pulse train, which is the typical characteristics of group velocity-locked VCS [29]. As described in Figs. 3(e) and 3(f), two RF peaks with peak-to-background ratios of >47 dB are observed. The fundamental repetition rates of both components are ~7.545552 MHz, corresponding to the cavity length of ~27 m. As a result, although the two polarization components operate at different wavelengths, they share the same fundamental repetition rate and group velocity. They copropagate as a unit in fiber laser. We note that the group velocity-locked VCS is attributed to the dynamic balance among soliton frequency shift, group velocity dispersion, and fiber birefringence [29]. The product of the soliton frequency shift and dispersion must be moderate to compensate the polarization dispersion induced by the fiber birefringence. In previous papers, the mode-locking states of VDS and VCS in EDF lasers with clearly different net cavity dispersion have been observed, however, no both VDS and VCS operations in the same large normal dispersion fiber laser have so far been reported.
4. Formation mechanisms of VDS and VCS
We have investigated the formation mechanism of VDS and VCS in our normal dispersion fiber laser. It is well known that a segment of PMF introduced into a laser cavity consisting of standard SMF can function as a fiber-based Lyot filter if laser cavity also consists of elements with polarization dependent loss [35]. Transmittance of a fiber-based Lyot filter can be written as follows [35,40,41]:
where T is the filter transmittance, Δn = nslow-nfast is the birefringence of PMF, Lp is the length of PMF, and λ is the wavelength. When a piece of PMF is inserted into a standard SMF based laser cavity (i.e. no other polarization-maintaining components), angle ψ can be assumed as arbitrary value [35]. Usage of element with polarization dependent loss (fused multiplexer/fiber coupler etc.) or polarizer in the laser cavity (polarizer/PBS etc.) leads to creation of fiber-based Lyot filter, even though the contrast of transmission function may be different depending on the polarization of the input radiation [35].In our experiment, polarization dependent loss is inserted by fused WDM and fused OC [35]. One piece of PMF is added between the WDM and SA to serve as a fiber-based Lyot filter. If the cavity includes a PC, the transmission spectra of PMF based Lyot filter exhibit different extinction ratio (ER). Angle ψ can be assumed as arbitrary value, which corresponds to the settings of the orientations of PC1 in the experiment. It can be seen that the different angle ψ indicates different ER. Figure 4 shows the corresponding transmission spectra under different values of ψ. During the calculation, the birefringence of the PMF is assumed to be 4.4 × 10−4. If ψ = π/20, corresponding to the transmission spectrum of T1, with relatively lower ER, the pulse propagating in the PMF will experience lower loss in all wavelength ranges, so the fiber-based birefringence filtering effect is not obvious but not completely disappeared. In this case, VDS with steep spectral edges, large pulse duration, and strong frequency chirp can be achieved in normal dispersion regime due to the gain bandwidth filtering effect. On the contrary, as ψ = π/6, corresponding to the transmission spectrum of T2, the PMF based Lyot filter has relatively higher ER. The pulse propagating in the PMF will experience clearly different loss at different wavelengths, as a result, the gain bandwidth filtering effect is not obvious compared to the fiber-based birefringence filtering effect. In this case, VCS with clear Kelly sidebands, sech2 temporal profile, and transform-limited pulse duration can be achieved in the same fiber laser due to spectral pulse shaping effect [42]. It is indicated that intra-cavity fiber-based birefringence filtering effect can also provide for pulse shaping [43,44].
Fig. 4 Transmission spectra of PMF based Lyot filter. For T1, ψ = π/20; T2, ψ = π/6. Note: Lp = 0.69 m, Δn = 4.4 × 10−4.
In this work, we have proposed and demonstrated an all fiber mode-locked EDF laser using fiber-based Lyot filter. In the presence of a PC in such a cavity, the contrast of the filter’s transmission function depends on the settings of the PC. It can be observed that at a fixed length of the PMF, tuning the PC allows tuning of the spectral width and pulse duration. This tuning is particularly significant for the shortest length of the PMF (<1 m).
To identify the impacts of the fiber based Lyot filter on the output spectrum and the pulse duration, a fiber laser with a constant cavity length and dispersion is further set up by using a piece of standard SMF to replace the PMF. With appropriately setting the orientations of PC1 and increasing the pump power beyond the mode-locking threshold, only dissipative soliton with rectangular spectrum profile and large spectral bandwidth can be achieved, as shown in Fig. 5. The central wavelength and 3-dB spectral bandwidth of the dissipative soliton are ~1565 nm and ~8.7 nm, respectively. Based on the measured AC trace, the pulse duration of the dissipative soliton is estimated as 9.8 ps if a Gaussian pulse is assumed. Therefore, it is indicated that a PMF based birefringence filter in our nanotube-mode-locked EDF laser may play a key role to generate group velocity-locked VCS by inducing spectral pulse shaping effect. Our study provides a new and simple method to achieve two different vector soliton sources, which is attractive for potential applications in fiber telecommunications or biomedical diagnostics.
5. Summary
In this paper, we have proposed a nanotube-mode-locked fiber ring laser that can generation both polarization-locked VDS and group velocity-locked VCS by exploiting a section of PMF. Attributing to the polarization-depended filtering characteristics of the fiber-based birefringence filter, the two types of vector solitons can be switched from one to the other by only tuning the orientations of the intracavity PC. The VDS, emerging in the case of relatively lower filter ER, has a spectral bandwidth of ~4.3 nm and pulse duration of ~23.4 ps. With a section of SMF, the VDS can be compressed to ~0.9 ps. However, the spectral bandwidth and pulse duration of the VCS resulted from spectral pulse shaping effect with relatively higher filter ER are ~1.5 nm and ~1.8 ps, respectively. It is the first time to realize the different types of vector solitons, by simply varying the operation condition without modifying the dispersion map.
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