We have experimentally observed conventional solitons and rectangular pulses in an erbium-doped fiber laser operating at anomalous dispersion regime. The rectangular pulses exhibit broad quasi-Gaussian spectra (~40 nm) and triangular autocorrelation traces. With the enhancement of pump power, the duration and energy of the output rectangular pulses almost increase linearly up to 330 ps and 3.2 nJ, respectively. It is demonstrated that high-energy pulses can be realized in anomalous-dispersion regime, and may be explained as dissipative soliton resonance. Our results have confirmed that the formation of dissipative soliton resonance is not sensitive to the sign of cavity dispersion.
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Fiber-based passively mode-locked lasers as an alternative source of the ultrashort optical pulses have been intensively investigated [1–3], and various applications have been proposed, such as ultrafast phenomena, optical communications, supercontinuum generation, nonlinear optics, and optical sensors [4–8]. By adjusting the cavity structure with appropriate dispersion management, fiber laser can operate either in the positive or negative cavity dispersion regime. Conventional soliton , stretched pulse , self-similar pulse , and dissipative soliton (DS) [12–14] have been obtained successively in the past decades. Generally, conventional chirp-free solitons arise from the balance of positive nonlinear effect and negative dispersion, and the lasers tend to operate at multiple-pulses emission due to the peak power clamping effect of the cavity in high pump regime. DSs have been investigated in large- or all-normal dispersion regime previously [15–17]. The gain and loss play essential roles in the formation of DSs, and various operations have been observed.
Recently, rectangular pulses without split at high energy have been extensively investigated both theoretically and experimentally [17–20]. Akhmediev et al. have predicted the existence of rectangular pulse theoretically in  through solving the cubic-quintic complex Ginzburg-Landau equation. Additionally, Chang et al. have theoretically demonstrated that rectangular pulse could be formed in anomalous dispersion regime with appropriate cavity parameters [21,22]. Experimental investigations about rectangular pulse have been demonstrated in erbium-doped fiber (EDF) laser operating at large normal dispersion system regime . Moreover, Matsas et al. have reported nanosecond noise-like pulse emerging from nonlinear polarization switching .
In this paper, we have experimentally observed conventional soliton and rectangular pulse in an EDF laser with anomalous dispersion by adopting nonlinear polarization rotation technique. The conventional soliton exhibits typical spectrum with sidebands, and the corresponding pulse duration is estimated as ~0.9 ps. However, the rectangular pulses always emit at fundamental cavity repetition rate, and exhibit quasi-Gaussian spectra with bandwidth of ~40 nm. The corresponding autocorrelation traces have triangular profiles, indicating that the output pulses have a rectangular shape. With the enhancement of the pump power, both the spectral bandwidth and pulse peak power keep almost unchanged while the pulse duration almost increases linearly from 156 to 332 ps. Based on experimental results, it is indicated that there are two different pulse shaping mechanisms existing in the laser cavity, where the conventional solitons arise from the balance between fiber nonlinearity and cavity dispersion while the rectangular pulses may be explained as dissipative soliton resonances (DSR) [21,22].
2. Experimental setup
The configuration of proposed fiber laser system is schematically shown in Fig. 1 . Two 980-nm laser diodes with the maximum pump power of 550 mW are used to provide bidirectional pump through two 980/1550 nm wavelength-division-multiplexers (WDMs). A ~11-m EDF with dispersion parameter D of −32 ps/nm/km acts as the gain media. The other fibers in the cavity are the standard single mode fiber (SMF) with D of 17 ps/nm/km and length of ~24.1 m. The net dispersion and fundamental repetition of cavity are estimated as −0.073 ps2 and 5.85 MHz, respectively. A polarization sensitive isolator (PS-ISO) together with two polarization controllers (PCs) works as an equivalent saturable absorber. An optical coupler (OC) with 10% output is placed after EDF as the output port. A power meter, an optical spectrum analyzer (OSA), an autocorrelator (AC), a radio-frequency analyzer (RFA), and a 11-GHz digital oscilloscope (DSO) with a 45-GHz high speed photodiode detector are employed to simultaneously monitor the output pulse.
3. Experimental results and analyses
Self-start mode-locking can be achieved by adjusting PCs states and the pump strength. When the forward and backward pumps reach 32 and 28 mW, conventional soliton with sideband can be easily achieved from continuous wave. As shown in Fig. 2(a) , the spectrum performs symmetrically distributed sideband waves, which demonstrates that the laser operates at anomalous dispersion regime . The full width at half maximum of the corresponding autocorrelation trace (blue curve) is ~1.5 ps, as shown in Fig. 2(b). If a Sech2 temporal profile (red curve) is assumed, the pulse width is estimated as ~0.9 ps. Based on the experimental result, we conclude that the cavity operates at conventional soliton state.
However, when the forward and backward pumps reach 132 and 124 mW, rectangular pulse emission is achieved with appropriate adjusting the PCs state. Figures 3(a) and 3(b) show the optical spectra and autocorrelation traces as a function of pump power, respectively. The inset of Fig. 3(a) is a zoom-in portion on the central part of spectra in linear scale. As shown in Fig. 3(a), the output optical spectra exhibit Gaussian profile and spikes on the top. The appearance of the spikes may cause pulse instability in temporal domain, just as shown in Fig. 3(c), the pulse intensity oscillates slightly with time. With the total pump power increasing from 400 mW to 1 W (both the pump powers P of forward pump and backward pump are set at the same value of 200, 300, 400, and 500 mW, respectively), although the spectral intensity increases remarkably, the 3-dB bandwidth is almost constant at ~40 nm ranging from 1530 to 1570 nm. It indicates that the nonlinear phase shift is limited in this mode-locking system. Figure 3(b) shows the corresponding autocorrelation traces which perform triangular profiles without other fine structure, so we conclude that the pulse must be rectangular shape in temporal domain. Furthermore, the autocorrelation traces broaden linearly with the increasing of the pump power. The pulse train present in Fig. 3(c) has an uniform interpulse interval of ~171 ns corresponding to the cavity round-trip time. The RF spectra in Fig. 3(d) show that signal/noise ratio is higher than 60 dB and the fundamental peak located at the cavity repetition rate is 5.846 MHz as determined by the cavity length. The inset of Fig. 3(d) performs the wideband RF spectrum up to 500 MHz, which confirms the stable mode locking and the absence of sidebands or harmonic frequencies. Based on the above analyses, we conclude that the fiber laser operates at stable single pulse mode locking rather than noise-like pulse emission .
Since half of the pedestal interval of the triangular autocorrelation trace is equal to the pulse duration, we can conclude that the narrowest stable rectangular pulse observed in our experiment is 156 ps, which corresponds to a time-bandwidth produce of ~799. So this kind of rectangular pulse possesses of strongly frequency chirp. It is worth to note that the pulse energy could enhance to a large value without pulse breaking or pulse shape distortion. The highest output average energy from the fiber laser is 18.9 mW, and is limited by the available pump power injected into the cavity. Considering the output couple ratio (10%) and the cavity repetition rate (5.846 MHz), the measured largest intra-cavity pulse energy is estimated as ~32 nJ. Compared with the conventional soliton whose single pulse energy is limit at ~0.1 nJ due to the cavity peak power claming effect, the energy of this rectangular pulse has been enhanced two magnitudes. Figure 4 shows the evolution of pulse energy and pulse duration versus the pump power. Both of them boost monotonously as the increase of the input pump power. Furthermore, no output power saturation phenomena or multi-pulse formation appear at the strongest pump (1.1 W). Based on the measured pulse parameters, we estimate that the peak powers of the pulse inside the cavity at different pump are about 94 W, which is two times higher than the result in . The rectangular pulse generated in anomalous dispersion is qualitatively distinct from the well-known conventional soliton, self-similar pulse, or dispersion-management pulse. However, it is somewhat similar with the rectangular DS generated in normal dispersion regime .
Chang et al. have theoretically predicated the effect of DSR in [21,22]. It indicates that when the cavity parameter is approaching the resonance, the pulse profile widens and assumes a nearly rectangular shape, moreover, the pulse duration and energy would increase infinitely while the corresponding peak power would keep constant. In additional, the theoretical research shows that the resonance effect could appear both in normal and anomalous dispersion regimes [22,24]. The experimental research of DSR in normal dispersion regime has already been reported extensively , while there is no paper about resonance investment in anomalous regime up to now to our best knowledge. The phenomena in our experiment matches with theoretical predication well, and we conclude that our result have experimentally confirmed the aforementioned DSR theory in anomalous regime. We also note that, predicated by the theoretical research, increasing the pulse energy intensively would result in formation of multiple peaks in the spectrum . However, the observed spectrum in our experiment does not show such characters even if the pump is enhanced to the maximum power of 1.1 W. This discrepancy could be due to that our current laser parameter selection is not perfect, and the laser could only reach a low resonance at the maximum pump. On the other hand, the spikes on the top of spectra increase in wavelength range and intensity with pump power. Thus, we suspect that the pulse gets more instable with the increase of pulse energy. Namely, the pulse energy could not be boosted infinitely in fact, and excess energy may result in multi-pulse emission. Nevertheless, since the largest pulse energy which could be achieved in DSR depends on the realistic laser parameter setting [24,25], one can further increase the output pulse energy by optimizing laser parameters.
Moreover, since rectangular DS exhibits steeper leading and trailing edges as well as flatted top in temporal domain, it is reasonable to presume that the chirp in central region of the pulse is linear and small while it is nonlinear at the pulse edges [26,27]. But in such a way, there arises a question that whether such pulse could be dechirped by devices with normal dispersion. We have experimentally tried to compress the rectangular DS by dispersion compensation fibers (DCF, D = −120 ps/nm/km) with the length of ~10 m and ~20 m, which supply positive dispersion about 1.53 and 3.06 ps2. It is found that the rectangular DS could not be compressed by DCF: the pulse duration keeps almost constant. We suspect that this may due to the high nonlinear chirp at the pulse edges [17,26], which can resist the influence of fiber dispersion that causes the linear chirp to pulse. And such a chirp property of rectangular pulse may help to maintain the pulse at a high energy level. Additionally, the spectral width of this mode-locking system is independent of the pump strength, so that it intrinsically overcomes the limit of bandwidth of gain fibers and has the capacity of generating ultra-high-energy pulses.
We have experimentally demonstrated that apart from the conventional soliton, the rectangular DS can also be delivered from an EDF laser operating in anomalous dispersion regime. The distinct pulse formation mechanisms with different pulse property of spectra, profile, and energies exist in the same ring cavity. The conventional soliton exhibits typical spectrum with sidebands in spectral domain. The rectangular DS performs broad quasi-Gaussian spectra with unchanged bandwidth, triangular autocorrelation traces, and fixed pulse peak power. Different from the conventional soliton which will cause multi-pulse emission under strong pump due to the energy quantization effect, the enhancement of pump power only induces the nearly linearly increase of pulse duration. Based on experimental results, we conclude that there are two different pulse shaping mechanisms in laser cavity. The balance between the nonlinear effect and fiber dispersion is responsible for conventional soliton while the DSR results in the formation of rectangular DS. The experimental results show that the energy of this kind of rectangular pulse could boost to a much higher level than that can be tolerated in conventional soliton shaping. So our work can be used to design laser systems for the generation of high-energy pulses.
This work was supported by the “Hundreds of Talents Programs” of the Chinese Academy of Sciences and by the National Natural Science Foundation of China under Grants 10874239 and 10604066. Corresponding author (X. Liu). Tel.: + 862988881560; fax: + 862988887603; electronic mail: email@example.com and firstname.lastname@example.org.
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