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Abstract
We experimentally demonstrate the generation of dissipative soliton resonance (DSR) in a passively mode-locked Bi-doped fiber ring laser based on nonlinear polarization rotation (NPR) technique. The DSR with the central wavelength of 1169.5 nm has a repetition rate of 343.7 kHz. By purely increasing the pump power, the DSR evolves from Gaussian shape to rectangular shape with the duration extending from 2.1 ns to 13.1 ns, while keeping the pulse amplitude and the 3-dB spectrum bandwidth almost constant. The single-pulse energy reaches 24.82 nJ. Furthermore, we construct a lumped model to reproduce the mode-locking process and the traits of the DSR pulse. The obtained results indicate that it could achieve higher pulse energy in mode-locked Bi-doped fiber laser by generating DSR.
© 2017 Optical Society of America
1. Introduction
Bi-doped fiber is a rising gain medium serving for fiber lasers and amplifiers because of its broad gain bandwidth ranging from 1100 nm to 1450 nm, which completely covers the wavelength gap between the Yb-doped and Er-doped fibers [1–6]. Since 2005, V.V. Dvoyrin et al. fabricated the first Bi-doped fiber by using modified chemical vapor deposition (MCVD) technique [7], various Bi-doped fiber lasers have attracted extensive concerns in recent years [8–20] due to their important applications in fields of laser guide stars (following frequency doubling), medicine, optical communications, fiber gyroscopes and metrology [21, 22]. Among them, the passively mode-locked Bi-doped fiber laser is a special optical source, which could generate different types of pulses. Indeed, versatile pulse formations have been observed in mode-locked Bi-doped fiber lasers based on different cavity designs, such as conventional soliton pulse in the net anomalous dispersion regime [18], the dissipative soliton in all normal dispersion regime [23] and the dispersion-managed soliton regime [24]. However, the development of passively mode-locked Bi-doped fiber lasers is still challenging due to the relatively low gain of Bi-doped fiber, which leads to high pump power and low pulse energy. At present, although it could reach up to a relative high average output power [25], the laser may suffer from multipulse oscillation with the increasing intracavity pulse energy [26, 27]. Hence, generating high energy pulse in Bi-doped fiber lasers is worth further investigating.
On the other hand, dissipative soliton resonance (DSR), as a wave-breaking free pulse, was proposed to increase the single-pulse energy from a fiber laser [28–32]. With the increasing pump power, the DSR could broaden the pulse width while keeping the amplitude constant. Thus, the pulse in DSR regime permits its energy to increase virtually indefinitely despite of the overdriven intracavity nonlinear effect. Up to date, a number of experimental researches on DSR have been reported in fiber lasers mode-locked by nonlinear polarization rotation (NPR) or nonlinear amplifying loop mirror (NALM) techniques [33–37]. Nonetheless, they all operated at gain regimes of Yb-doped fibers and Er-doped fibers. Therefore, it would be interesting to know whether the DSR could be generated from a passively mode-locked Bi-doped fiber laser, which would improve the pulse energy and explore more applications of Bi-doped fiber lasers.
In this work, we present the first demonstration as we know, of generating DSR in a passively mode-locked Bi-doped fiber laser based on NPR technique. Stable pulse train with a repetition rate of 343.7 kHz, centered at 1169.5 nm, is obtained. With the increase of pump power, the duration of the DSR pulse broadens from 2.1 ns to 13.1 ns, while the peak power almost maintains a constant value. The single-pulse energy reaches 24.82 nJ. Moreover, we develop a numerical model to confirm the DSR mode-locking regime around 1169 nm. The results provide a guideline for improving the pulse energy of the Bi-doped fiber laser.
2. Experiment setup and results
The schematic of the Bi-doped fiber laser for generating DSR is shown in Fig. 1, which is a typical setup using NPR mode-locked technique. The pump source with maximum output power of 1.8 W is a single-mode Yb-doped fiber laser. A 36 m long Bi-doped fiber used as the gain medium is pumped by the Yb-doped fiber laser through a 1060/1160 nm wavelength division multiplexer (WDM). The Bi-doped fiber was fabricated by the MCVD technique, which has absorption of 0.8 dB/m at 1060 nm, a core diameter of ~6 μm and cutoff wavelength of ~1 μm [12]. Two polarization controllers (PCs) are used to adjust the polarization state of the circulating light. A polarization-dependent isolator (PD-ISO) provides the unidirectional operation and the polarization selectivity. The output is taken by a 10% fiber coupler. A 550 m long single-mode fiber (SMF-28) with dispersion of 18 ps2/km at 1160 nm is added into the laser cavity to increase the nonlinear effect and manage the dispersion of the cavity. An optical spectrum analyzer (Annritsu MS9710C), an oscilloscope (Agilent DSO-X 3052A, 500 MHz) with a photodetector (Newport 818-BB-35F, 12.5 GHz) and a radio-frequency (RF) spectrometer (Agilent E4407B) are employed to analyze the laser output spectrum, pulse train and RF spectrum, respectively.
The CW regime of the Bi-doped fiber laser was achieved at a pump power of about 500 mW due to the relatively low gain of the Bi-doped fiber. When the pump power was above 730 mW, the mode-locked pulse operating at the cavity fundamental repetition rate was always formed by appropriately adjusting the PCs. Figure 2 shows a representative operation state of a rectangular pulse at the pump power of 1.34 W. The central wavelength and the 3-dB spectral bandwidth of the rectangular pulse are 1169.5 nm and 1.6 nm, respectively, as shown in Fig. 2(a). Figure 2(b) presents the corresponding pulse train with the repetition rate of 343.7 kHz, which is determined by the 601 m cavity length. For better clarity, the temporal profile of the pulse is shown in Fig. 2(c), which has rectangular shape with the duration about 9.3 ns. Here, the corresponding peak power of the pulse is also calculated to be 1.89 W, which leads to the narrow spectrum of the pulse [38]. Figure 2(d) is the registered RF spectrum. The signal-to-noise ratio (SNR) of the rectangular pulse exceeds 50 dB.
Fig. 2 The mode-locked operation with rectangular pulse at pump power of 1.34 W. (a) optical spectrum, (b) pulse train, (c) the single pulse, and (d) RF spectrum.
Note that there are generally two types of rectangular pulses generated from passively mode-locked fiber lasers, namely, the rectangular noise-like pulse and the DSR. The rectangular noise-like pulse has very similar characteristics with DSR pulse [33, 34]. In order to rule out the existence of rectangular noise-like pulse in our fiber laser, we further measured its autocorrelation trace. However, we could only observe a constant level without any fine structures in a 190 ps-scanning-range autocorrelator. It is clearly distinguishable from the rectangular noise-like pulse which can easily measure the autocorrelation trace with a narrow coherent peak riding on a broad pedestal [39]. Furthermore, when we further adjusted the PCs, the rectangular pulse did not split. It is different from the rectangular noise-like pulse which could split to multiple rectangular noise-like pulses by rotating the PCs [40]. Therefore, we believed that this rectangular pulse is operating in DSR regime.
In order to further verify that the generated rectangular pulse is DSR, the dynamic evolution of the rectangular pulse spectrum and the pulse profile were investigated with the increased pump power. It is worth noting that we fixed the PCs and changed only pump power once the mode-locked pulse is formed. The results are shown in Fig. 3. We can clearly see that the central wavelength of the pulse keeps at the 1169.5 nm and the 3-dB bandwidth changes very slightly as the pump power increases. Correspondingly, the width of the pulse broadens from 2.1 ns to 13.1 ns with pump power increasing from 0.73 W to 1.77 W. The profile of the pulse changes from Gaussian shape to rectangular shape during the process of increasing pump power. From these dynamic evolution characteristics of the mode-locked pulse, we can further confirm that the rectangular pulse is DSR, as reported in [29]. In addition, the pulse in DSR regime permits the pulse energy to increase indefinitely in theory, while maintaining the amplitude at a constant level. It is because that appropriate laser design allows utilizing peak power clamping effect for linear pulse duration tuning via increasing the pump power [41].
Fig. 3 The dynamic characteristics of the mode-locked pulse at different pump powers. (a) spectra, (b) pulse broadening process.
To better show the generated DSR characteristics, Fig. 4 exhibits the variations of the DSR duration and pulse energies with respect to the pump power. At the initial state, the duration of the DSR with Gaussian shape is 2.1 ns, while the maximum pulse duration of the DSR is 13.1 ns at the pump power of 1.77 W. In our experiment, the largest output power is 8.5 mW at the pump power of 1.77 W. Therefore, the output pulse energy is 24.82 nJ. Considering that 10% port of the OC is used as the output port, the intracavity pulse energy of the fiber laser is as large as 248.2 nJ. As pointed out above, our maximum pump power is only 1.8 W. Thus, it is considered that a higher pulse energy could be achieved with a larger pump power, since no output power saturation was observed.
3. Simulation results
From theoretical point of view, we built a model to approximately represent the laser configuration and try to reproduce the mode-locking process of the DSR. A schematic illustrated in Fig. 5 is given to clarify the model. The simulation is implemented by the lumped model while the artificial saturable absorber is realized by nonlinear polarization evolution technique. Subsequently, to determine the function of the artificial saturable absorber, an averaged cavity is utilized by averaging the effect of dispersion and gain bandwidth. In this case, iterative procedure is implemented by a split-step averaging method, where the light field is considered to be perturbed in the single roundtrip by dispersion, gain bandwidth and nonlinearity. The light field can be expressed as:
whereun is the light field and n is the index of the roundtrip number. The matrices Mp, MA, Mo, and MPC account for the polarizer, analyzer, output coupler and PC, respectively, in which α1 and α2 are orientation angles of the PC and analyzer, respectively; α3 is the phase delay induced by the PC. B is the transmitted ratio of the coupler. Lk is the birefringence matrix with fiber birefringence k and cavity length L. β2 and γ are second-order dispersion and nonlinearity of the averaged gain fiber, respectively. For the gain model, g is the saturable gain coefficient g = g0exp(-‖u‖2/Es), where g0, Es and Ω are small-signal gain, gain saturation energy and gain bandwidth, respectively. L2-norm ‖u‖2 denotes the pulse energy.In terms of Eq. (1), the intensity-dependent function is written as:
Here only the intensity modulation is regarded. In summary, the main body of the adopted model is lumped where the artificial saturable absorber is characterized by a governing function derived from an averaging method [42]. The selected parameters in the simulation are shown: 1) fiber-related: β2 = 18 ps2/km (relevant GVD: −25.9 ps/nm/km), γ = 2 W−1km−1, k = 1, g0 = 1 m−1, Es = 650 pJ, Ω = 20 THz (relevant spectrum bandwidth 28 nm). Note that the dispersion management is not considered in order to be consistent with the approximations made in the averaging technique. 2) cavity-related: L = 601 m (averaged model), Lgain = 36 m and Lpassive = 565 m (lumped model), B = 0.9, α1, α3 are 0.73 and −2.57 while α2 = α1 + π/2. The fiber attenuation is not taken into account.
In this case DSR is numerically achieved, which is analogous with the experimental phenomenon. By virtue of numerical simulation the evolution towards stable operation of DSR incorporates two typical processes, manifesting as noise-burst and long-lived dark soliton regimes in Fig. 6. In noise-burst regime as illustrated in Figs. 6(a-c), it is found that radiation spreads out in the beginning to a rather wide envelope and subsequently dissipates when evolving from an initial white noise covering a range of ~350 ps. At the 450th roundtrip, incoherent sub-pulses are considered to be suppressed and a long, localized light field, albeit with certain fluctuations, is established. As revealed by R. I. Woodward and E. J. R. Kelleher [43], dark solitons are spontaneously generated together with long pulse formation in normal dispersion region and can be quite long-lived owing to the near-uniform pulse intensity. As revealed by the results shown in Figs. 6(d-f), it is not surprising to unveil that a dark soliton distributed in flat-top structure is able to last for thousand-roundtrip-time before moving to edge and accelerated by the background gradient. In addition, phase of the dark structure is plotted in Fig. 6(f) and exhibits an abrupt jump of π, indicating one of the most representative characteristics of dark soliton. After evolving through 4750 roundtrips, the dark solitons decay and flat-top DSR referred to as background retains. The temporal and spectral profiles of DSR after converging to the stationary solution are shown in Figs. 7(a) and 7(b), respectively. To enable a qualitative comparison with the experimental results, we further demonstrate the pulse evolution at different gain saturation energies ES in Fig. 7(c). As expected, continuous increase in pulse duration combined with a transition of pulse shape (from Gaussian-like to flat-top) is realized [31, 32]. Note that due to the limited width of the time window, gain saturation energy is kept below 1 nJ to avoid possible boundary reflection in the computation. Figure 7(d) quantitatively summarizes the evolving process shown in Fig. 7(c), indicating the linear extension of pulse width and linear growth of pulse energy with respect to DSR. Consequently, good qualitative agreement with experimental facts is attained, which theoretically corroborates the formation of DSR at this less-studied wavelength.
Fig. 6 Evolution from noise signal to DSR. (a-c) the noise-burst regime. The evolved process in temporal domain is shown in (a), typical temporal profile and spectrum are illustrated in (b) and (c), respectively. (d-f) regime with long-lived dark soliton. Evolution of pulse from 1800th to 3250th roundtrip is shown in (d), the details of dark soliton are demonstrated in (e) and (f) when zoomed in.
Fig. 7 Numerical results of DSR. (a) pulse profile and (b) spectrum at gain saturation energy Es = 650 pJ, (c) pulse evolution under increasing Es, (d) pulse widths and pulse energies versus Es.
4. Conclusion
In conclusion, the DSR generation in a Bi-doped fiber laser based on NPR mode-locked technique is investigated both experimentally and numerically. The DSR centered at wavelength of 1169.5 nm was observed, which could evolve from Gaussian shape to rectangular shape as the increasing pump power. Correspondingly, the pulse duration could broaden from 2.1 ns to 13.1 ns. The maximum output pulse energy is 24.82 nJ. In numerical analysis, we built a lumped model to represent the laser configuration and reproduce the mode-locking process and the features of the DSR pulse. The obtained results indicate that the DSR in Bi-doped fiber can be employed for improving the single-pulse energy, which could extend the applications of Bi-doped fiber lasers.
Funding
National Natural Science Foundation of China (Grant Nos. 61378036, 11304101, 11474108, 61307058); Science and Technology Program of Guangzhou (Grant No. 201607010245); Open Fund of the State Key Laboratory of Luminescent Materials and Devices (South China University of Technology) (Grant No. 2016-skllmd-12); Key Program of Natural Science Foundation of Guangdong Province (Grant No. 2014A030311037); Guangdong Natural Science Funds for Distinguished Young Scholar (Grant No. 2014A030306019); Program for the Outstanding Innovative Young Talents of Guangdong Province (Grant No. 2014TQ01X220).
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