We propose a new solution to flexibly generate the coherent rectangular pulse from an ultrafast fiber laser based on the dispersive Fourier transformation (DFT) technique. The rectangular dissipative soliton (DS) spectra emitted from a net-normal dispersion mode-locked fiber laser is mapped into a time-domain coherent rectangular waveform through the DFT technique. The rectangular pulse can be broadened flexibly with the adjustments of the pump power. The coherence and shot-to-shot fluctuations of the achieved rectangular pulses are further verified by the Mach-Zehnder interference experiment and the recorded single-shot pulse train, respectively. The results demonstrate that the combination of DS mode-locked laser and DFT technique might be indeed an effective and flexible way to achieve highly coherent rectangular pulses.
© 2015 Optical Society of America
Passively mode-locked fiber lasers as the excellent platforms for investigating soliton dynamics have attracted considerable attention in laser community due to its abundant nonlinear phenomena and various kinds of solitons, i.e., conventional soliton , noise-like (NL) soliton [2,3 ], dissipative soliton (DS) [4–6 ], dissipative soliton resonance (DSR) [7–12 ], multi-soliton patterns [13,14 ], and so on. Generally, different solitons possess different pulse characteristics, such as energy and shape, which would make them find different applications in the specific fields. For instance, distinguishing from the conventional hyperbolic secant or Gaussian-like shape, the coherent rectangular pulses could act as the optical square-wave clock signals which are expected to optimize signal-processing capabilities in the optical domain due to their steep edge . Meanwhile, the rectangular pulses would be an attractive source for laser micromachining because of their suitable pulse duration and superiority in pulse energy . Therefore, there is always a strong motivation to develop new methods to generate coherent rectangular pulses. Recently, N. Akhmediev et al. theoretically proposed a coherent rectangular pulse formation mechanism, namely DSR [7–9 ], and which was further confirmed by the experiments in fiber lasers [10–12 ]. However, the generation of DSR pulse requires rigorous cavity parameter selections, which makes it inconvenient to be achieved in fiber lasers. Later then, it was found that the NL pulse packet also could possess a rectangular envelope and exhibit similar pulse dynamics of the DSR pulse . Nevertheless, it should be noted that the NL wave packet is not a single pulse but consists of a bunch of short pulses with stochastic duration and peak power. Hence, comparing to the mode-locked single soliton, the pulse-to-pulse phase coherence across the NL rectangular packet degrades seriously. In fact, as the important parameter of an optical pulse, the high coherence would extend their applications in chemistry, communication, frequency metrology, and so on. Therefore, a question naturally arises as to whether it is possible to find a flexible and effective way to generate coherent rectangular pulse from a fiber laser.
On the other hand, with the distinguished advantages with real-time measurement, the dispersive Fourier transformation (DFT) technique has aroused strong research enthusiasm in fast continuous single-shot measurements in optical sensing, spectroscopy and imaging, or capture of rare events such as optical rogue waves and rare cancer cells in blood [18–21 ]. DFT is an optical real-time diagnostic method that exploits the analogy between paraxial diffraction and group velocity dispersion (GVD). Briefly, when an optical pulse enters a large dispersive element, the output temporal waveform mimics its spectrum by simply propagating in the dispersive medium. Enlightened by the unique characteristic of DFT technique, it would inspiringly open a new horizon for us to find out whether it is possible to explore a rectangular mode-locked spectrum instead of coherent rectangular pulse. Interestingly, the rectangular mode-locked spectrum indeed exists in fiber laser, named DS. Comparing to the traditional solitons, the typical DSs, which possess advantages of rectangular-shaped spectra and high output pulse energy, are formed by a composite balance between several effects in normal dispersion cavity, such as gain, loss, nonlinearity, and dispersion [4,22 ]. The DSs could be achieved in net-normal dispersion fiber laser based on different mode-locked techniques [23,24 ]. Moreover, the rectangular-shaped spectral width could be flexibly changed by controlling the cavity parameters such as pump power. Therefore, from the viewpoint of finding an alternative approach for coherent rectangular pulse generation, it would be natural to explore whether the rectangular DS spectra could be mapped into time-domain coherent rectangular pulses directly through the DFT technique.
In this work, we report on the experimental generation of coherent rectangular pulses from a DS fiber laser by DFT technique. A carbon nanotube (CNT) mode-locked net-normal dispersion Er-doped fiber laser is proposed to provide stable DSs. By varying the pump power, the DS spectral profiles can keep rectangular shape, and 3-dB bandwidth is increased from 10.2 nm to 15.4 nm. The corresponding rectangular pulse duration changes from 2.9 ns to 4.1 ns. A Mach-Zehnder interferometer is then adopted to confirm the pulse-to-pulse phase coherence across the rectangular pulse train [25,26 ]. Taking advantage of high speed real-time oscilloscope, roundtrip-to-roundtrip intensities of rectangular pulses further verify the pulse-to-pulse stability. The results provide a new flexible approach to generate coherent rectangular pulses by utilizing the DFT technique and DS fiber laser.
2. Experimental setup
In order to achieve stable rectangular mode-locked spectra, a CNT mode-locked normal dispersion Er-doped fiber laser was constructed, as shown in Fig. 1 . A piece of 15 m erbium-doped fiber (EDF) with a dispersion parameter of was used as the gain medium and compensated the dispersion, which makes the laser operate in DS regime. The total length of other standard single mode fiber (SMF) was 10.03 m. Therefore, the net cavity dispersion is 0.11 ps2. The unidirectional operation was undertaken by a polarization-independent isolator (PI-ISO). A polarization controller (PC) was used to adjust the polarization state of the light and the CNT film inserted between fiber connectors acts as the saturable absorber . The spectral properties were analyzed with an optical spectrum analyzer (OSA, Anritsu MS9710C). Outside the laser cavity, a section of 15.5 km SMF with the dispersion amount of −340 ps2 plays the role of a dispersive element to realize DFT. A real-time oscilloscope (Tektronix DSA-70804, 8 GHz) with a photodetector (Newport 818-BB-35F, 12.5 GHz) is employed to monitor the characteristics of rectangular pulses.
3. Results and discussions
Self-started DS mode-locking operation occurred at a pump power of ~20 mW. However, the fiber laser could sustain mode locking state when the pump power was decreased to 20 mW by virtue of the pump hysteresis phenomenon . For better performance, the pump power was further increased to 28 mW. Figure 2(a) shows the mode-locked spectrum with a 3-dB bandwidth of 12.8 nm centered at 1560.3 nm in linear coordinate, which exhibits the typical rectangular shape of the DSs. The corresponding pulse trains are presented in Fig. 2(b). The repetition rate is 8.21 MHz, which is determined by the cavity length of 25.03 m. A commercial autocorrelator was then employed to measure the pulse width. The measured result in Fig. 2(c) indicates that the fiber laser delivers a mode-locked pulse-train with duration of 14.14 ps if the Gaussian profile was assumed. To verify the stability of the mode locking operation, the RF spectrum of the pulse signal was measured, as presented in Fig. 2(d). The peak locates at the fundamental repetition rate of 8.21 MHz with a signal-to-noise ratio of over 55 dB, indicating the fiber laser operates in a stable mode-locking regime.
Then, the DFT induced by a ~15.5 km SMF was employed to maps the rectangular spectra of a DS to a temporal rectangular waveform. Figures 3(a) and 3(b) show the pulse-train and a 3.4 ns single rectangular pulse after the DFT under the pump power of 28 mW, respectively. It should be noted that the pulse roof appears slight intensity fluctuations, comparing to the smooth spectrum in Fig. 2(a). We attribute this difference to the average measurement mode of OSA. By analyzing the pulse characteristic before and after DFT, it was found that the DS could be effectively mapped into rectangular pulse.
In principle, the rectangular pulse duration could be flexibly controlled by changing the initial spectral width of a DS or the GVD of outside SMF. To demonstrate this point, here we fixed the ~15.5 km SMF and observed the relationship between the final rectangular pulse duration and the initial spectral width of the mode-locked DS by increasing the pump power. The experimental results are shown in Fig. 4 . It should be noted that the mode-locked spectrum could keep the rectangular profile during the variation of the pump power. By increasing the pump power from 22 to 36 mW, it can be seen that the spectral width broadens from 10.2 to 15.4 nm and the corresponding pulse duration expands from about 2.9 ns to 4.1 ns. In this case, the output power and pulse energy varied from 57 to 131 μW and 6.9 to 16 pJ, respectively. Note that when the pump power is higher than 36 mW in our laser cavity, the multi-pulse operation was observed due to the soliton energy quantizationin effect induced by the cavity nonlinear effect. Since the cavity nonlinear effect is mainly related to the CNTs and cavity length, we believed that the output power could be improved by using other mode locking techniques or optimizing the cavity length. In addition, the pulse energy could be further scaled by the optical amplification outside the cavity for the purpose of practical applications. From the experimental results, the pump power fluctuations would influence the pulse width. However, as the pump source used in this work is stable, no evident variation of pulse width if we fixed the pump power level. It is also to note that the rectangular pulse only has a fixed repetition rate. Therefore, for flexibly controlling the pulse intervals or the repetition rates, the multiwavelength mode-locked scheme with different repetition rates or the distributed ultrafast fiber laser could be employed [29,30 ].
In order to check the coherence of the obtained rectangular pulse, a Mach-Zehnder pulse interferometer is used to perform spectral interferometry between consecutive pulses from the output [25,26 ], as shown in Fig. 5 . The front 3-dB coupler is used to split the laser output into two interferometer arms. The SMF (~25.03 m) placed in the longer arm is used to match the pulse repetition rate. A free-space variable delay line was incorporated into the shorter interferometer arm with 20 cm adjustable range allowing for precise tuning of the temporal delay between two adjacent pulses. In this way, two adjacent pulses come across at the latter optical coupler. Here, it can be expected that the two pulses would show interference patterns on the spectrum if the mode-locked pulses are coherent. When the rectangular pulse after the DFT was injected into the setup for coherence measurement, the stable distinct fringes could be clearly seen on the pulse spectrum, as shown in Fig. 6(a) . It indicates that almost the total pulse-to-pulse phase coherence was obtained. It can be seen that the interference patterns shown in the Fig. 6(a) and its inset seem to be a little different, which is due to the limited resolution of the OSA. Note the spectral interference pattern of the mode-locked pulse at the exit of the laser before propagation along the 15.5 km SMF fiber was similar to that of Fig. 6(a), indicating that there is almost no loss of coherence during the DFT process. As a comparative experiment, the incoherent NL pulse was also measured by the same method. As presented in Fig. 6(b), no evident interference fringes could be observed, which shows the lacking of phase correlations among the NL pulses. Hence, the results suggest that the obtained rectangular pulse exhibits significant pulse-to-pulse phase coherence and stability.
To further demonstrate the stability of the obtained rectangular pulse, we single-shot the pulse-train after the DFT technique and record the roundtrip-to-roundtrip pulse variations at the pump power of 28 mW. The results are shown in Fig. 7 . Here, we show the pulse intensities over 300 consecutive roundtrips of the fiber laser. We can clearly see that the intensity and the profile of the rectangular pulse are both nearly indistinguishable from one another. These observations demonstrated that the obtained rectangular pulse was stable, and further suggested that the longitudinal modes constituting the spectrum are coherent .
To conclude, we have reported on a flexible generation of coherent rectangular pulse from a DS fiber laser. Increasing the pump power, the pulse broadens accordingly while keeping its rectangular shape. The Mach-Zehnder type interference experiment further demonstrated that the rectangular pulse by the DFT technique exhibit significant pulse-to-pulse phase coherence. In addition, the real-time recorded roundtrip-to-roundtrip pulse train further manifests the stability of the rectangular pulse. The results reveal an alternative method to flexibly generate coherent rectangular pulses by DFT technique, which might find important applications in the related fields.
We thank Dr. Dong Mao (Northwestern Polytechnical University) for providing the CNT/PVA film. This work was supported in part by the National Natural Science Foundation of China (Grant Nos. 61378036, 61307058, 11304101, 11474108), the Key Program of Natural Science Foundation of Guangdong Province, China (Grant No. 2014A030311037), and the Graduate Research and Innovation Foundation of South China Normal University, China (Grant No.2014ssxm18). Z.-C. Luo acknowledges the financial support from the Guangdong Natural Science Funds for Distinguished Young Scholar (Grant No. 2014A030306019), Program for the Outstanding Innovative Young Talents of Guangdong Province (Grant No. 2014TQ01X220), and the Pearl River S&T Nova Program of Guangzhou (Grant No. 2014J2200008).
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