1. Introduction

Mode-locked fiber lasers have been extensively investigated for their important practical and potential applications [1–7]. Conventional chirp-free soliton formed by the balance between the fiber nonlinearity Kerr effect (i.e., self-phase modulation (SPM)) and anomalous group-velocity dispersion (GVD) has attracted considerable attention thanks to the ultra-short duration and stable operation feature. However, the spectral bandwidth of soliton is so narrow according to its transform-limited feature, which limits the application areas of soliton fiber laser.

In recent years, dissipative soliton (DS) lasers based on Yb-doped fibers have attracted considerable attentions [8–11]. DS lasers depend strongly on dissipative process (linear gain and loss, saturable absorption, and spectral filtering) as well as phase modulations, to shape the pulse [12]. Balanced by the rules of the dissipative system, DSs have rectangular-shape spectrum profile with much larger bandwidth than soliton, and larger energy with stronger nonlinear phase (1-2 orders of magnitude greater). The remarkable thing is that the dissipative soliton continually renews itself: nearly linear chirp induced by SPM broadens the spectrum, the saturable absorber (SA) or spectral filtering effect cuts the edges of the spectrum, then the pulse is restored after traversal of the cavity [13]. So DSs usually exist in passive mode-locked lasers. For enhancing the tunability of the laser, we investigated DS generation in an actively mode-locked laser by a special modulation format [9]. The modulator plays the role of SA, which indicates that the traditional SA (e.g. semiconductor saturable absorber, nonlinear polarization evolution or grapheme) is not a must for DS formation.

Fiber nonlinearity provides the spectrum broadening, which is a necessary factor for DS pulse shaping. However, larger nonlinearity needs higher power or longer fiber in the fundamentally mode-locked laser, so DSs usually have repetition rate of ~hundreds MHz [14, 15]. Sufficient nonlinearity cannot be accumulated in the ultra-short cavity for large nonlinear phase shifting, even though high-repetition-rate fundamentally mode-locked fiber laser can be realized by extremely short gain fiber. Therefore, the laser cavity is difficult to be so small for supporting high-repetition-rate (e.g. 10 GHz) optical frequency comb generation. However, for some special applications, including waveform generation [16], photonic analog-to-digital converters [17], arbitrary optical waveform measurement [18], and photonic RF channelization [19], large comb line spacing of the broadband output spectrum is the key point of the systems.

In this paper, we propose a dissipative system without the fiber nonlinear Kerr effect to generate broadband spectrum under large comb line spacing. Instead of the conventional SPM, quadratic phase modulation (induced by a phase modulator (PM)) broadens the spectrum of the pulse, and then supports the linear dissipative soliton (LDS) formation in an anomalous dispersion cavity. We demonstrate DS and LDS in two distinct (all-normal-dispersion (ANDi) and anomalous GVD) fiber lasers operating in actively mode-locked regime. The formation mechanism is discussed. A comparison between the pulse characteristics of DS and LDS confirms the similar pulse shaping regime. Many fiber lasers containing phase modulator have been proposed [2, 20–22], but the pulses generated in that lasers are general solitons (formation by the balance of SPM and GVD). Unlike all previous lasers with phase modulation, the linear-chirped pulse in our system is stretched, which supports the LDS pulse shaping. At last, we propose a simple injection-locking method to stabilize the laser, and then generate 10 GHz low noise frequency comb.

2. Experimental setup and results

2.1. LDS formation mechanism

The experimental setup of the ANDi fiber laser for DS pulse shaping is conceptually similar to prior DS laser in [9], but with different length of Yb-doped fiber (YDF) and 1060 nm single-mode-fiber (SMF). The YDF in the DS fiber laser is ~2 m, and the total length of the cavity is ~7.5 m. Figure 1(a) shows schematic diagram of the experimental setup of the LDS laser. In this laser, a 1.5 m Er-doped fiber (EDF) with absorption of 55 dB/m @ 1530 nm is used, which is pumped by a 980-nm laser diode through a WDM. A dual-drive amplitude modulator (AM) is used for active mode locking and supermode noise suppression. A PM is inserted in the cavity for linear chirp modulation (imposing a quadratic phase onto the pulse). The polarizer ensures the AM works at the correct polarization state. An isolator is employed for unidirectional operation, and a 30% optical coupler (OC) outputs the laser pulses. The phase shifter (PS) is used for making sure the minimum point of the quadratic phase is aligned to the center of the pulse. The EDF and other SMFs in the cavity are polarization-maintained to prevent any polarization fluctuation. The pulse-intensity feed-forward path, which consists of an optical tunable delay line (ODL), a fast photo detector (PD), and a microwave amplifier with tunable gain (VGA), is employed for supermode noise suppression, which is explained in [23].

 

Fig. 1 Schematic diagram of the actively mode-locked fiber laser for LDS generation. RF: RF sinusoidal source. Note: the feed-forward path with dotted line is used for noise suppression, and has no relationship with LDS shaping mechanism.

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In our experiment, the frequency of the pulse pattern generator (PPG) in DS laser and RF sinusoidal wave in LDS laser are both 10 GHz. For DS pulse shaping, the pattern of the PPG is set as only one “1” every 377 symbols, then the repetition rate of the electric pulse sequence is the same as the fundamental frequency of the DS cavity. Therefore, the AM can play the same role as that a SA in a passive mode-locked laser for DS formation [9]. For LDS pulse shaping, the PS is a key device, which ensures the linear down-chirp induced by quadratic phase modulation, and the pulse are broadened in the SMFs after the PM. By tuning the PS to a proper value, we select out the stretched, rather than the compressed, pulse from the laser. Stable mode locking can be realized by appropriately adjusting the frequency of PPG in DS laser and RF source in LDS laser. When the pump power is beyond a threshold value, e.g., 89 mW in DS laser and 125 mW in LDS laser, the proposed lasers emit the typical DS and LDS, respectively.

The typical results for the output of the DS laser and LDS laser are shown in Fig. 2, where they share the same typical characteristics. Figure 2(a) shows the comparison of the output spectrum. A striking feature is that the both spectrums have steep spectral edges and their profiles approach a rectangular shape. The edge-to-edge width (20 dB bandwidth) of DS and LDS are 10.7 nm and 11 nm, respectively. There are some ripples at the top of the LDS’s spectrum because of the large mode spacing of the laser. The autocorrelation traces of the pulses are shown in Fig. 2(b). The full width at half maximum (FWHM) of DS is 10.52 ps, and the pulse duration is given as 7.5 ps if a Gaussian fit is used. The pulse duration of LDS is 12.4 ps, which indicates that the pulse is highly chirped. The pulses can be compressed to several hundred fs. By a programmable liquid crystal spatial light modulator [24], which is set to have an all-pass amplitude response with however a parabolic phase response (i.e. a reversed linear frequency chirp with LDS), then the LDS can be compressed. As shown in Fig. 2(c), the pulse width of the compressed DS and LDS are 420 fs and 763 fs, respectively. The compressed LDS duration is close to the transform limit (610 fs), which implies an approximately linear chirp of the pulse. The little pedestal of compressed LDS shown in Fig. 2(c) is mainly caused by the nonlinear chirp introduced by the sinusoidal phase modulation. The above experimental results demonstrate that the generated LDS with large chirp in linear dissipative system is very different from soliton.

 

Fig. 2 Experimental results of DS and LDS fiber lasers. (a) Optical spectrum, (b) Autocorrelation trace, (c) Autocorrelation trace of the compressed pulses, (d) RF spectrum. Inset in Fig. 2(a) is the linear scale spectrum of the LDS. Besides, inset in Fig. 2(b) is the 10 GHz pulse train of the LDS.

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The repetition rate of DS and LDS are ~26.5 MHz and ~10 GHz, respectively. The peak-to-background ratio of the LDS RF spectrum is >70 dB, implying a good mode-locking stability. Base on the experimental results, we conclude that the fiber laser operates at a stable LDS mode-locking state. The measured output power of LDS is 4.7 mW. Accordingly, the maximum single-pulse energy inside the cavity is estimated to be 1.6 pJ, so the fiber nonlinearity is so small that can be negligible in our LDS fiber laser.

The LDS fiber laser is all polarization maintained, keeping clear of polarization disturbance. However, the laser suffers environment perturbations such as physical vibration and temperature fluctuations, which induce cavity length fluctuations and degrade the laser’s stability. By placing the fiber in a thermostatic and shockproof box, and shortening the fiber in the cavity, the long term stability of the laser can be strongly enhanced.

2.2. Optical frequency comb generation

The LDS fiber laser can keep stable mode locking for hours with our feed-forward technique for supermode noise suppression. However there is no particular set of optical modes that can stably dominate the spectrum over time. The spectrum can appear smooth for each of the wavelength peaks, which indicates that this type of operation is not suitable for frequency comb based applications. So, we use the injection locking method to select out one supermode and to suppress all others [25], as well as lower the optical linewidth of the individual comb lines of the resulting comb out. However, the injection-locking state is sensitive to the wavelength drift of the reference laser and to the ambient temperature drift. Therefore, the unstable state is necessary to be detected and the error signal should be feed back into the cavity to maintain the locking state.

The optical frequency comb generation setup based on LDS fiber laser is shown in Fig. 3. Part of the polarization-maintain fiber is wound on a piezoelectric transducer (PZT) to realize a fiber phase shifter and the cavity length is changed by the supplied voltage to the PZT. An 18 nm optical filter (centered at 1550 nm) is inserted in the cavity to remove the gain peak around 1530 nm and to force lasing at the injection seed frequency. A CW narrow linewidth (~100 Hz) laser at ~1550.2 nm is used as the injection seed source while the injection power is controlled by a polarization-maintaining variable optical attenuator (VOA). All the fiber and elements in the laser cavity are polarization maintained.

 

Fig. 3 Schematic of the optical frequency comb generation setup.

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Part of the output is coupled into the feedback control loop, which is composed of a wavelength tunable filter (WTF) with 1 nm bandwidth, a 100-KHz PD, a proportional and integral control (PIC) circuit and a high voltage amplifier (HVA). The DC power of the wavelength selected by the WTF is detected by the low-pass PD, which is then suitable processed by the PIC.

When the error correction loop is switched on, an ultra-flat comb with high quality can be produced, as shown in Fig. 4. The frequency comb is locked to the seed source with −1 dBm optical power. The 3 dB bandwidth of the frequency comb is 7.6 nm, as shown in Fig. 4(a). The inset depicts the close-in view of the optical comb with 0.02 nm resolution. There is no drop out of any particular comb lines, which indicates the stable injection-locking state. A sampling oscilloscope trace can be seen in Fig. 4(b), clearly showing a ~10 GHz pulse train. The coherence of the comb line is demonstrate in Fig. 4(c), which shows the ~80 dB SNR without supermode noise spurs visible above the noise floor. The corresponding phase noise is shown in Fig. 4(d). It is observed that the frequency comb exhibits low phase noise of – 132.4 dBc/Hz at 1 MHz.

 

Fig. 4 Experimental results of the optical frequency comb, (a) optical spectrum, (b) 10 GHz pulse train, (c) RF spectrum, (d) residual phase noise spectrum (red) and noise floor of our RF generator (black).

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Figure 5 shows the PIC operation monitor signal from the PD without and with PIC feedback control. In the former part of the Fig. 5 the frequency comb power changes due to the fiber length fluctuation induced mode-hopping. The gain competition cause a random fluctuation rapidly appears in comb line power. The monitor signal is maximum when the power of the filtered frequency comb lines is at its peak, which is exactly the injection locking state. This indicates that the mode hopping can be successfully detected by the PIC circuit. And then, when the PIC circuit is switched on, the injection locking state can be completely maintained. The frequency comb exhibit good long-term stability without any changes in the pulse parameters, which is limited only by the dynamic range of the fiber phase shifter.

 

Fig. 5 Monitor signal from the PD without and with PIC feedback control.

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3. Discussion

Formation of the DS in a fiber laser is theoretically independent of the sign of cavity dispersion [13]. However, in the anomalous dispersion fiber laser, because of the existence of the intrinsic soliton shaping mechanism caused by the interplay between the GVD and SPM, and the fact that its formed solitons have normally a far narrower spectral width than that of the laser gain, the function of the laser gain is to simply balance the cavity losses, and no gain filtering actually occurs. Consequently the formed solitons dominantly the nonlinear Schrodinger equation solution features rather that the dissipative soliton features. However, in our proposed linear dissipative system, soliton shaping mechanism is blocked because of the lack of SPM, and then dissipative process can be realized in an anomalous cavity by selecting the stretched pulse after linear chirping.

In a regular phase-modulation-based active mode locking, the cavity dispersion will de-chirp and compress the pulse after phase modulation, which supports the soliton pulse shaping. On the contrary, in our design the cavity dispersion will broaden the temporal pulse, then realizes a linear dissipative system. Although PM is used in our fiber laser, the pulse properties of LDS indicate that the laser is not working at soliton shaping regime. Furthermore, the PM can impose either positive or negative linear chirp onto the pulse [26], so that stable spectral broadening can be achieved by either anomalous or normal cavity dispersion under proper timing of the PM, which is very different from the nonlinearity-based spectral broadening: the soliton exists in anomalous-dispersion cavity, while the DS exists in a normal-dispersion one.

4. Conclusion

In conclusion, we experimentally demonstrated the LDS generation in an anomalous-dispersion fiber laser. Linear dissipative process is realized in an actively mode-locked fiber laser, where the conventional fiber nonlinearity is replaced by quadratic phase modulation. The strongly-chirped pulse was 12.4 ps, which was de-chirped to 763 fs. The spectrum of the LDS is 11 nm with rectangular-like profile. By injection locking method, 10 GHz optical frequency comb is achieved with low phase noise. Due to the nonlinearity-free requirement, the LDS laser can be more compact by replacing the fiber by dispersion elements, and using integrated modulators (without fiber pigtail) and waveguide amplifier. Then, the integrated and compact LDS laser with ultra-short cavity length can be very stable for generating low-noise high-repetition-rate optical frequency comb.