Abstract: We present an L-band dissipative soliton (DS) fiber laser, which can deliver 87.5 fs pulses at 1.6 μm band. Numerical simulations are used to confirm the DS generation, and prove the pivotal component of the invisible filter with proper bandwidth in the formation of DS pulses. Such a robust, compact ultrafast laser source with higher pulse energy is hence an excellent seed source for L-band amplifiers. The mechanism revealed in the simulations is helpful to develop a unified theory for understanding various mode-locking regimes in normal dispersion lasers.
© 2016 Optical Society of America
Ultrashort pulse lasers, due to their performances of shorter pulse duration, and higher peak power, have gained much attraction for wide applications in optical communications, sensors, fine manufacturing, medical diagnose and others [1–5]. Mode-locking is the most common method to generate ultrashort pulses. Now, the mainstream of mode-locked fiber lasers (MLFLs) is to explore novel mode-locking regimes and to expand the working wavelength, so as to improve the laser performances such as the pulse duration and energy [6–8]. Dissipative soliton (DS) fiber lasers are regarded as an attractive way to overcome the limitation on the duration and energy of conventional solitons (CSs) [9,10]. The formation of DSs in laser oscillators needs composite balances among several effects including nonlinearity and dispersion, gain and loss . Especially the balance between gain and loss plays a dominant role. DSs have been achieved in normal dispersion cavity fiber lasers . Peng et al reported 4.5 nJ 78.9 fs DS pulses in 1550 nm band . Also, the Yb-doped fiber laser employing a nonlinear optical loop mirror  was reported to deliver 340 fs dechirped DS pulses . Besides, there are a lot of reports on DS lasers operating at 1 μm or 1.55 μm or 2 μm [15,16]. However, it is expected to break through the limitation on the working wavelengths of rare-earth doped fibers, as well to offer great performances for ultrafast fiber lasers.
L-band MLFLs can widen the transmission capacity of optical communications and also find various applications in spectroscopy, biomedical diagnostics and surgery [17–19]. It has been known that the emission wavelength of lasers depends on the linear cavity loss, fiber length and dopant concentration [20,21]. Sanchez’s group reported the mode-locking operation at 1.6 μm in an Er-doped fiber laser by controlling the linear cavity loss . They also built a 1.6 μm MLFL based on graphene saturable absorber (SA) . However, these lasers are running in soliton regime, and thus the pulse duration and energy are limited. The pulse duration and energy in Ref . are limited to 2.9 ps and 8.8 pJ, respectively. Although extending the Er-doped fiber (EDF) length can force the laser emit in L-band, it is hard to obtain stable mode-locking for L-band ultrashort pulses. Although the L-band DS fiber laser could be realized by inserting a 30 m EDF in the cavity , the laser can only deliver chirped pulses with duration of ~20 ps with a spectral width of ~20 nm. According to the Fourier-transform limitation, the dechirped pulse duration cannot be shorter than 200 fs. Shortening the EDF length causes the working wavelength shift towards 1.55 μm. Hence, exceptional technologies are required to produce L-band ultrashort pulses.
In this paper, we present the generation of 1.6 μm DSs in an EDF laser (EDFL) with net normal dispersion. Two segments of EDFs with different absorption ratio and group velocity dispersion (GVD) parameters were cascaded in the cavity, acting not just as the gain medium, but also as a controller to limit the population inversion in EDF for lasing at 1.6 μm. This also allows regulating the cavity dispersion for producing DSs. The output pulses can be dechirped to 87.5 fs by using single mode fibers (SMFs). Numerical simulations are used to find out the pulse dynamics, unveiling the critical role of the filter bandwidth on the DS generation.
2. Experimental setup and principle
Figure 1 depicts the experimental setup of the proposed EDFL. Two types of EDFs with disparate parameters serve as the gain medium in the cavity. One is a 2.4 m segment of EDF1 with the GVD of −26 ps/km/nm at 1550 nm and another one is a 0.8 m EDF2 with GVD of −48 ps/km/nm at 1550 nm. The peak absorption ratios at 1530 nm of these two EDFs are 30 dB/m and 80 dB/m, respectively. Two 980 nm laser diodes (LDs) were used to bidirectionally pump the EDFs. The maximum power of the former LD is 605 mW and that of the backward one is 610 mW. The artificial SA for mode-locking is based on the nonlinear polarization rotation (NPR) , which consists of two polarization controllers (PCs) and a polarization sensitive isolator (ISO). The ISO also force the laser unidirectional circulation in the cavity. A 50:50 optical coupler (OC) extract 50% of the generated laser for measurement. The remaining fibers are SMFs and the total cavity length was 5.16 m. The output spectrum was measured with an optical spectrum analyzer, and the pulse train was monitored with an oscilloscope after a 20 GHz photodetector (PD). The pulse duration was analyzed by an autocorrelator.
In a cavity with normal GVD, distinct regime of DS operation can exist for a set of cavity parameters. To generate high energy pulses with large positive chirp , the DS regime can be extended to large net dispersion > 1 ps2. In our experiment, the total cavity dispersion is 0.09 ps2. It is therefore the reason for DS operation in the cavity. Dissipative effects such as spectral filtering and saturable absorption enable the stabilization of the chirped pulses in the presence of the nonlinearity and the normal dispersion . Hence, this artificial SA functioned as a bandwidth tunable filter  is critical for stabilizing the pulses in the cavity.
In essence, the method for realizing L-band emission in EDFs is to limit population inversion at a low level (~30%-40%) . In this case, the EDF can provide a positive gain at 1600 nm, but negative at 1550 nm. A simple way to limit the population inversion is to insert a segment of EDF2 with higher absorption ratio (80 dB/m at 1530 nm) in the cavity. Then, it in turn guarantees a moderate population inversion, allowing for lasing at 1.6 μm. The length of the EDF2 is optimized by the experiments. The reason that we don’t use a longer piece of EDF1 to regulate its population inversion is to achieve better pulse performances, since the short laser cavity usually favors broader spectrum and shorter pulse duration. The third-order dispersion effect on pulses in the cavity must be avoided whenever possible .
3. Experimental results
Mode-locking occurs when the pump power exceeds 750 mW. Figure 2(a) presents the mode-locked optical spectrum. It is a near rectangle with steep rising and falling edges, indicating the DS operation. The central wavelength locates in 1.6 μm, and the whole spectrum is in the L-band with a bandwidth of 40.6 nm. Compared with previous reports on DS EDFLs, the working wavelength is red-shifted 30~40 nm. Figure 2(b) shows the temporal traces of mode locked pulses. The repetition rate is 38.76 MHz, as determined by the cavity length. The evolution of the spectral width via the pump power is presented in Fig. 2(c). Clearly, the spectrum broadens with increasing the pump power. This is consistent well with theoretical predictions [27, 28] and experiments . As the pump power increase from 750 to 1215 mW, the spectral width continuously broadens with the output power growing up (see Fig. 2(d)). The reason can be attributed to growing accumulated self-phase modulation (SPM) effects. The maximum output power is 57 mW. Considering the repetition rate, the single pulse energy is 1.47 nJ, which is the highest pulse energy achieved in L-band to date.
Figure 3 shows (a) the optical spectrum of the shortest pulses and (b) the autocorrelation (AC) traces of the dechirped pulses. Inset in Fig. 3(b) gives the AC trace of the corresponding chirped pulses. Assuming a Gaussian profile, the duration of the chirped pulse is 3.1 ps, and it can be dechirped to 87.5 fs by using 1.8 m SMF as the compressor outside the cavity. To the best of our knowledge, this is the shortest pulse generation in 1.6 μm band so far. Combined with the 49.7 nm bandwidth, the time-bandwidth product is 0.5. This is larger than the Fourier transform limited value of 0.44 for Gaussian pulses, suggesting that the pulses are still chirped. It can be verified by the clear pedestal on the AC trace of the dechirped pulse because of the existed higher-order dispersion [9, 28]. According to the area integral in Fig. 3(b), the pulse contains more than 65% of the energy and its peak power is calculated to be 11 kW. In view of the nonlinear chirp characteristic of DS pulses, shorter pulse can be achieved by using more complicated compressors. The radio spectrum (RF) of the pulse train shown in Fig. 3(c) gives a SNR of 64 dB, indicating low-amplitude fluctuations. The resolution used to characterize the RF spectrum is 1 kHz. A RF spectrum over a wide range of 1.8 GHz with the resolution of 10 kHz shown in the inset demonstrates the single-pulse operation and stable mode locking.
4. Simulation and discussion
To confirm the generation in the laser, we use a scheme depicted in Fig. 4 to model the DS operation. The components and the parameters for simulations are the same as those in the experiments as follows: a 2.4 m EDF-1 with GVD β2 = 0.033 ps2/m and the nonlinear coefficient γ = 9.32e−3 m−1W−1, a 0.8 m EDF-2 with β2 = 0.06 ps2/m and γ = 9.32e−3 m−1W−1, a 0.5-m SMF1 with β2 = −0.02 ps2/m and γ = 2e−3 m−1W−1, a 50:50 coupler, a SA, a Gaussian shaped filter centered at 1600 nm with a variable bandwidth Δλ and one more piece of 1.46 m SMF2. It is reasonable to assume a filter centered at 1600 nm existing in the cavity, since the wavelength tunable characteristic of the NPR-based invisible filter has been revealed [25, 30]. The total cavity dispersion is 0.09 ps2 and the cavity length is the same as the experiment.
Pulse evolution stars from EDF-1 with white noise. We use a generalized Ginzburg-Landau equation to describe the pulse formation and propagation :32]. m0 is the modulation depth, P(t) is the input pulse power and Psat is the SA saturation power. We set m0 = 0.8, Psat = 100 W and Esat = 200 pJ.
The numerical model is solved by a split-step Fourier method. For simplicity, we assume that the small signal gain g0 of EDF-1 is the same as that of EDF-2. The EDF gain is assumed to be a Gaussian shape with a bandwidth Δλgain of 100 nm . Starting from the white noise with pulse energy of 0.1 pJ, the stable DS generation can be realized by tuning Δλ and g0 in a certain range. Δλ is normalized to Δλgain in our simulations. Fixed g0 = 3 m−1, Δλ/Δλgain = 0.2, stable DS solution is obtained and depicted in Fig. 5(a). The formation of DSs is clearly found after 20 roundtrips. The spectral width is 40.6 nm, which is close to the experimental results. Figure 5(b) shows the simulated results of changing the bandwidth versus g0. It broadens linearly with g0 increasing. Compared with the experimental results obtained during increasing the pump power, the trend in simulation is in agreement with the experiments. All the qualitative features of the experimental DS results exhibit in agreement with the simulations, especial for the sharp peaks at the two spectral edges in simulated results. In the inset in Fig. 2(a), the structured edges exist but with small amplitudes, not as sharp as peaks in simulated results. The sharp peaks at two spectral edges in simulations maybe caused by strong SPM effects, as the gains of two EDFs are considered as equivalent for simplifying the simulations.
In simulations, stable DS formation only exists in the range of 0.2 < Δλ/Δλgain < 0.43, when other parameters are fixed and g0 varies from 3 to 6.9 m−1. To further reduce the filter bandwidth results in multi-pulse operation. When Δλ/Δλgain is more than 0.43, it is hard to get stable mode-locking regardless of how to adjust g0. This can be explained as follows: the filter plays a significant role on the DS formation in a net normal dispersion cavity. It cuts away the spectrum and restores its original pulse duration, working together with the SA to balance the linear phase accumulation to stabilize the pulses. In our simulations, when the Δλ/Δλgain is 0.43, the 3 dB bandwidth of the pulse spectrum is near 40 nm, which is very close to the filter bandwidth (43 nm), resulting in a weak spectral filtering effect. In consequence, it could cause more difficulty to obtain stable mode-locking operation .
This laser elicits several enlightenments from the feature. It is simple to explore a longer wavelength operation in MLFLs by optimizing the cavity parameters such as the linear cavity loss and the dispersion through cascading different kinds of gain fibers in the cavity. The technology explored here can be extended to other wavelength regions. This contributes to potential ability for developing new working wavelength of rare-earth ion doped gain media. Besides, the performance of 1.47 nJ pulse energy and sub-90 fs duration working within L-band makes it very practicality in some applications.
In summary, we have achieved for the first time a sub-100 fs ultrafast EDFL operating at L-band band. 1.47 nJ 87.5 fs pulses were obtained at the repetition rate of 38.76 MHz and the central wavelength of 1.6 μm. To our knowledge, this is the shortest pulse duration ever obtained in EDFLs above 1.6 μm. Numerical simulations not only confirm the stable DS formation, but also give the important role of the optical filter in the DS formation.
The research was supported by National Natural Science Foundation of China (NSFC) (Grants 61178014 and 11274231) and in part by Natural Science Foundation of Hubei Province of China (Grant 2015CFB609).
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