We observed dissipative soliton resonance phenomenon in a graphene oxide mode-locked Yb-doped fiber laser, which delivered square-shaped pulse of 0.52 ns~60.8 ns and single pulse energy of 159.4 nJ at 1064.9 nm. The 3dB-bandwidth of Lorentz-shaped spectrum was 0.19 nm. We pointed out that the reverse saturable absorption played a big role in generating square-shaped or flat-top pulses, which verified by additional simulation work.
© 2015 Optical Society of America
Since ultrafast fiber laser  based on mode-locking technique has been realized, people never stop their pace in pursuit of high energy pulse generation. The delivered pulse has experienced conventional soliton, stretched soliton and similariton. The possibility of conventional soliton formation in optical fibers was suggested as early as 1973 , which were first observed in an experiment . Such solitons always live in anomalous dispersion regime, but the energy of conventional soliton is limited to 0.1 nJ due to area theory. After that, dispersion management has been adopted in the cavity design. Stretched pulses  have been obtained with output energy reaching nJ level. Then another kind of soliton called “similariton” has been demonstrated . Similariton has a parabolic pulse shape and higher tolerance of nonlinear effect, leading to high pulse energy more than 10 nJ . At the same time, the dispersion regime where laser operates has been shifted from anomalous to normal regime. Soon the dissipative solitons (DS) have been demonstrated in normal dispersion which have relative higher pulse energy beyond 20 nJ . After that, another novel concept called “dissipative soliton resonance (DSR)” has been proposed first in 2008 .It can be modeled using complex cubic-quintic Ginzburg–Landau equation (CGLE), which adding cubic and quintic saturable absorption terms [8–12]. In this phenomenon, pulse energy can increase infinitely theoretically, delivering flat-top or square-shaped pulse. The pulse width increases as pump power increases while amplitude remains constant . It is an efficient way to enhance the level of the pulse energy, which increases linearly with pump power without wave breaking.
Since the demonstrations on graphene mode-locked fiber lasers were reported in 2009 [14,15], graphene has been widely investigated as a novel saturable absorber for femto/pico-second pulse generation [16,17]. Recently, graphene oxide (GO), as one of graphene derivatives, has also attracted wide attentions. As a semi-product, the graphene oxide is much easier and cheaper to obtain than graphene. Graphene oxide also has characteristics of ultrafast recovery time and broadband saturable absorption, which is comparable to that of graphene. It has already been utilized in femtosecond fiber laser as a saturable absorber at 1.5μm wavelength . Here, we demonstrate a mode-locked Yb-doped fiber laser with graphene oxide at 1μm, delivering square pulses from hundreds of picoseconds to tens of nanoseconds.
2. Experimental setup
The graphene oxide mode-locked fiber laser is constructed in a ring cavity configuration as shown in Fig. 1(a). The total length of the cavity is about ~216 m, which contains 8m Yb-doped double cladding fiber and ~200 m Nufern 1060-XP single mode fiber (SMF). The laser is cladding pumped by a 976 nm 10 W multimode diode which coupled into the gain fiber by a 2 × 1 pump combiner. And the main output port coupler 1 is after the gain fiber which has a 50% splitting ratio, and coupler 2 has a splitting ratio of 20% out of the cavity to monitor the optical spectrum. Polarization controller is utilized to adjust polarization for mode-locking optimization and a 4th order Gaussian shaped filter with a 3dB bandwidth of 2.68 nm is also adopted for controlling the laser wavelength.
The graphene oxide saturable absorber is consisted of two fiber connectors. One of connectors was deposited a thin film of graphene oxide on the surface. This was handled by dripping a drop of the graphene oxide hydrosol on the surface of the fiber connector and air-dried. The graphene oxide hydrosol with concentration of 2 mg/ml was prepared by ultrasonic peeling of graphite oxide in aqueous suspension. The transmission of the graphene oxide increases as incident power increases, whose modulation depth is about ~1.5%, as shown in Fig. 1(b).
3. Experimental results and discussion
By adjusting the distance of the connectors and polarization controller properly, stable mode-locked pulses of the fiber laser occurred at ~567 mW pump power and the repetition rate was 927 kHz, which agreed with the cavity length. Increasing the pump power to 2.6 W, the output power was 147.8 mW, corresponding to single pulse energy of 159.4 nJ. For the safety of the components, we didn’t increase the pump power further.
As shown in Fig. 2(a), the output power and pulse width increased linearly as the pump power increased. The pulse presented square wave shape for the whole range from the pump power of 567 mW to 2617 mW. The pulse width increased from 0.9 ns to 60.8 ns linearly as the pump power increased, while the peak power almost remained constant as shown in Fig. 2(c), which had agreement with the DSR theory. The center wavelength located at 1064.9 nm and the spectral width was ~0.19 nm measured by an optical spectral analyzer with resolution of 0.02 nm. The spectrum presented good Lorentz-fitting as shown in Fig. 2(b). The spectrum seemed to have little change when we increased the pump power as shown in Fig. 2(d). The radio-frequency spectrum as shown in Fig. 3(a) had also been measured. The signal-to-noise ratio was nearly 60 dB, indicating good mode-locking stability. In addition, we had measured the output properties of couple 2. We found that the pulse width and the spectrum had little difference both in time and frequency domains, except the power.
Moreover, we had tried the second and the third setups. In second setup, we reduced the output coupling ratio of coupler 1 from 50% to 30%. In the third one, whose coupler 1 had a 30% output coupling ratio as well, the length of single mode fiber was reduced to 50 m, corresponding to repetition rate of 2.99 MHz. We measured the pulse width under different pump powers in such three setups, as shown in Fig. 3(b). Compared the result of basic setup with the second one, pulse width became larger when the output loss had been reduced. We believed that more energy stayed in the cavity as the output ratio decreased, and further broadened the pulse width as DSR pulse preferred getting stronger horizontally instead of vertically. In the third setup, the pulse had much shorter pulse width obviously at the condition of 50 m SMF. Because the dispersion had been reduced as the SMF length was reduced, while dispersion could broaden the pulse width significantly in normal dispersion regime. The shortest pulse we obtain in third setup was 523 ps. Furthermore, the pulse began to break up when the pump power reached ~1.9 W. Because in the normal dispersion regime, laser system favors DSR when dispersion is large enough; otherwise the multi-pulsing instability will occur .
The phenomenon has already been modeled by cubic-quintic Ginzburg-Landau equation (CGLE), which has additional cubic and quintic saturable absorption terms and quintic nonlinear term, compared with conventional Ginzburg-Landau equation. The quintic nonlinear term seems to have little influence relatively in the condition of generating DSR pulse in normal dispersion through the results in . However the quintic saturable term which stands for reverse saturable absorption plays a big role in pulse shaping from bell to flat-top or square . That is why most DSR phenomenon were reported in a fiber type mode-locking mechanism such as NPR and nonlinear loop mirror, as both of which have a nonlinear transmission of sinusoid curve. The transmissivity deduces as instantaneous power increases in an appropriate range, which is the reverse saturable absorption effect. And the DSR phenomenon could be present when the peak power enters into the reverse saturable absorption region.
As the results, we believe that there must be reverse saturable absorption effect in our cavity, though it is mode-locked by real SA of graphene oxide instead of NPR mechanism. And it turns out that the structure of a pair of non-touch fiber connectors has brought in such effect. We utilized an ASE source at 1μm with bandwidth of 36 nm, which is propagated through a 2.68 nm filter with shape of 4th order super Gaussian and a pair of non-touch fiber connectors with graphene oxide film on one end. The ASE spectrum turns to a multipeak structure due to etalon effect which caused by interference of the reflection light from two fiber connectors’ ends as shown in Figs. 4(a)-4(c). The periodic multipeak structure can be tuned by changing the distance of the two fiber connectors. Then we put the fiber connectors and filter back into the cavity (keeping the distance between the two fiber ends unchanged), we can obtain the DSR operation by tuning the polarization controller. The centre of DSR spectrum located at the wavelength where has a largest loss due to the etalon effect as shown in Fig. 4(d). This means light in central wavelength has a larger loss while longer and shorter wavelengths light have less. As in all-normal-dispersion regime, leading to giant up chirp, the longer and shorter wavelengths light locates at the wings of the pulse, which has lower instantaneous power; while the central wavelength in the central of the pulse which has larger instantaneous power. So the peak of the pulse in time domain experiences more losses than the wings’, just only considering the loss caused by etalon effect. This is exactly the reverse saturable absorption we are looking for. Actually, assuming a traditional Gaussian shape filtering spectrum, the filtering effect can provide some saturable absorption effect more or less . And here, it is just the opposite condition in our experiment. We have tried different distances between the fiber connectors as shown in Figs. 4(b) and 4(c), and the DSR central wavelength always located at maximum loss wavelength indicating it’s not a coincidence. If the distance between the fiber connectors is too small or too larger, we can’t obtain the DSR operation.
In addition, the latent NPR effect has also contributed to the reverse saturable absorption, as the components in the cavity have some polarization dependent loss more or less which can lead to small amount of NPR effect. In other traditional saturable absorbers such as SESAM, the modulation depth usually is relative large. It is easy to reach 10%, even 40%. Comparing to the large modulation depth, the small amount of latent NPR power modulation effect could be ignored. But here, the modulation depth of saturable absorber we used here is just 1.5%. The total saturable absorption effect in the cavity should consider the influence of latent NPR modulation effect. As the result, tuning of the PC would influence the shape of the square pulse, even whether generating DSR pulse or not. In the experiment, the DSR pulse can be tuned by polarization controller, from slim tall square pulse to fat low pulse within certain realm, which indicating the existence of latent NPR effect.
4. Simulation results and analysis
Furthermore, we have also taken simulation work, modeled by scalar generalized nonlinear Schrodinger equation (NLSE) qualitatively instead of CGLE, for further proofing that the square-shaped pulse generation is relative to the reverse saturable absorption, and providing clear physical image.
The proposed mode-locked fiber ring laser is schematically shown in Fig. 5(a). The ring consists of a piece of ytterbium doped fiber (YDF) with a length of 1 m, a piece of single mode fiber (SMF) with a length of 65 m. The corresponding repetition rate is 2.99 MHz, which is the same with third experimental setup above. The other components are Gaussian shaped filer with bandwidth of 8 nm, an output coupler (OC) with output ratio of 80% and a saturable absorber. All the fiber in the ring has the same group velocity dispersion and nonlinear coefficient corresponding to β2 = 0.025 ps2/m and γ = 3 W−1km−1, respectively. The saturable absorber here is assumed to be a nonlinear polarization rotation (NPR) device, which has a sinusoid shape transmission curve verse instantaneous power. The curve containing reverse saturable absorption effect is shown in Fig. 5(b). SA has a saturable absorption property within the range of power 0~10 W, transmissivity increases as power increases; while demonstrates reverse saturable absorption in the other (10~20 W), in which transmissivity decreases as power increases.
When we set small signal gain as 4 m−1, and gain saturation energy is 12 nJ, we obtain flat-top pulse with 456 ps width as shown in Fig. 5(c). The peak power is 12.5 W, and it has already located in the reverse saturable absorption realm. The spectrum has a very narrow bandwidth of 0.07 nm, which presenting a nearly perfect Lorentz-fitting as well as the experimental result. But in the experiment, the spectrum bandwidth ranged from 0.1 nm to 0.4 nm which is larger than the simulation result. This is because, in the numerical work, there is no fluctuation in amplitude of the pulse in time domain, which introduced less SMP effect which leading to wider spectrum ; while a little fluctuations can be observed in amplitude of experimental pulses. So the reverse saturable absorption has clamped the peak power, preventing flat-top pulse from further growing up to be a traditional dissipative soliton. And the narrow spectrum is agree with the DSR theory as well .
In summary, we have observed square-shaped pulse delivering from graphene oxide Yb-doped mode-locked fiber laser. The pulse width increases linearly as pump power increases within a range of 0.52 ns-60.8 ns, and the single pulse energy can reach as 159.4 nJ, limited by the damage threshold of fiber components. The Lorentz-shaped narrow spectrum of 0.19 nm has been obtained as well, which agrees with the DSR properties in normal dispersion regime. We highlight the importance of reverse saturable absorption in DSR operation and indicate that the reverse saturable absorption effect is induced by etalon effect from a pair of non-touched fiber connectors and latent NPR effect in the cavity. In addition, we have simulated the DSR pulse generation by the model of conventional scalar generalized nonlinear Schrodinger equation instead of Cubic and Quintic Ginzburg-Landau Equation. Flat-top pulse of 456 ps width and Lorentz-shaped spectrum of 0.07 nm bandwidth have been obtained, based on a SA containing reverse saturable absorption.
The authors acknowledge the financial support from the National Natural Science Foundation of China (NSFC, Nos. 61235010 and 61177048), the Beijing Municipal Science & Technology Commission (No. Z131100003213010), the NSF of Tianjin (No. 12JCZDJC27400) and the Beijing University of Technology, China.
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