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A tunable L-band dissipative soliton (DS) fiber laser with nonlinear polarization rotation (NPR) playing the roles of both a saturable absorber (SA) and a tunable filter has been demonstrated experimentally and numerically. By appropriate adjustment of the states of the polarization controllers (PCs) and the pump power, DSs with continuously tunable wavelengths have been observed over the wavelength range from 1583.0 to 1602.4 nm with a 3-dB spectral bandwidth of around 20 nm and from 1581.9 nm to 1602.6 nm with a 3-dB spectral bandwidth of around 4 nm. In addition, we have observed that by increasing the pump power, the 3-dB spectral bandwidth of the DS could be increased without pulse breaking. Numerical results for the characteristics of the DSs are in accord with the experimental data.
© 2016 Optical Society of America
1. Introduction
L band lasers have been widely used in modern optical telecommunication systems [1] because they can increase the transmission capacity. Compared with bulk laser systems, fiber lasers have the practical advantages of being compact, inexpensive, robust, and of having efficient heat dissipation [2–4 ]. In addition, silica fibers have low losses in the L band. Because of these practical advantages, in recent years researchers have paid increasing attention to L-band fiber lasers [5–12 ].
In addition to expanding the telecommunications window, L band mode-locked fiber lasers also have various other potential applications including material processing [13], coherent Raman scattering microscopy [14], supercontinuum generation [15, 16 ], and terahertz generation [17]. Since mode-locked fiber lasers with different center wavelength have different roles, such as powerful mode-locked pulses with different center wavelength can provide different focus depth or a different material absorption in the material processing [13]. L-band wavelength-tunable mode-locked fiber lasers have attracted a great deal of research interest. Experimentally, by using a tunable-ratio optical coupler to adjust the wavelength dependent intra-cavity loss, Lin et al. demonstrated an L-band wavelength-tunable mode-locked erbium-doped fiber-ring laser [18]. More recently, Wang et al. presented a widely tunable mode-locked fiber laser using a carbon nanotube absorber and a fiber-optic W-shaped spectral filter [19].
Since the net cavity dispersion in both of the above experiments was anomalous, only conventional solitons could be generated, and the soliton energy was limited to ~0.1nJ by the soliton energy quantization effect [20]. Recently, it has been shown, both experimentally and theoretically, that another type of soliton, the dissipative soliton (DS), can be formed in fiber lasers with net normal or all-normal dispersion [21, 22 ]. Due to the fact that the formation of DSs is a result of the mutual nonlinear interactions between the normal cavity dispersion, the fiber Kerr nonlinearity, the laser gain and cavity loss, a DS fiber laser can naturally generate large energy, strongly chirped optical pulses [23, 24 ]. Zhang et al. have demonstrated experimentally that tunable DSs can be formed in an erbium doped fiber laser with atomic layer graphene as the mode locker [25]. Han et al. have also investigated experimentally and numerically a tunable DS fiber laser based on a single-wall carbon nanotubes (SWNTs) and nonlinear polarization rotation (NPR) technique [26].
The SA is a key element in passively mode-locked fiber lasers, and the properties of the SA are central to the development of high performance lasers. In particular, SAs based on the NPR technique [27, 28 ] and nonlinear optical loop mirrors [29–31 ] both have the advantage of a high damage threshold compared to graphene [32, 33 ], carbon nanotubes [34] and other nanoscale carbon materials [35]. It should also be noted that the NPR technique can be utilized as an effective SA to realize self-starting passive mode locking in fiber lasers, and can be used as an effective filter to realize wavelength tunability [36–38 ]. Unlike filters based on tunable-ratio optical couplers [39, 40 ], tunable filters [41–43 ], Fabry-Perot semiconductor optical amplifiers [44], or fiber gratings [45, 46 ], which add the tunable components into the cavity, the NPR uses only the intrinsic artificial birefringence of the fiber to realize wavelength tunability [36]. To date, L-band wavelength tunable passively mode-locked erbium-doped [37] and Er:Yb-doped double-clad [38] fiber ring lasers with anomalous dispersion using the NPR effect have be reported. However, to the best of our knowledge, no L-band wavelength-tunable, DS, mode-locked fiber lasers using NPR as both the SA and tunable filter have been demonstrated.
In this paper, we report the experimental and numerical investigation of an L-band wavelength-tunable DS fiber laser based on the NPR technique. Using the intrinsic birefringence spectral filtering as a filter, which has a sinusoidal transmission function for the linear and nonlinear phase shifts of light in the cavity, we have realized tunability of both the 3-dB spectral bandwidth and the central wavelength with appropriate adjustment of the polarization controllers (PCs) and pump power. We have also observed that the 3-dB spectral bandwidth of the DSs can be changed from 20.8 nm to 23.7 nm without pulse breaking when the pump power is increased. Numerical results have verified the generation of DSs with different spectral bandwidths.
2. Experimental setup
The experimental setup of the DS fiber laser is shown in Fig. 1 . A laser diode operating at 976 nm was used to pump a ~30 m segment of high concentration erbium doped fiber (HCEDF) through a wavelength division multiplexer (WDM). The HCEDF had peak absorption of 20 dB/m at 976 nm and a group velocity dispersion (GVD) of 17.6 ps2/km. All the other fiber (~13.5 m in total) used in the cavity was standard single-mode fiber (SMF) with a GVD of –22 ps2/km. The total cavity length was ~43.5 m, and the corresponding net cavity dispersion was approximately 0.231 ps2. Unidirectional operation of the laser was enforced using a polarization-dependent isolator (PD-ISO), and two PCs were used to control the polarization of the light. The combination of the PD-ISO and the two PCs can act as both a wavelength-dependent filter and a SA based on the NPR technique, and can thus be used to realize both self-starting mode locking and tunable wavelength operation of the laser. A 90:10 output coupler (OC) located after PC2 was used to output 10% of the signal power. An optical spectrum analyzer (Yokogawa AQ6317C) with a maximum resolution of 0.01 nm, a 1-GHz digital sampling oscilloscope (Yokogawa DL9140) with a photodetector with a 1 GHz bandwidth, a commercial optical autocorrelator (FP-103XL) and a 20 GHz oscillograph (Agilent 86100D&86105D module) with a 25 GHz high speed photodetector (Newport 1414) and a radio frequency (RF) spectrum analyzer (Agilent N9020A) with a maximum measurable RF frequency of 26.5 GHz were used to monitor simultaneously the optical spectrum, temporal pulse shape, pulse width and stability of operation.
Fig. 1 Schematic setup of the DS fiber laser system. WDM: wavelength division multiplexer, HCEDF: high concentration erbium doped fiber, PC1 and PC2: polarization controllers, PD-ISO: polarization-dependent isolator, OC: 90:10 output coupler.
3. Experimental results and discussion
Once the pump power exceeded the mode locking threshold, DSs were easily obtained with appropriate PCs states. Figure 2(a) shows a typical DS spectrum at a pump power of 281.4 mW, that may be seen to have an approximately parabolic top and steep sides. The central wavelength of the DS was ~1593.6 nm and the soliton had a 3-dB bandwidth of 21.7 nm. Figure 2(b) shows the equally-spaced uniform pulse trains with a period of ~217.5 ns, corresponding to the total cavity length of 43.5 m. The average output power was 5.7 mW, corresponding to an output pulse energy of ~1.24 nJ. The autocorrelation trace of Fig. 2(c) shows that the full width at half maximum (FWHM) was ~21.2 ps assuming a Gaussian profile (red dotted line). The calculated time bandwidth product (TBP) was ~54.3, which indicates that the mode-locked pulses were strongly chirped. The large pulse FWHM can be compressed using the anomalous dispersion compensation technique. Figure 2(d) shows the wideband RF spectrum up to 100 MHz. The fundamental repetition rate was ~4.60 MHz, and the signal to noise ratio was as high as 47 dB, indicating that the laser operated in a stable regime.
Fig. 2 Characteristics of a typical DS at 1593.6 nm. Optical spectrum (a). Oscilloscope trace (b). Autocorrelation trace (c). Wideband RF spectrum up to 100 MHz (Insert: narrow bandwidth RF spectrum up to 10 MHz) (d).
By fixing the states of the PCs and changing the pump power from 259.0 mW to 299.0 mW, the 3-dB spectral bandwidths could be continuously broadened from 20.8 nm to 23.7 nm, these changes arise because the self-phase modulation (SPM) effect increases with the pump power increasing. In addition, the pulse duration narrowed from 24.5 ps to 20.8 ps as shown in Fig. 3 , the pulse energy and the peak power increased from 1.23 nJ to 1.84 nJ and from 51.90 W to 88.46 W. At the highest pump power of 299.0 mW, we obtained a pulse with a duration of 20.8 ps as shown in the inset of Fig. 3(a). Considering its 3-dB spectral bandwidth of 23.7 nm, one can calculate that its TBP was ~58.1. Because of safety concerns for the components, we did not increase the pump power further.
Fig. 3 Continuously tunable spectral bandwidths. Optical spectra for three different values of the pump power (Insert: autocorrelation trace under a pump power of 299 mW) (a). The 3-dB spectral width from 20.8 nm to 23.7 nm and pulse duration from 24.5 ps to 20.8 ps as a function of the pump power (b). The pulse energy and peak power as a function of the pump power (c).
Unlike previously discussed tunable wavelength mechanisms using additional optical filters [41–46 ], in our experiment, the spectral filtering was provided by the intrinsic birefringent filtering of the NPR mode-locking mechanism [47]. With this approach, the central wavelength can be shifted with different wave plate settings and the pump power. As an example, Fig. 4(a) illustrates the optical spectra at six typical central wavelengths of 1583.0, 1587.0, 1591.2, 1593.0, 1595.5 and 1602.4 nm at pump powers of 272.0, 281.2, 281.2, 281.2, 281.2 and 299.0 mW, respectively. The corresponding 3-dB spectral bandwidths were 16.5, 20.7, 22.8, 24.3, 22.8 and 18.7 nm, respectively, as shown in Fig. 4 (b). It is obvious that the rectangular shapes of the spectra remained almost unchanged, and the characteristics of the pulse trains also showed no significant differences. In the experiment we also found that, in order to realize a wide tunable range and obtain a stable output pulse, both the pump power and the orientation of the PCs had to be adjusted simultaneously. In addition, since changing the pump power could alter the strength of the SPM effect, while adjusting the PCs could change the transmission bandwidths, which corresponded to altering the polarization dependent loss of the cavity, there existed no definite relationship between the spectral width and the central wavelength. This conclusion is similar to that of Ref [25] and Ref [26].
Fig. 4 Optical spectra of the continuously tunable wavelength from 1583.0 nm to 1602.4 nm (a). 3-dB spectral width and pulse duration at different center wavelengths (b).
When pump power was decreased continually, the temporal and spectral profiles became extremely unstable, if we further adjusted the PCs in a suitable position, then another stable pulse which with a narrow spectrum was formed. Figure 5(a) shows the spectrum of this pulse at a pump power of 224.0 mW. It can be seen that this spectrum also has steep sides. The central wavelength was about 1597.0 nm with a 3-dB bandwidth of 4.2 nm. The equally-spaced uniform pulse train shown in Fig. 5(b) indicates that the pulse spacing was 217.5 ns. The pulse duration was 405 ps monitored using a 20 GHz oscillograph with a maximum resolution of 20 ps and a 25 GHz high speed photodetector, as shown in the inset of Fig. 5(b), corresponding to the TBP of ~200.1. The average output power was 3.42 mW, corresponding to a pulse energy of ~0.74 nJ.
Fig. 5 DS generation at 1597.0 nm. Optical spectrum (a). Oscilloscope trace (Insert: 20 GHz oscilloscope trace) (b).
Comparing Fig. 2(a) with Fig. 5(a) we can see that although both the spectra had steep edges, the spectrum in Fig. 5(a) was very narrow. We can understand this as follows. With a high pump power (corresponding to Fig. 2), the SPM effect was strong, as was the NPR effect. Correspondingly, the NPR effect dominated the pulse self-consistent evolution and formed stable mode-locked pulses. However, at a low pump power (corresponding to Fig. 5), the SPM effect was weakened. Correspondingly, the group velocity dispersion (GVD) effect became strong, which resulted in the increase of the pulse duration. On the other hand, since the birefringence filter has a sinusoidal transmission function for the linear and nonlinear phase shifts of light in the cavity, varying the cavity birefringence can change the transmission bandwidths. Therefore, by adjusting the PCs, narrow transmission bandwidths could be formed, which corresponds to a laser with a narrow band filter in the cavity. In addition, we used a ~30 m erbium-doped fiber as the gain medium, which meant that the gain filtering effect could not be ignored because of the intense gain dispersion effect. The effective gain bandwidth of the laser cavity was limited by the gain filtering effect, so both the narrow band filter and the gain filtering effect cut off the wings of the power spectrum. As a result, they could act as an effective saturable absorber and realize mode-locking operation [48–50 ]. From the above discussion we can see that, because of the different mode-locking mechanism, the resulting pulses had different characteristics. With careful examination of the experiment results it may be seen that the pulses with a narrow spectrum had lower pulse energy and broader pulse duration than those with a broad spectrum.
Once this DS pulse had been formed, by appropriately adjusting the orientation of the PCs and the pump power, the central wavelength of this type of DS could be continuously tuned. Figure 6 shows the optical spectra of four DSs. Their central wavelengths were 1581.9, 1591.6, 1597.0 and 1602.6 nm, with the 3-dB spectral bandwidths of 3.9, 3.3, 4.2 and 3.6 nm at pump powers of 220.7, 220.7, 224.0 and 237.9 mW, respectively. The range of wavelength tunability was 20.7 nm from 1581.9 nm to 1602.6 nm. We note that in this experiment, in order to maintain stable DS operation as the PCs orientation was changed, the pumping strength had also to be adjusted. Throughout the course of adjusting the wavelength, the characteristics of the pulse trains showed no significant changes.
Fig. 6 Continuously tunable wavelength from 1581.9 nm to 1602.6 nm obtained by adjusting the PCs and pump power.
The generation of different DSs further demonstrates that the transmission of the NPR varies with the cavity birefringence. To highlight this point, we used the follows equation to express the power transmission of the cavity [36]:
Where θ 1 and θ 2 are the azimuth angles of the polarizer and the analyzer with respect to the fast axis of the fiber. ∆φL and ∆φNL are the linear and nonlinear phase delays, respectively, and can be expressed as ∆φL = ∆φ 0 + 2π(1- δλ/λs) L/Lb, and ∆φNL = 2γLPcos(2θ 1)/3, where ∆φ 0 is the initial phase delay between the two orthogonal modes propagating in the fiber; λs is the central wavelength of the optical pulse; δλ is the wavelength detuning against λs; L, Lb and γ are the total length, the birefringence beat length, and the nonlinear coefficient of the fiber, and P is the instantaneous power of the optical pulse.
From Eq. (1) we can see that when θ 1, θ 2, P and L were fixed, changing Lb could alter both the transmission peak wavelength and transmission bandwidth. This was confirmed by simulation results as shown in Fig. 7(a) . On the other hand, since the nonlinear phase delay, ∆φNL can be either negative (90◦<2θ 1<180◦) or positive (0◦<2θ 1<90◦), when θ 1, θ 2, Lb and L were fixed while P increased, the power transmission curve of the cavity moved to the shorter (longer) wavelength side when ∆φNL was negative (positive). Correspondingly, the gain peak moved towards C-band (L-band), as shown in Figs. 7(b) and 7(c). This was also confirmed by the experimental results of Fig. 3.
Fig. 7 Different transmission peak locations and transmission bandwidths for different values of Lb (a). Different transmission peak locations for different values of P, with 90◦<2θ 1<180◦ (b). Different transmission peak locations for different values of P, with 0◦<2θ 1<90◦ (c).
4. Simulation results
To confirm the experimental observations, we have also simulated numerically the formation of DS pulses in the oscillator by solving the extended Ginzburg-Landau equation:
Here A(z,τ) is the slowly varying envelope of the pulse along the fiber, z is the propagation distance of the center of the pulse, τ is the time when the pulse center is at position z, Ω is related to the gain bandwidth, β2 is the second order group velocity dispersion, γ is the Kerr nonlinear coefficient, g(Epulse) is the net gain, which is nonzero only for the gain fiber, and Epulse is the pulse energy. g(Epulse) and Epulse can be expressed as
where g 0 is the small-signal gain, Esat is the gain saturation energy, and TR is the cavity round-trip time.To approximate the experimental conditions of our laser, we used the following components and parameters for our simulations: a 5-m-long SMF (SMF1) with GVD and Kerr nonlinear coefficients of −22 ps2/km and 2 W−1/km, a 30-m-long gain fiber with GVD and nonlinear coefficients of 17.6 ps2/km and 4.5 W−1/km, and one more piece of 8.5-m-long SMF (SMF2) with the same parameters as SMF1. In this paper, we used a scalar model Ginzburg-Landau equation, and the intensity-dependent transmittance of the NPR function is assumed to be TSA = 1-l 0/[1-P(τ)/Psat], where l 0 = 0.8 is the modulation depth; P(τ) is the instantaneous pulse power, and Psat is the saturation power. The OC was placed after the NPR, and had an output of 10%. The cavity loss was assumed to be 0.2. The simulation results are shown in Fig. 8 . It may be seen from Fig. 8 that the 3-dB spectral bandwidth could be reduced from 33.9 nm to 4.9 nm [Fig. 8(a) and blue curve in Fig. 8(b)] while the pulse duration [green curve in Fig. 8(b)] could be increase from 11.7 ps to 25.5 ps by decreasing the small-signal gain, g 0, of the gain fiber from 36 dB to 9.7 dB, which is equivalent to reduce the pump power, both of which observations are in good agreement with the experimental results.
Fig. 8 Simulation results. Optical spectra for five different values of the small-signal gain (g0) (a). The 3-dB spectral width and pulse duration as a function of g0 (b).
5. Conclusion
In conclusion, like a C-band flexible pulse-controlled picosecond fiber laser with the wavelength-tunable range of ~20 nm based on controlling the bandwidth of the fiber Bragg grating filter reported by Liu et al. [51], we have experimentally and numerically demonstrated an L-band wavelength-tunable DS fiber laser with NPR playing the roles of both a SA and a tunable filter. Properly adjusting the PCs and the pump power varies the transmission function of the NPR, and allows the central wavelength of the DSs to be tuned. We have also observed that the 3-dB spectral bandwidth of the DSs at the central wavelength around 1595.5 nm could be increased from 20.8 nm to 23.7 nm without pulse breaking when the pump power was increased, which further confirmed by the numerical simulation.
Acknowledgments
This research was supported by grants from the National Natural Science Foundation of China (Grant nos. 11074065, 11374089 and 61308016), the Hebei Natural Science Foundation (Grant nos. F2012205076 and A2012205023), the Specialized Research Fund for the Doctoral Program of Higher Education of China (Grant no. 20101303110003) and the Technology Key Project of Colleges and Universities Hebei Province (Grant nos. ZH2011107 and ZD20131014).
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