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We report a regeneratively FM mode-locked erbium fiber laser operating at 9.2 GHz, in which a SESAM saturable absorber and a higher-order soliton effect are combined to generate a 440 fs pulse train. Higher-order solitons have a narrow center peak while accompanied by pedestals on the wing, but such components can be well suppressed by the saturable absorber, which enables very efficient pulse narrowing. As a result, 440 and 480 fs transform-limited sech pulses were successfully obtained at output powers of 15 and 45 mW, respectively.
© 2016 Optical Society of America
1. Introduction
Actively mode-locked fiber lasers that can emit a pico- to subpicosecond pulse train in the GHz region are an attractive pulse source for ultrahigh-speed optical transmission, signal processing, and metrology applications. In particular, FM mode locking has the potential to greatly reduce the pulse width by increasing the bandwidth with a high modulation index. To generate a 10−40 GHz pulse train, a harmonic mode-locking technique has been employed [1, 2]. However, it has remained difficult to reduce the pulse width below 1 ps in the 10−40 GHz region and this has only been realized by using an electro-optic modulator with a very low Vπ such as an MQW modulator [3]. On the other hand, passively mode-locked fiber lasers can generate femtosecond pulses in a simple configuration such as with nonlinear polarization rotation or saturable absorbers, but their repetition rate is typically limited to 1 GHz or below [4, 5]. To take advantage of the benefits of these two mode-locking schemes, a hybrid mode-locked laser has been demonstrated that provides a very short pulse through passive mode locking while retaining a high repetition rate with active mode locking [6]. For example, a 480 fs pulse was obtained at 1 GHz by incorporating both a phase modulator and nonlinear polarization rotation in the cavity [7], and a 4 GHz, 730 fs pulse was generated by installing an SWNT saturable absorber in an actively mode-locked fiber laser [8]. In addition, we have also reported a hybrid mode-locked erbium fiber laser that can emit a 440 fs pulse train at 9.2 GHz [9]. The laser includes a semiconductor saturable absorber mirror (SESAM) [10] and incorporates a higher-order soliton effect in the cavity to generate a subpicoescond pulse. The higher-order soliton has a sharp center peak with pedestals on the wing. Such pedestals can be efficiently removed by the ultrafast SESAM saturable absorber, resulting in transform-limited subpicosecond pulse generation.
In this paper, we describe in detail a regeneratively FM mode-locked erbium fiber laser that uses a combination of higher-order solitons and a SESAM saturable absorber. We present detailed numerical analyses and new experimental results related to the SESAM nonlinear saturable absorption characteristics, transient pulse evolution into a steady-state and its pulse transition in the laser cavity. Furthermore, we investigate the possibility of pulse width reduction with strong saturable absorption and an increase in the output power with laser cavity optimization.
2. Laser configuration and cavity optimization
Figure 1 shows the configuration of our mode-locked erbium fiber laser. As a gain medium, we use a 2.5 m erbium-doped fiber (EDF) that is bidirectionally pumped with 1.48 μm InGaAsP laser diodes (LDs). The laser contains a 0.5 m highly nonlinear fiber (HNLF) with a dispersion D = 2 ps/nm/km and a nonlinear coefficient γ = 20 W−1 km−1, a SESAM saturable absorber coupled through an optical circulator, a 30% output coupler, an optical etalon with an FSR of 9.2 GHz to suppress mode hopping, a LiNbO3 phase modulator as an FM mode-locker, a 40 nm optical filter, and a 1.0 m dispersion-compensating fiber (DCF). All the fibers in the cavity are polarization maintaining. The dispersion profile of the laser cavity is shown in Fig. 2. The cavity length is 8.6 m including SMF pigtails with a total length of 4.6 m, and the average dispersion is 2.8 ps/nm/km. The cavity also contains a regenerative mode-locking electrical loop comprising a high-speed photodetector (PD), a 9.2 GHz high-Q dielectric bandpass filter (BPF) with Q~1000, a phase shifter and a driver amplifier. They are used for extracting a harmonic beat signal between the longitudinal laser modes and feeding it synchronously to the modulator [11].
Fig. 1 Configuration of a 9.2 GHz regeneratively FM mode-locked fiber laser with SESAM. The abbreviations are defined in the text.
The SESAM we used is commercially available and composed of InGaAs MQW absorbers and AlAs/GaAs Bragg-reflecting mirrors attached to a GaAs substrate. Figure 3 shows the reflectivity of the SESAM, which we measured with a 500 fs pulse. The result is fitted by a curve R = exp[−α(Pp)L], where α(Pp) = α1 + α0/(1 + Pp/Psat), L ( = 1 μm) is the thickness of the MQW absorber layer, and Pp is the peak power of the incident light. The reflectivities in the linear and saturated regimes were Rlin = R(Pp<<Psat) = 58.4% and Rnl = R(Pp >>Psat) = 61.0%, respectively, and the data were fitted with α0 = 0.04 × 106 m−1, α1 = 0.50 × 106 m−1, and the saturation power Psat = 20 W. Therefore, the peak power of the pulse incident to the SESAM must be at least 20 W to induce a saturable absorption effect. When the average power is 200 mW at a repetition rate of 9.2 GHz, for example, a peak power of 20 W can be obtained with a 1 ps pulse width. This indicates that, for the efficient operation of passive mode locking even at such a high repetition rate, the pulse before the SESAM should be sufficiently narrow (less than 1 ps) with a sufficiently high power to induce saturable absorption.
To realize these conditions simultaneously, we intentionally introduced the higher-order soliton effect by installing a 0.5 m HNLF in front of the SESAM. A higher-order soliton characteristically has a very sharp peak with pedestals on the wing. However, such wing components can be efficiently absorbed by the SESAM, and only the sharp center part can survive as a steady-state single pulse with no pedestals. As a result, it is possible to maintain stable short pulse oscillation as a fundamental soliton.
3. Numerical simulations
We first undertook a numerical simulation to evaluate the relationship between the pulse width and the optical power in the cavity and to confirm the stable pulse oscillation. A numerical model corresponding to the experimental setup given by Fig. 1 is shown in Fig. 4. In the numerical model, we used the split-step Fourier method to solve the nonlinear Schrödinger equation given by
(β2: second-order dispersion, γ: nonlinear coefficient) to calculate the pulse propagation in the fiber with the dispersion profile shown in Fig. 2. The gain in the EDFA, which compensates for the cavity loss, was calculated by including gain saturation as g = g0/(1 + P/Ps) where g0 is the small-signal gain and Ps is the saturation power. The SESAM was modeled based on the fitting curve exp[−α(Pp)L] described in Sec. 2, and phase modulation was applied with a sinusoidal function at 9.2 GHz with a modulation index of 5π.Figure 5 shows the transient waveform evolution starting from the initial ASE noise seed. The waveform was observed at a location prior to the SESAM, and the average power was 150 mW. The figures on the right are an expanded view of those on the left. Pulse evolution without SESAM, i.e. under active mode locking alone, is plotted in Fig. 5(a). It is seen that the stable pulse oscillation cannot be maintained along the circulations in the cavity, because a higher-order soliton is excited continuously as the pulse propagates over many circulations. On the other hand, the result obtained with SESAM inserted in the cavity is shown in Fig. 5(b). In this case, the waveform converges to a steady state after ~400 round trips, and the peak power exceeds 20 W. This level is sufficient to induce saturable absorption at the SESAM. It can be clearly seen from the expanded view that the pedestals are successfully suppressed. The waveform and spectrum of the output pulse after chirp compensation are shown in Fig. 6(a) and 6(b), respectively, and the change in the pulse width during propagation in the cavity in the steady state is shown in Fig. 6(c). The pulse width was 560 fs before chirp compensation, and it was compressed to 500 fs after chirp compensation. The time-bandwidth product was 0.32, indicating that a transform-limited sech soliton pulse was successfully obtained. Here, the soliton order was calculated to be N = 1.7, and therefore just above the threshold (N = 1.5) of continuous higher-order soliton excitation. These results clearly indicate that SESAM can effectively remove the pedestal components on the wing while retaining the short pulse width of the main lobe in a higher-order soliton, and thus successfully suppress the continuous excitation of higher-order solitons observed in Fig. 5(a).
Fig. 5 Transient evolution of a laser pulse starting from the initial ASE noise seed (a) without SESAM and (b) with SESAM in the cavity. The figures on the right are an expanded view of those on the left.
Fig. 6 Waveform (a) and spectrum (b) of an output pulse after chirp compensation from a 9.2 GHz mode-locked fiber laser, and the change in the pulse width inside the cavity in a steady state (c).
We also studied the relationship between the pulse width and the optical power in the cavity numerically. The results with and without the SESAM are summarized in Fig. 7. The optical power is defined as the average power in front of the SESAM. The yellow region indicates the condition required for the saturable absorption to take place at the SESAM, i.e., peak power > 20 W. Without inserting the SESAM, as shown by the red curve, the pulse width is gradually shortened as the power increases and it is reduced to ~800 fs at 150 mW. However, no further narrowing occurs with higher optical power, which is because of the continuous excitation of higher-order solitons in the cavity. With the present mode locking, as shown by the blue curve, the pulse width first gradually decreases as the power increases in the same way as active mode locking, and then drops rapidly at around 120 mW, i.e., once the power reaches the yellow region. Here, the pulse through the HNLF is first compressed by the higher-order soliton effect. The pulse is then further narrowed both by the pulse shortening effect caused by saturable absorption and by the wing removal effect of a higher-order soliton at the SESAM. The pulse width was further reduced to 500 fs at below 150~200 mW without suffering from the continuous excitation of higher-order solitons in contrast to active mode locking.
Fig. 7 Relationship between pulse width and optical power in a cavity obtained by numerical simulation.
A much stronger saturable absorption effect is needed if we are to pursue the possibility of further reducing the pulse width by increasing the optical power while avoiding higher-order soliton excitation. We carried out a numerical simulation assuming that a SESAM has a stronger saturable absorption effect. Figure 8(a) shows a waveform and spectrum of an output pulse at an optical power of 280 mW assuming a higher linear absorption of α0 = 0.1 × 106 m−1 (Rlin = 55%), which is 2.5 times the actual value. It can be seen that a pedestal remains in the waveform, indicating that the saturable absorption is still insufficient to suppress the higher-order soliton excitation in a high power regime. Figure 8(b) shows the result when α0 is further increased to 0.2 × 106 m−1 (Rlin = 50%). In this case, pedestals still did not appear even when the average power was increased to 380 mW. The pulse width was then shortened to 300 fs and the spectral width was broadened to 8.9 nm, which corresponds to a time-bandwidth product of 0.33. Although the soliton order reaches N = 2.1 in this case, a nearly transform-limited sech pulse can be obtained that does not suffer from higher-order soliton excitation, due to strong saturable absorption.
Fig. 8 Waveform and spectrum of an output pulse after chirp compensation from a 9.2 GHz hybrid mode-locked fiber laser obtained by a numerical simulation assuming a strong saturable absorption in the SESAM. (a) α0 = 0.1 × 106 m−1 and the optical power is 280 mW, (b) α0 = 0.2 × 106 m−1 and the optical power is 380 mW.
Figure 9 shows the pulse width and the corresponding soliton order for various α0 values. By increasing the linear absorption to 0.4 × 106 m−1 (Rlin = 40%), the pulse width can be reduced to 200 fs with a soliton order reaching N ~2.2, and these values are limited by the gain bandwidth of EDF. These results indicate the potential of the proposed mode-locking technique for generating ultrashort transform-limited pulse train even in a higher-order soliton regime by incorporating a strong saturable absorption effect, as long as the SESAM is not damaged by the incident power.
4. Experimental results
Here we show experimental results for the mode-locked fiber laser described in Fig. 1. Figure 10 shows the measured relationship between the pulse width and the optical power. We obtained a similar result to that shown in Fig. 7, and the pulse width was reduced to 520 and 440 fs for average powers of 150 and 170 mW, respectively. These results correspond to a soliton order of N = 1.7, and the soliton period is 27 m. On the other hand, such a narrow pulse width was not obtained with active mode locking alone, due to the higher-order soliton effect remaining in the cavity without SESAM. Figure 11(a) and 11(b) show an autocorrelation waveform and an optical spectrum of the output pulse from the present mode-locked fiber laser, obtained with an average power of 150 and 170 mW, respectively. The spectral width was 4.9 and 5.8 nm, which yields a time-bandwidth product of 0.31 in both cases. This indicates that a transform-limited sech pulse was successfully generated. Figure 11(a-3) and 11(b-3) show RF spectra of the output pulse train detected with a high-speed photodetector. It contains only one spectral component at 9.2 GHz, in which the noise was suppressed to ~−80 dB. The output optical power obtained through the output coupler was 15 mW. We also carried out an experiment using a 1 m HNLF instead of a 0.5 m HNLF. In this case, the pedestal was not sufficiently suppressed due to excessive nonlinearity.
Fig. 11 Laser output pulse characteristics for average powers of 150 mW (a) and 170 mW (b). (a-1), (b-1): Autocorrelation waveform, (a-2), (b-2): optical spectrum. (a-3), (b-3): RF spectrum of the output pulse train detected with a high-speed photodetector.
To increase the output power, we moved the HNLF and SESAM after the output coupler. The average dispersion was optimized to 3.5 ps/nm/km. The laser output in this setup is shown in Fig. 12. The output power was increased to 45 mW with a pulse width of 480 fs and a time-bandwidth product of 0.31. Here, the soliton order was calculated to be N = 1.3.
Fig. 12 Laser output pulse characteristics when the HNLF and SESAM were moved to after the output coupler (a): Autocorrelation waveform, (b) optical spectrum.
5. Conclusion
We demonstrated a new mode-locked soliton laser, in which a SESAM was installed in a regeneratively FM mode-locked erbium fiber laser. A combination of higher-order soliton compression in a short piece of HNLF and saturable absorption enabled us to generate a shorter soliton pulse with no pedestals. A pulse width of 440 fs was successfully obtained at a repetition rate of 9.2 GHz and with a 15 mW output power. A 480 fs transform-limited sech pulse was also obtained at the same repetition rate with a 45 mW output power.
Funding
Japan Society for the Promotion of Science (JSPS) Grant-in-Aid for Specially Promoted Research (26000009).
References and links
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