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Abstract
We report on the first demonstration of dual-wavelength square-wave pulses in a thulium-doped fiber laser. Under appropriate cavity parameters, dual-wavelength dissipative soliton resonances (DSRs) and domain wall solitons (DWSs) are successively obtained. Meanwhile, dark pulses generation is achieved at the dual-wavelength DWSs region due to the overlap of the two domain wall pulses. The fiber-based Lyot filter, conducted by inserting PMF between an in-line PBS and a PD-ISO, facilitates the generation of dual-wavelength operation. The polarization-resolved investigation suggests that the cross coupling between two orthogonal polarization components in the high nonlinear fiber plays an important role in the square-wave pulses formation. The investigation may be helpful for further understanding the square-wave pulse formation and has potential in application filed of multi-wavelength pulsed fiber lasers.
© 2017 Optical Society of America
1. Introduction
Mode-locked thulium-doped fiber lasers operating in the eye-safe spectral region of 2-μm continue to attract substantial attention as promising sources in various applications such as eye-safe surgery, mid-infrared supercontinuum generation, metrology, and remote sensing [1–4]. On the other hand, optical pulse shaping [5–8] is a rich and fascinating subject of fiber laser physics due to applications in the fields of optical communications, material processing, and ultrafast optics. Recently, the generation of square-wave pulses in nanosecond time scales becomes a hot topic exhibiting potential applications in developing all-optical square-wave clocks [9], laser micromachining [10], and optical sensing [11]. Two novel concepts of square-wave pulse formation mechanism have been proposed in recent years, known as the dissipative soliton resonances (DSRs) [12–24] and the domain-wall solitons (DWSs) [25–37].
The DSRs region is the most widely investigated square-wave pulse formation mechanism in the past decade, since first theoretically proposed by N. Akhmediev et al. in 2008 [12]. The DSRs region features that the width and energy of wave-breaking-free square pulse monotonously increase with the increasing pumping power while maintaining constant amplitude, circumventing the limitation of the soliton area theorem [12–14]. The idea of high-energy pulse generation in DSRs region has inspired extensive researches, leading to an outburst of publications realized with appropriate set of resonator parameters in all major fiber lasers (i.e., Yb-, Er-, and Tm-doped fiber lasers), implemented with various mode-locking techniques including nonlinear polarization rotation (NPR), nonlinear optical loop mirror (NOLM), nonlinear amplifier loop mirror (NALM), and real saturable absorber (SA) [15–24]. Up to now, most of the DSRs researches focus on high-energy pulse generation operating at a single wavelength. Despite the few reported works on dual-wavelength DSRs pulse generation at 1-μm and 1.5-μm bands [16–20], there has not been to date any report of dual-wavelength DSRs at the 2-μm band. Considering the important applications of the multi-wavelength pulsed fiber lasers in optical sensing, optical signal processing, wavelength division multiplexing communication, and precision spectroscopy, it would be interesting to give more insight into the dual-wavelength DSRs phenomenon at the 2-μm wavelength region.
Another square-wave pulse formation mechanism demonstrated more recently is the domain-wall solitons [25–37]. Polarization domain-wall solitons (PDWSs) was first theoretically proposed by M. Haelterman et al. in a dispersive Kerr medium [25,26]. The PDWSs phenomenon originates from the formation of polarization domains which was theoretically predicted by V. E. Zakharov et al. in Kerr medium [27] in analog to the formation of the magnetic domains. PDWSs are stable localized nonlinear structures separating adjacent domains of different polarization eigenstates of dispersive Kerr medium [28-29]. It was further discovered that the mutual interaction of two optical waves at different wavelengths with the same polarization could also lead to the formation of the DWSs [30]. The DWSs phenomenon in fiber laser systems has been attracting increasing interest in the past few years [28, 29, 31–37], since the first successful observation in an erbium-doped fiber laser by H. Zhang et al. [31]. In their work, the DWSs were formed through cross coupling between two orthogonal polarization light components. Both dark pulse and square-wave pulse generation have been achieved in the DWSs investigations [28, 29, 31–37]. However, the DWSs research in fiber laser systems is insufficient with no experimental observation of the DWSs in fiber lasers at 2-μm.
Given that the investigation on square-wave pulse formation mechanism is deficient at 2-μm, it would be beneficial to make further research at this wavelength region, considering also the related parameter changes - lower effective nonlinearity and larger anomalous dispersion. In this paper, we report on the first investigation of dual-wavelength DSRs and DWSs phenomenon in a thulium-doped fiber laser. Dark pulses are also obtained at the dual-wavelength DWSs region. We provide polarization-resolved study of the pulse dynamics, and our results indicate that the cross coupling between the two orthogonal polarization components plays an important role in square-wave pulses formation.
2. Experimental setup
The fiber laser for square-wave pulse generation is schematically shown in Fig. 1. It has a ring cavity comprising ~2.3-m thulium-doped fiber (TDF) with a group velocity dispersion (GVD) parameter of −0.073 ps2/m, ~13-m single mode fiber (SMF) with a GVD parameter of −0.067 ps2/m, and ~20-m high nonlinear fiber (HNLF) with a GVD parameter of −0.020 ps2/m. The HNLF is utilized to enhance the nonlinear effects in the cavity. The HNLF exhibits nonlinear coefficient of 11.68 W−1km−1, zero dispersion wavelength of 1550 nm, respectively. A cw 1550 nm laser diode (LD) seeded erbium-doped fiber amplifier (EDFA) serves as the pump source and is coupled into the cavity with a 1550/2000 nm wavelength division multiplexer (WDM). A fiber-based Lyot comb filter is conducted by inserting ~0.45-m polarization-maintaining fiber (PMF) (Nufern PM-1950, the beat length specified as ≤5.2 mm) between an in-line polarizing beam splitter (PBS) and a polarization-dependent isolator (PD-ISO) [38]. The PM fiber output of the PBS is spliced to the PMF with the angle between the two axes set to be 45°. The channel spacing between the two successive transmittance wavelengths, estimated to be about ~20 nm, is given by Δλ = λ2/(ΔnL), where Δn is the birefringence of the PMF, λ is the wavelength and L is the length of the PMF. The 50:50 output is measured by an optical spectrum analyzer (Yokogawa AQ6375) with 0.05 nm resolution, a 1 GHz photodetector recorded by a 2 GHz oscilloscope (Agilent Infiniium DSO80204B), a second-harmonic autocorrelator (FR-103XL), and a radio frequency (RF) signal analyzer (Agilent N9020 A).
Fig. 1 Scheme of the experimental setup. OC: optical coupler; WDM: wavelength division multiplexer; PC: polarization controller; PD-ISO: polarization-dependent isolator; TDF: thulium-doped fiber; HNLF: high nonlinear fiber; SMF: single mode fiber; PMF: polarization-maintaining fiber.
3. Experimental results and discussion
3.1 Dual-wavelength DSRs phenomenon
Stable conventional mode-locking is not observed, due to the high nonlinearity of the HNLF, leading to large nonlinear phase shift and intense pulse interaction. By increasing the pumping power to 1.0 W while adjusting the PCs in the cavity, the mode-locked dual-wavelength square-wave pulses can be directly obtained. As depicted in Fig. 2(a), the spectrum exhibits two spectral humps centered at 1888.1 nm and 1927.6 nm, nearly twice of the channel spacing of the Lyot filter. The corresponding 3-dB spectral bandwidths are 3.11 nm and 3.28 nm, respectively. The uniform pulse train is shown in Fig. 2(b) with a round-trip time of 170.9 ns. To give more insight into the square-wave pulses, we further increase the pumping power with fixed PCs setting. The pulse characteristics are measured under different pumping power. As shown in Fig. 3(b), the duration of the square-wave pulses broadens with the increasing pumping power while the peak power of the pulses almost keeps constant. Despite of the variation of temporal trace, the corresponding spectrum under different pumping power remains almost invariable except the slightly increasing spectral intensity. These characteristics are typical of the DSRs operation. Average output power and pulse duration are measured versus the pumping power. The graphs depicted in Fig. 4 confirm that the average output power, pulse energy and pulse duration almost linearly increase when the pumping power is up to 2.2 W, the upper limit currently linked to the maximum output power of the EDFA. The pulse duration increases from 4.2 ns to 15.7 ns when the pumping power increases from 1.1 W to 2.2 W. Correspondingly, the average output power monotonically increases from 14.8 mW to 47.75 mW with the increase of the pumping power. Considering the repetition frequency of 5.854 MHz, the maximum output pulse energy is calculated to be 8.157 nJ under the maximum available pumping power of 2.2 W. The peak power is also plotted in function of the pumping power in Fig. 4(c). The peak power remains at a comparable level, and reaches a maximum of 0.42 W, caused by the effect of peak power clamping (PPC) [21, 39, 40]. The RF spectrum characteristics of the output pulses are also analyzed. The measurements registered at the maximum pumping power are depicted in Fig. 4. The resolution bandwidth of the RF spectrum is 10 Hz. The signal to noise ratio (SNR) is 47.7 dB at the fundamental cavity frequency of 5.854 MHz, indicating high stability. Another feature of the DSRs operation is the amplitude envelope modulation exerting in the recorded RF spectrum for a wider span. The envelope modulation period originates from the duration of the generated square-wave pulses, and decreases with the increase of the pulse duration. As shown in Fig. 4(d), under the maximum pumping power of 2.2 W, the envelope modulation period is about 0.064 GHz, inversely proportional to the pulse duration of 15.7 ns.
Fig. 2 Dual-wavelength DSRs operation for the pumping power of 1.1 W. (a) Spectrum; (b) corresponding pulse train.
Fig. 3 Dual-wavelength DSRs operation under different pumping power. (a) Spectrum; (b) corresponding temporal trace.
Fig. 4 Dual-wavelength DSRs operation. (a) Average output power and pulse energy in function of pumping power; (b) RF spectrum over a 10 kHz span at the fundamental repetition frequency for the maximum pumping power of 2.2 W (inset: autocorrelation trace for a 160 ps scan range); (c) pulse duration and peak power in function of pumping power; (d) RF spectrum over a 0.4 GHz span.
Given appropriate conditions, the generation of noise-like pulse (NLP) mode-locking can also lead to noise-like square-wave mode-locked pulses [41]. To further distinguish the generated DSRs operation from the NLP feature [24], the autocorrelation trace is also measured over a 160-ps span, shown in inset of Fig. 4(b). The NLP-characteristic of narrow coherent peak upon wide pedestal is absent in our case, confirming the pure DSR mode-locking operation.
To further characterize the dual-wavelength DSRs operation, an extra-cavity PBS is employed to achieve polarization-resolved measurement. Figure 5 shows the laser emission measured along the two orthogonal polarization axes of the PBS. The spectrum evolution for each polarization direction are shown in Figs. 5(a) and 5(c). Laser emissions along the two orthogonal polarization axes have different central wavelengths, indicating incoherent coupling between the two polarization components.
Fig. 5 Polarization-resolved measurement of dual-wavelength DSRs operation. (a) Spectrum of the horizontal axis; (b) corresponding temporal trace of the horizontal axis; (c) spectrum of the vertical axis; (d) corresponding temporal trace of the vertical axis.
As depicted in Figs. 5(b) and 5(d), the pulse profiles along the two polarization axes broaden with the increase of pumping power, with clamped peak power. Figure 6 presents the pulse duration and relatively peak power plotted in function of the pumping power. When the pumping power increases from 1.1 W to 2.2 W, the pulse duration of the horizontal axis increases from 3.55 ns to 13.8 ns while the pulse duration of the vertical axis increases from 2.68 ns to 10.9 ns. The relative peak powers along the two polarization axes remain at a comparable level.
Fig. 6 Polarization-resolved measurement of dual-wavelength DSRs operation. (a) Pulse duration plotted in function of pumping power; (b) relatively peak power plotted in function of pumping power.
The wavelength of the dual-wavelength DSRs can be shifted by adjusting the PCs. In general, due to the GVD of the cavity, two pulse trains at different central wavelengths possess different group velocities, leading to two different fundamental repetition rates on the RF spectrum [42]. However, in our case the dual-wavelength pulses trap each other, and propagate as a unit and coexist in the cavity, which is confirmed by the RF spectrum with only one fundamental repetition rate. The observation indicates that the dual-wavelength pulses are group velocity locked (GVL). Such phenomenon has been previously observed in dual-wavelength DSRs operation but no physical explanation was proposed [16–20]. As discussed in [43] by C. R. Menyuk et al., two orthogonally polarized pulses can trap each other through cross-phase modulation, leading to single entity propagating in the fibers. Given the strong nonlinear effects in the long HNLF, the formation of dual-wavelength DSRs could be related to the cross coupling between the two different wavelength beams along orthogonal polarization axes in the cavity.
3.2 Dual-wavelength DWSs phenomenon
Interestingly, by further changing the cavity parameters of pumping power and PCs states, another fascinating square-wave pulse formation is also obtained, known as the DWSs.
Figure 7 presents the dual-wavelength DWSs operation at the pumping power 1.31 W. Under the same pumping power, the average output power of the DWSs remains comparable to that of the DSRs operation, while the peak amplitude is an order of magnitude smaller. This feature is very similar to the early investigations of DWSs in [28-29, 32–37], where the pulsations are surrounded by an important noise level. As depicted in Fig. 7(a), the two orthogonal polarization components have different central wavelengths of 1880.2 nm and 1900.8 nm, indicating the incoherent coupling between two polarization components. The corresponding 3-dB spectral bandwidths are 0.46 nm and 0.42 nm, respectively. Figure 7(b) shows the measured initial total laser emission and polarization-resolved pulse trains after the PBS. It clearly shows that along two polarization axes, the laser emits square-wave pulse trains with different pulse durations and amplitudes. Each of the two pulse trains owns the same period of 170.8 ns, corresponding to the fundamental cavity frequency. Since the total laser emission is the combination of the two domain walls, with appropriate temporal interval between the two domain wall pulses, the dark pulse trains can be achieved at the region where the domains switch, which is depicted in Fig. 7(b). The duration of the dark pulse trains is 11.8 ns. The RF spectrum is also measured. The RF spectrum of the total laser emission is shown in Figs. 7(c) and 7(d). The spectrum is regular for a span of 1 GHz, limited by the bandwidth of our detector. As depicted in Fig. 7(d) with a resolution bandwidth of 10 Hz, the SNR is 36 dB at the fundamental repetition rate of 5.854 MHz, indicating that the operation is not as stable as the conventional mode-locking, whose SNR is usually higher than 40 dB. The single fundamental repetition rate suggests that the dual-wavelength domain wall pulses form a single entity propagating in the cavity, due to the pulse trapping which originates from the cross-coupling between two polarization components in the HNLF.
Fig. 7 Dual-wavelength DWSs operation. (a) Polarization-resolved spectrum of the two orthogonal polarization axes; (b) DW dark pulses at the initial laser output and the domains of the two orthogonal polarization axes; (c) RF spectrum over a 1 GHz span at the initial laser output; (d) RF spectrum over a 10 kHz span at the fundamental repetition frequency at the initial laser output.
In order to further investigate the characteristics of the dual-wavelength DWSs, the cavity parameters are carefully adjusted. The pulse durations and amplitudes of the two DWSs, as well as the temporal interval between the two DWSs can be changed with the variation of the cavity parameters. Provided that the two DWSs overlap each other, thus the total laser emission can be changed. As shown from Figs. 8-10, different types of dual-wavelength DWSs operation are observed. Figure 8 shows the dual-wavelength DWSs at the pumping power of 1.34 W. The two orthogonal polarization components have different central wavelengths of 1894.4 nm and 1931.7 nm with the corresponding 3-dB spectral bandwidths of 0.59 nm and 0.31 nm, respectively. Figure 8(b) presents the dark-bright pulse pairs with a period of 170.8 ns. The pulse trains of the horizontal and vertical axes are bright and dark pulses, respectively. As shown in Figs. 8(c) and 8(d), the RF spectrum of the total laser emission is regular for a span of 1 GHz and the SNR, measured from the noise sidebands just around the fundamental repetition rate of 5.854 MHz, is about 34 dB.
Fig. 8 Dual-wavelength DWSs operation. (a) Polarization-resolved spectrum of the two orthogonal polarization axes; (b) DW bright-dark pulse pairs at the initial laser output and the domains of the two orthogonal polarization axes; (c) RF spectrum over a 1 GHz span at the initial laser output; (d) RF spectrum over a 10 kHz span at the fundamental repetition frequency at the initial laser output.
Fig. 9 Dual-wavelength DWSs operation. (a) Polarization-resolved spectrum of the two orthogonal polarization axes; (b) DW bright-dark pulse pairs at the initial laser output and the domains of the two orthogonal polarization axes; (c) RF spectrum over a 1 GHz span at the initial laser output; (d) RF spectrum over a 10 kHz span at the fundamental repetition frequency at the initial laser output.
Fig. 10 Dual-wavelength DWSs operation. (a) Polarization-resolved spectrum of the two orthogonal polarization axes; (b) DW bright-dark pulse pairs at the initial laser output and the domains of the two orthogonal polarization axes; (c) details of the DW bright-dark pulse pairs; (d) RF spectrum over a 10 kHz span at the fundamental repetition frequency at the initial laser output; (e) RF spectrum over a 1 GHz span at the initial laser output.
In Fig. 9, by further carefully adjusting the PC settings at the same pumping power of 1.34 W, another kind of dual-wavelength DWSs, namely bright-dark pulse pairs are obtained through the incoherent coupling between the orthogonal polarization components. The central wavelengths of the two orthogonal polarization components are 1893.8 nm and 1931.3 nm, respectively. The two orthogonal polarization components have different 3-dB spectral bandwidths of 0.62 nm and 0.46 nm. The RF spectrum of the total laser emission is also depicted in Fig. 9(d), with 31 dB SNR, calculated from the noise sidebands near the fundamental cavity frequency of 5.854 MHz. The SNR indicates that the short-term stability of this operation is lower than conventional mode-locking.
Very interestingly, with appropriate PCs state, dual-wavelength DWSs composed of two domains of quasi-square pulse domain and soliton bunching domain can be observed at the pumping power of 1.37 W. As shown in Fig. 10, the horizontal component of soliton bunching domain corresponds to the longer wavelength centered at 1898.1 nm with 3-dB bandwidth of 2.63 nm, while the vertical component of quasi-square pulse domain corresponds to the shorter wavelength centered at 1861.6 nm with 3-dB bandwidth of 0.55 nm. The two domains exhibit the same period of 170.8 ns, implying that the orthogonally polarized components are group velocity locked, which is also confirmed by the RF spectrum in Fig. 10(d) with single fundamental repetition rate. It is important to note that the RF spectrum over 1 GHz span exhibits a localized intensity peak at the frequency of 0.556 GHz, corresponding to the inner sub-pulse separation of the soliton bunching domain.
3.3 Discussion
The combination of Lyot filter and HNLF plays an important role in the generation of dual-wavelength DSRs and DWSs. The fiber-based Lyot filter, conducted by inserting PMF between an in-line PBS and a PD-ISO, serves as the comb filter, facilitating dual-wavelength operation. By changing the cavity parameters of pumping power and PCs settings, the strong cross coupling between the two orthogonal polarization components of emission propagating in the HNLF is adjusted. Under appropriate cavity parameters, two different square-wave pulse formation mechanisms of DSRs and DWSs can be successively achieved in same cavity. Moreover, the polarization-resolved measurement shows that the two orthogonal polarization components exhibit different wavelength distribution. This observation, in conjunction with the single fundamental repetition rate of the total laser emission in the RF spectrum, suggests that the two orthogonal polarization components are in fact group velocity locked.
Although in fiber lasers without Lyot filter, it has been reported that dual-wavelength DSRs [16–20] and DWSs [31, 32] can be observed, in our experiments, similar results of dual-wavelength DSRs and DWSs are not observed without the Lyot filter, indicating the importance of Lyot filter to generate dual-wavelength square-wave pulses in a more controllable method.
The long-term stabilities of the two kinds of square-wave pulses operations have also been measured. Both the DSRs and the DWSs operations can sustain for several hours without disturbance. It is worth to note that high speed oscilloscope gives further insight into the internal structure of the square-wave pulses dynamics, which will be conducted in our further investigations.
4. Conclusion
In conclusion, we experimentally demonstrate the generation of dual-wavelength square-wave pulses in a thulium-doped fiber laser. Under appropriate operating parameters, dual-wavelength DSRs and DWSs formation are obtained, attributed to the enhancement of cross coupling between two orthogonal polarization components in the ~20-m HNLF. Our investigation could further enhance the understanding of the square-wave pulse formation mechanism and has potential in application filed of multi-wavelength pulsed fiber lasers.
Funding
This research is supported by National Natural Science Foundation of China (NSFC) (61377039, 61575106, 51527901).
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