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Abstract
Relying on the nonlinear multimode interference in multimode fibers and the nonlinear polarization rotation, these two mode-locked techniques are combined in our proposed fiber laser. Stable optical soliton and multi-pulse regimes with a constant frequency of 11.44 MHz have been generated experimentally. Through altering intra-cavity conditions, bound-state pulses with diverse properties are observed. To the best of our knowledge, the obtained bound-state pulse constituted by more than thirty sub-pulses is achieved for the first time. Moreover, the center wavelength of bound-state pulse could be switched in a certain range covering the entire C band.
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1. Introduction
Passively mode-locked fiber lasers have been widely researched for obtaining different types of pulse, including conventional soliton [1], dispersion management soliton [2], dissipative soliton [3–5], dissipative soliton resonance [6], and self-similar pulse [7]. With excessive nonlinear phase shifts in the laser cavity, single soliton tends to evolve into multiple-soliton state, among which bound-state pulse is of great significance for both academic and industry. In recent decades, bound-state pulse has attracted much attention owing to its wide applications in the fields of high-speed optical communication system and advanced time-resolved spectroscopy [8].
Determined by the energy and momentum balanced equation [9], the temporal interval between adjacent pulses has a major influence on the formation of bound-state pulse. Accordingly, bound-state pulse could be divided into loosely bound state and tightly bound state [5]. Dispersive waves based on intra-cavity periodic perturbations and long-range interactions among pulses are critical for establishing loosely bound state [10]. For tightly bound state, its formation is mainly attributed to direct interactions between closely spaced pulses [11]. Heretofore, simple-structure bound states have been generated by various mode-locked schemes including nonlinear polarization rotation (NPR), nonlinear optical loop mirror (NOLM) as artificial saturable absorbers (SAs) and carbon nanotube, graphene, topological insulators (TIs) as real SAs [12–15]. Meanwhile, hybrid mode-locked schemes are also employed in ultrashort pulse fiber lasers [16,17]. However, bound state composed of numerous pulses with complex inner structure is still lack of research. Therefore, the exploration on abundant pulse dynamics within bound state is urgent to be further boosted.
Benefiting from the compactness and high coupling efficiency, the all-fiber structure SA based on nonlinear multimode interference (NL-MMI) has become an excellent candidate in passively mode-locked fiber lasers [18–20]. Theoretical and experimental studies have been reported since the first work on utilizing a segment of graded-index multimode fiber (GIMF) between single mode fiber (SMF) as SA proposed by Nazemosadat et al. [20]. Although designs and performances of the all-fiber structure SA have been improved, it is still challenging to generate mode-locked pulse with versatile properties via this type of SA.
In this work, we report on a multi-pulse bound state with switchable center wavelength in a fiber laser mode-locked by the NL-MMI and NPR mechanism. Pulse characteristics are manageable depending on the intra-cavity conditions. Switchable center wavelength covering entire C band and diversiform shapes of spectrum are realized due to the induced wavelength-dependent loss and spectral filtering effect. Except for the bound-state pulse, exaggerated nonlinearity under a high pumping level favors the generation of noise like pulse (NLP). The proposed fiber laser with different types of lasing output may have potential application in ultra-high-capacity optical communications, high-resolution femtosecond spectroscopy and enrich the investigation of nonlinear soliton dynamics in ultrashort pulse fiber lasers [21–23].
2. Experimental setup
As plotted in Fig. 1, the proposed SA is constituted by a segment of GIMF (Yangtze Optical Fiber, length 20 cm, core/cladding 62.5/125 µm), a segment of step-index multimode fiber (SIMF) (Yangtze Optical Fiber, length 395 µm, core/cladding 105 /125 µm) and a segment of GIMF (Yangtze Optical Fiber, length 20 cm, core/cladding 50/125 µm). The transmittance spectrum of artificial SA measured by a broadband source is also provided. One can find that the transmittance is basically constant from 1500 to 1600 nm, which denotes that the transmittance has little dependence on the operating wavelength [24]. The SIMF inserted in the middle of two segments of GIMF contributes to exciting more high-order modes and relieving the limitation on the length of GIMF [25]. Moreover, the symmetrical-structure SA attributes to a high coupling efficiency and a remarkable long-term stability of lasing output [24].
Fig. 1. Schematic diagram of the proposed GIMF-SIMF-GIMF mode locker and optical transmittance spectrum of artificial SA.
The configuration of fiber laser is schematically described in Fig. 2. A 976 nm laser diode (LD) with a maximum power of 500 mW serves as a pump source which is injected into the ring cavity through a 980/1550 nm wavelength division multiplexer (WDM). A piece of erbium-doped fiber (EDF, length 4.5 m) with the group velocity delay of −16.3 ps/nm/km at 1550 nm serves as the gain medium for providing sufficient gain and acquiring a stable output. Next to EDF, a 90:10 optical coupler (OC) extracts ∼ 10% optical power from the cavity. The all-fiber structure SA (length 0.4 m) is fused after OC for mode-locking. Two polarization controllers (PCs) as well as a polarization dependent isolator (PD-ISO) are applied to manage the intra-cavity birefringence and achieve laser unidirectional operation. Simultaneously, NPR mechanism is also executed based on this combination. All devices are connected by SMF with the group velocity delay of 18 ps/nm/km at 1550 nm and the total length of ring cavity is ∼ 17.7 m. Accordingly, the fundamental repetition rate is ∼ 11.44 MHz and the net dispersion is estimated to be −0.16 ps2 in anomalous dispersion region. The optical spectrum is measured by an optical spectrum analyzer (OSA, AQ6370C, resolution: 0.02 nm). The pulse train is detected by a high-speed photodetector (Newport 818-BB-35F, 12.5 GHz) and monitored by an oscilloscope (InfiniiVision DSOX3024 T, 200 MHz). The radio frequency (RF) spectrum and autocorrelation (AC) trace are measured by a signal analyzer (CXA Signal Analyzer N9000A, 9 kHz-7.5 GHz) and a commercial autocorrelator (FR-103XL).
Fig. 2. Schematic graph of the mode-locked laser oscillator. LD: laser diode; WDM: wavelength-division multiplexer; EDF: erbium-doped fiber; OC: optical coupler; AF-SA: all-fiber saturable absorber; PC: polarization controller; PD-ISO: polarization-dependent isolator; SMF: single mode fiber.
Supported by the proposed all-fiber structure SA, stable mode-locked pulse and bound state have been found and discussed in our previous work [24,26]. However, due to the lack of a wavelength-tunable device inside the cavity, the operating wavelength is frequently located at ∼ 1560 nm. As a consequence, we employ the dual mode-locked mechanism in this work. The dual mode-locked mechanism is applied in fiber lasers where one mode-locker is utilized for initiating mode-locking, the other one is used to regulate properties of mode-locked pulses [27]. During the experiment, it has been found that the designed all-fiber structure SA is inclined to facilitate the generation of bound-state pulse. Specifically, with the accumulation of nonlinearity inside the cavity, a single pulse would be continuously narrowed and split into multiple pulses due to the pulse shaping and peak power clamping effects originated from the all-fiber structure SA [26]. Subsequently, bound-state pulse could be formed and delivered stably as a unit in virtue of intensive nonlinear interactions between closely spaced pulses [28]. In the meantime, NPR mechanism can not only reduce the power threshold for mode-locking but also induce wavelength-dependent loss to achieve spectral filtering [29]. Through manipulating intra-cavity birefringence, the switching of center wavelength could be fulfilled.
3. Experimental results and discussions
Similar to most of mode-locked fiber lasers, typical continuous wave (CW) emission appears initially at a low pump level. Once the pump power exceeds the threshold of 67 mW for mode locking, paddles of PCs are rotated precisely to trigger the mode-locked operation, enabling the laser to switch the operation from CW emission to mode-locked state. Figure 3 reveals a representative mode-locked state at the pump power of 156 mW. Equally spaced pulses in Fig. 3(a) possess the same intensity and the separation between adjacent pulses is about 87.4 ns, corresponding to the fundamental repetition rate of 11.44 MHz. The spectrum in Fig. 3(b) has a center wavelength of 1561.9 nm and a 3-dB bandwidth of 6.0 nm. The formation of an optical soliton is confirmed by four pairs of Kelly sideband distributed on both sides of the center wavelength. A slight asymmetry of those sidebands is caused by the unflatness of gain spectrum. The AC trace of pulse is measured and plotted in Fig. 3(c). Since the center peak of AC trace has a full width at half maximum (FWHM) of 1.07 ps, the pulse duration is estimated to be 0.69 ps assuming a Sech2-shape profile. The calculated time-bandwidth product (TBP) is 0.49. This value is larger than the transform limitation of 0.315 for a Sech2-shape pulse, which means that the soliton is slightly chirped. The local RF spectrum over a range of 15 MHz with a resolution bandwidth of 2 kHz in Fig. 3(d) shows the repetition frequency at 11.44 MHz with a signal to noise ratio (SNR) of 51 dB. The inset of Fig. 3(d) (a range of 500 MHz with a resolution bandwidth of 100 kHz) denotes that the obtained pulse train is relatively stable.
Fig. 3. Features of conventional soliton. (a) Pulse train; (b) Optical spectrum; (c) Autocorrelation trace; (d) RF spectrum (inset: the RF spectrum with a range of 500 MHz).
Next, as we increase the pump power to 232 mW for arousing pulse splitting phenomenon, the fiber laser tends to operate in the multi-pulse regime. Rotating two PCs to adjust the mode-locked condition in the meantime, bound-state pulses are observed immediately. As shown in Fig. 4(b), the spectrum with a 3-dB bandwidth of 5.2 nm locates at 1527.9 nm. Apparently, regular interference fringes in the spectrum suggests that the mode-locked pulse belongs to bound-state pulse. The corresponding AC trace in Fig. 4(a) exhibits twenty-seven peaks symmetrically distributed which basically occupy the entire detection window of the autocorrelator. From the AC trace, it could be inferred that a temporal interval between sub-pulses within the bound-state pulse is 6.3 ps. According to the Fourier transform theory [30], the 6.3-ps interval corresponds to the 1.24-nm peak-to-peak spacing in the spectrum (centered at 1527.9 nm), which is rather coincident with the observational result in Fig. 4(c). Since the intensities of sub-solitons and phase relationship between sub-solitons within the multi-pulse bound state may not be precisely consistent, extra spectral modulations may exist [31]. The nonlinear decline of peak intensity in the autocorrelation trace is due to the difference of sub-soliton intensity within the bound state [32,33]. Figure 4(d) shows the stable RF feature which is similar to that of the fundamental mode-locking.
Fig. 4. Features of bound-state pulse at 1527.9 nm. (a) Autocorrelation trace; (b) Optical spectrum; (c) Zoomed-in optical spectrum at 1527.9 nm; (d) RF spectrum (inset: the RF spectrum with a range of 170 MHz).
For further investigating the impact of spectral filtering effect on pulse property, the pump power is fixed at 232 mW and the intra-cavity birefringence is adjusted for acquiring pulse evolutions. A redshift on center wavelength of mode-locked pulse and the formation of versatile bound-state pulses are found subsequently. In Fig. 5(b), due to a large intra-cavity gain, it can be observed that intensive CWs locate at ∼ 1530 nm. In this scenario, the center wavelength locates at 1546.7 nm, which implies a coexistence of CWs and mode-locked pulse in the cavity. Limited by the detection range of autocorrelator (195 ps), only one-sided AC trace is presented in Fig. 5(a). It reveals a temporal interval of 16.6 ps and twelve peaks within the detection window. (A temporal interval is calculated by difference between the maximum and minimum delays divided by the total number of peak interval.) The interval can match with the peak-to-peak spacing of 0.48 nm in Fig. 5(c). It is worthy of mentioning that except for those twelve peaks, undetected peaks may exist outside the detection window, implying that the bound-state pulse is constituted by more than twelve sub-pulses. As expected, by rotating the micrometer on the autocorrelator for shifting the detection window, more peaks with lower intensities appear. The number of peaks is fourteen totally, which manifests the bound-state pulse is composed of fourteen sub-pulses. At this point, a 14th-order bound-state pulse is obtained. The output power is 1.36 mW. From Fig. 5(e), it is clear that after two PCs are slightly rotated, the center wavelength of lasing emission could be further shifted towards longer wavelength as the change of NPR transmittance curve. The center wavelength is 1552.2 nm and the 3-dB bandwidth is 4.2 nm seen from Fig. 5(e). The corresponding AC trace in Fig. 5(d) has nine peaks. The interval of 20.6 ps matches with the spectral fringe period of 0.39 nm according to the Fourier transform theory. The output power is 1.42 mW. The center wavelength can reach 1557.0 nm with a 3-dB bandwidth of 4.8 nm as depicted in Fig. 5(h). The measured AC trace in Fig. 5(g) presents eight peaks within the detection window. Accordingly, we consider that the bound-state pulse is composed of eight sub-pulses. The temporal interval is 17.5 ps, corresponding to the spectral peak-to-peak spacing of 0.46 nm displayed in Fig. 5(i). The output power is 1.40 mW. The spectrum and AC trace of 12th-order bound state centered at 1566.8 nm are depicted on Fig. 5(k) and Fig. 5(j). The temporal interval of 15.5 ps corresponds to a spectral peak-to-peak spacing of 0.53 nm theoretically, which is in agreement with the observational result in Fig. 5(l). The output power is 1.51 mW. Under the same pump power, the output powers of bound states show differences as a result of the variation of intra-cavity loss caused by the adjustments of PCs. Particularly, as the variation of mode-locked condition, bound-state pulse would evolve into NLP regime. A typical result in Fig. 6(a) shows that instead of regular interference fringes, the spectrum has a smooth and broad profile whose center wavelength is 1530.0 nm with a 3-dB bandwidth of 7.1 nm. The AC trace in Fig. 6(b) displays a double-scale structure where a narrow spike rides on top of a wide pedestal. Without doubt, these results are representative properties of NLP. The rotation of PC results in a variation of the wavelength-dependent transmittance curve, which has an influence on the nonlinear loss [34,35]. Depending on the intra-cavity gain and loss, the wavelength-switchable behavior occurs even without an insertion of any optical filtering device. In addition, the accumulation of nonlinear phase shifts and pulse splitting are correlated with the interval and number of sub-pulses due to the variations of nonlinear gain and loss [36,37]. With a modification of intra-cavity gain and loss, the wave breaking and multi-pulse interactions may aggravate. Newly formed ultrashort sub-pulses could bunch tightly as an NLP through nonlinear forces among each other. Therefore, the pulse regime could be switched from bound-state pulse to NLP.
Fig. 5. Measured autocorrelation traces (a, d, g, j), optical spectra (b, e, h, k) and zoomed-in optical spectra (c, f, i, l) of bound-state pulse under 232 mW.
We also explore the influence of pumping condition on properties of bound-state pulse. Enlarging the pump power to 312 mW, Fig. 7 displays measured spectra and AC traces of bound-state pulses with different intra-cavity polarization states. Obviously, bound states with more sub-pulses are generated and the operating wavelength covers from 1528.8 nm to 1570.0 nm. Centered at 1528.8 nm, the bound-state pulse composed of more than thirty sub-pulses could be verified by Fig. 7(a) and Fig. 7(b). The peak-to-peak spacing of 1.19 nm in Fig. 7(c) corresponds to the temporal interval of 6.7 ps in Fig. 7(a). A total of thirty-three peaks can be distinguished after the shift of detection window. Next, the spectrum centered at 1561.4 nm with a 3-dB bandwidth of 6.8 nm is depicted in Fig. 7(e). The AC trace in Fig. 7(d) presents fifteen peaks within the detection window, indicating that a 15th-order bound-state pulse is obtained. The temporal interval between sub-pulses is 9.7 ps, corresponding to the peak-to-peak spacing of 0.85 nm in Fig. 7(f) uniformly. At near 1569.9 nm, the 18th-order bound state could be formed after the intra-cavity birefringence is finely adjusted. From the AC trace in Fig. 7(g), eighteen peaks are equally spaced distributed with an interval of 10.1 ps, which matches with the spectral peak-to-peak spacing of 0.84 nm in Fig. 7(i). We also notice that even in the vicinity of the same wavelength, the number of sub-pulse contained by a bound-state pulse is adjustable. As shown in Fig. 7(k), the center wavelength remains at 1570.0 nm while the spectral profile shows much difference. Figure 7(j) exhibits nine peaks with an interval of 19.5 ps, corresponding to the spectral spacing of 0.44 nm in Fig. 7(l). We think that the consecutive spectral redshift phenomena could be attributed to the self-phase modulation under the gain saturation induced refractive index change and wavelength selection of intra-cavity spectral filter. Since the CW components play a main role in determining the properties of bound state [38,39], one can find in spectra of Fig. 5 and Fig. 7 that the intensities and frequency offsets from center wavelengths of different CW components are not consistent, which leads to different intervals of sub-solitons in each bound state.
Fig. 7. Measured autocorrelation traces (a, d, g, j), optical spectra (b, e, h, k) and zoomed-in optical spectra (c, f, i, l) of bound-state pulse under 312 mW.
Properties of bound-state pulse from different mode-locked fiber lasers are presented in Table 1. It can be found that the obtained pulse in this work possesses the largest number of sub-pulses with a wide range of center wavelength. Meanwhile, the bound-state pulse with more than thirty sub-pulses is achievable under a low pumping level.
Table 1. Properties of bound-state pulse from different mode-locked fiber lasers
The intra-cavity dispersion and nonlinearity have essential influences on pulse properties. More specifically, from the average soliton model, the area theorem can be described by Eq. (1) [1]:
The transmittance function of NPR is expressed by Eq. (3) [44]:
According to our experiment, wavelength-switchable and multi-pulse bound states are achieved by the dual mode-locked mechanism. In previous researches [2341–43], the number of sub-pulse within a bound state is generally less than twenty. In this work however, a bound-state pulse with more than thirty sub-pulses is observed for the first time. The pulse width is effectively compressed as a result of the combination effect of NL-MMI and NPR mechanism. Through selecting appropriate broadband devices and decreasing the fusion loss between different types of fiber, intra-cavity loss is manipulated at a low level, which is beneficial to the generation of bound state with more sub-pulses. The shift of center wavelength is ascribed to the mutual effects of spectral filtering induced by NPR mechanism and wavelength-dependent gain spectrum [35]. In terms of coverage, the spectral ranges in [45,46] show better performances. While the all-fiber structure laser in this work could deliver versatile bound-state pulses with switchable center wavelengths. From a practical viewpoint, such a compact, low-cost ultrafast laser with distinct outputs may have abundant applications such as C-band seed sources and capacity expansion of optical communications.
4. Conclusion
In summary, the all-fiber structure SA and NPR mechanism are combined for jointly mode-locking in a fiber laser. With the increment of effective gain level, pulse splitting occurs and multi-pulse states could evolve into different types of bound-state pulse. The center wavelength of bound state covers from 1527.9 nm to 1570.0 nm. For the first time, a bound-state pulse composed of more than thirty sub-pulses is observed. During the evolution of bound-state pulse, the pulse shaping as well as peak power clamping effects from all-fiber structure SA and spectral filtering effect from NPR mechanism play significant roles in determining properties of bound state. This work may promote the investigation on nonlinear dynamics of bound-state pulse and serves as a guideline for the design of multifunctional fiber lasers.
Funding
Science and Technology Planning Project of Shenzhen Municipality (JCYJ20210324132605014, JSGG20190819175801678).
Disclosures
The authors declare no conflicts of interest.
Data availability
Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.
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