Multiwavelength passively mode-locked fiber lasers have attracted widespread research attention because of their versatile applications in wavelength-division multiplexing, optical metrology, optical sensing, optical communication, and so on^[1–4]. Specifically, dual-wavelength lasers have emerged as key tools for dual-comb spectroscopy, microwave and terahertz signal generation, and pump-probe measurement^[5,6]. Moreover, these lasers can service as an ideal platform to explore rich soliton dynamics. So far, various methods have been proposed to achieve dual-wavelength operation, mainly including intracavity loss control^[7], and the introduction of cascaded fiber Bragg gratings (FBGs)^[8,9] or some artificial comb filters into laser cavities^[10–16]. In particular, the incorporation of a comb filter into the cavity has been proven to be an effective solution for suppressing mode competition and achieving stable multiwavelength operation^[10]. It can be achieved in different ways, such as the Lyot filter^[11], the Mach–Zehnder interferometer^[10], the Sagnac loop mirror^[12,13], and the grade-index multimode fiber device^[14]. In addition, these comb filters can provide great flexibility in adjusting filter bandwidth, central wavelength, and modulation depth^[15–17]. By simply changing the fiber length or imposing external physical perturbations on fibers, filters with different transmission spectra can be obtained. Thus, the utilization of comb filters can be a favorable choice for generating tunable dual-wavelength pulses and further exploring novel soliton dynamics.

As is well known, different soliton operating regimes require specific conditions for their formation, generally leading to the generation of identical soliton types at the two central wavelengths of pulses. This phenomenon has been confirmed in various dual-wavelength fiber lasers, including conventional soliton (CS)^[11–13], dissipative soliton (DS)^[14], dissipative soliton resonance (DSR) pulse^[18], and noise-like pulse (NLP)^[15] lasers, etc. However, there are relatively few studies on dual-wavelength pulses with the coexistence of diverse pulse patterns, thus arousing increasing research interest. Recently, Mao et al. reported the simultaneous generation of CS and DS in an Er-doped fiber (EDF) laser by exploiting chirped FBG and four-port circulator^[19]. The coexistence of DS and self-similar pulses, as well as the coexistence of DS and stretched pulses, has been observed experimentally in two dual-wavelength EDF lasers with near-zero cavity dispersions^[20,21]. A composite operation regime of high-order harmonic soliton molecules and rectangular NLP was experimentally generated in a figure-eight EDF laser^[22]. Then the coexistence of NLP and high-order harmonic CS was observed in a dual-wavelength mode-locked Tm-doped fiber (TDF) laser with a Lyot filter^[23]. Very recently, a heterogeneous pulse pattern of the coexistence of one NLP at 1559 nm and one CS at 1565.8 nm was obtained in a double-cavity EDF laser^[24].

However, the aforementioned dual-wavelength fiber lasers with coexistence of distinct operating regimes do not contain a dark pulse. In some long-distance transmission applications, dark pulses as the optical source are more promising than bright solitons because they are less sensitive to background noise, and their broadening rate is almost half that of bright solitons when propagating in the fiber^[25,26]. Then a question arises: could different pulse states containing a dark pulse coexist? Recently, bright–dark pulse pairs^[27–30] have been reported in some fiber lasers, featuring the coexistence of CS and dark pulse at different central wavelengths. The formation reason can be the cross-phase modulation (XPM) between different wavelengths or two orthogonally polarization axes^[27–32]. In addition, a dual-wavelength hybrid step-like and dark pulse was also generated in a Ti:Bi2Se3-based EDF laser^[28]. These interesting phenomena revealed rich soliton dynamics in the dual-wavelength operating regime. However, to our knowledge, there have been no reports on lasers with the coexistence of NLPs and dark pulses at different central wavelengths.

In this paper, we investigated the coexistence of NLPs and dark pulses in a mode-locked EYDF laser with a Sagnac loop filter and a piece of highly nonlinear fiber (HNLF). The experimental setup of the net-anomalous dispersion mode-locked EYDF laser is presented in Section 2. The NPR technique is used as the artificial saturable absorber (SA). In Section 3, the experimental results of the hybrid pulses with the coexistence of NLPs and dark pulses are presented. Then, by adjusting the PC in the Sagnac loop, the central wavelengths of two peaks can move from 1560 to 1577.8 nm, and from 1581.8 to 1605.4 nm, respectively. In addition, the influence of the length of polarization-maintaining fiber (PMF) in the Sagnac loop filter on the generation of composite states of NLPs and dark pulses is investigated. Finally, Section 4 summarizes the conclusions.

The proposed mode-locked EYDF laser based on the NPR mode-locking technique is schematically shown in Fig. 1(a). The gain medium is a 4.6-m-long EYDF (Nufern, SM-EYDF-6/125-XP) with a core absorption of 45 dB/m near 1535 nm and pumped by a 3 W multimode laser diode (LD1) at 976 nm through a (2+1)×1 pump combiner. A 20:80 optical coupler (OC) is used to extract 20% of the pulse power from the cavity. A 3.1-m HNLF with the near-zero negative dispersion at the 1550 nm waveband is used to enhance the nonlinear effect in the cavity. A polarization-dependent isolator (PD-ISO) is used to ensure the unidirectional propagation of pulses in the cavity while combining with two PCs to enable the NPR operation. An optical circulator is used to connect the Sagnac loop filter into the ring cavity. A 2.8-m-long EDF (LIEKKI Er30-4/125) placed in front of the filter is used to balance intracavity losses and further flatten the gain spectrum combined with that of the EYDF. As shown in Fig. 1(b), the intensities of amplified spontaneous emission (ASE) spectrum in the EDF are higher than those in the EYDF on the long-wavelength side. The EDF is pumped by two 976 nm laser diodes (LD2 and LD3) through 976/1550 nm wavelength-division multiplexers (WDMs). The fiber pigtails of the pump combiner and WDM are SM-GDF-6/125 of 1.6 m and OFS980 of 1.6 m, respectively. The other fibers are SMF segments with a total length of ∼7.8m. Therefore, the total cavity length is ∼26.57m and net-cavity dispersion is −0.173ps2. In addition, an optical spectrum analyzer (Deviser AE8600, OSA) is used to measure the output spectra. A photodetector (PD) with the 6-GHz bandwidth together with an electrical spectrum analyzer (Agilent Technologies, N9010A, ESA) and a digital sampling oscillograph (0.3 GHz, Tektronix DPO3032) are employed to monitor the stability of output pulses. The temporal width is evaluated by a commercial optical autocorrelator (FEM-TOCHROME, FRXL). A tunable flat-top filter (WL Photonics, WLTF-WM-S/12) with a bandwidth of 12 nm is used to extract the output pulses with tunable central wavelengths. A polarization beam splitter (PBS) is employed to achieve polarization-resolved measurement. Then a 50:50 OC is used to observe pulse waveforms in both temporal and spectral domains simultaneously. P₁, P₂, and P₃ represent the pump powers of LD1, LD2, and LD3, respectively. In order to achieve high output power, P₂ and P₃ are set to the maximum LD power of 0.2 W.

In the experiment, the Sagnac loop filter, acting as a fiber-loop mirror, consists of a 2×2 OC with a splitting ratio of 50:50, a PC, and a 0.3-m-long PMF (YOFC, PM 1550_125/250). The transmission curve of the Sagnac loop filter can be expressed as^[33]T=sin2θcos2(πΔnLPMFλ).(1)

θ is the rotation angle of the original coordinate system induced by the PC, which determines the amplitude of transmission profile. For simplicity, θ is set to π/2. The phase difference φ between the fast and slow axes of the PMF can be expressed as φ=πΔnLPMF/λ. LPMF is the length of the PMF, and λ is the operating wavelength. The birefringence Δn of the PMF is ∼3.5×10−4, and the wavelength interval between adjacent spectral peaks can be written as Δλ=λ02ΔnLPMF.(2)

In this case, Δλ can be calculated to be ∼23nm, as shown in Fig. 2(a). The experimentally measured transmission spectrum is shown in Fig. 2(b). The interval between two adjacent peaks is 23.2 nm, which is almost consistent with the theoretical value. However, when removing the PMF from the Sagnac loop, no comb-like structure can be observed in the output spectrum.

When the pump power P₁ was increased to 0.3 W, a mode-locked operation with the two central wavelengths was initiated by appropriately adjusting PCs in the cavity. Furthermore, the stable mode-locked state can remain unchanged as P₁ increased. When P₁ reaches its maximum value of 3 W, Fig. 3(a) shows the two-peak spectrum near 1565.3 and 1594.2 nm, located at two passband windows of the Sagnac loop filter. Since no two-peak pulse spectrum can be observed without a PMF in the Sagnac loop, the periodic transmittance of the filter rather than the intensity-dependent loss induced by NPR effect plays a critical role in a two-peak spectrum. The 3-dB bandwidths of two spectral peaks are 3.5 and 0.7 nm, respectively. The different spectral patterns in two spectral regions can indicate the coexistence of distinct pulse types. The pulse train shown in Fig. 3(b) has a temporal period of ∼132.7ns, which is consistent with the fundamental repetition rate of ∼7.53MHz in Fig. 3(d). As shown in Fig. 3(c), the autocorrelation (AC) curve of the output pulse exhibits a dual-scale structure with a narrow spike riding on a broad pedestal, which is a typical feature of NLP^[34,35]. It can further imply the coexistence of an NLP in the laser. A signal-to-noise ratio (SNR) of 64.76 dB suggests the stable operation of the composite state pulses, as shown in Fig. 3(d).

To further investigate the characteristics of the output pulse, a tunable flat-top filter is used to separate the two-peak wavelength components centered at 1565.3 and 1594.2 nm, respectively, as shown in Fig. 4(a). The AC curve of the pulse with blue components exhibits the typical double-scale feature of NLP, as shown in Fig. 4(b). The corresponding pulse train with a temporal interval of 132.7 ns is shown in Fig. 4(c). As shown in Fig. 4(e), it is interesting to note that the output pulse corresponding to the 1594.2-nm components exhibits a dip in the continuous-wave (CW) background; hence the name, dark pulses^[26,36]. Visualization 1 shows the dynamic evolution of filtered pulses via the oscilloscope and the OSA. First, the dark pulse train appears in the oscilloscope when the central wavelength (λf) of the tunable filter is 1594.2 nm. As λf shifts toward shorter wavelengths, the amplitudes of both the dip and the CW background decrease, leading to an unstable state when λf reaches the dip between two spectral peaks. As λf further decreases, the temporal intensity peak gradually emerges on the CW background, and the peak can reach its maximum value when λf is 1565.3 nm. Consequently, the coexistence of different types of pulses is obtained in our proposed fiber laser, featuring an NLP on the blue side and a dark pulse on the red side. As shown in Visualization 1, the peak amplitude of the NLP is much larger than that of the dark pulse, which results in an unobvious dark pulse trace in the composite state [see Fig. 3(b)]. In addition, in both two cases, SNRs above 65 dB indicate their stable operations.

Furthermore, the polarization characteristics of the output pulse are investigated via polarization-resolved measurement using an extracavity PBS and a PC4. By finely adjusting the PC4, linearly polarized NLP and dark pulse can be individually observed at the two output ends of the PBS, whose oscilloscope pulse traces are depicted in Fig. 5(a). Obviously, the NLP and the dark pulse trains have the same temporal interval of ∼132.7ns, indicating that two pulses are synchronized in the laser cavity. The corresponding spectra are shown in Fig. 5(b). The dark pulse is located on the long-wavelength side of the dual-peak spectrum, while the NLP is located on the short-wavelength side. Consequently, the formation of the composite state of NLP and dark pulse can be attributed to the XPM between the two different wavelength components along two orthogonal polarization axes^[27,31].

The evolutions of average output power and pulse energy with the pump power P₁ are plotted in Fig. 6(a). Clearly, as P₁ increases from 0.3 to 3 W, the output power linearly increases from 17.8 to 74.7 mW, and the pulse energy increases from 2.37 to 9.93 nJ. Moreover, the stability of output power is measured within 4 h when P₁ is 3 W, as shown in Fig. 6(b). The power fluctuation from the average value is ∼1.85%, indicating that the EYDF laser can operate at stable state for a long time in the lab.

First, by carefully adjusting the PC in the Sagnac loop filter, wavelength-tunable coexistence states of NLPs and dark pulses are obtained when P₁ is 3 W, as shown in Fig. 7(a). The spectral peak on the blue side can be shifted from 1560 to 1577.8 nm, while the spectral peak on the red side can be tuned from 1581.8 to 1605.4 nm. Both central peaks vary within a range of less than 24 nm due to the limited gain bandwidth of the active fibers. Moreover, the wavelength intervals between two spectral peaks for the curves 1, 2, 3, 4, and 5 are 21.8, 27.5, 34.2, 32.9, and 27.6 nm, respectively. The uneven interval is related to the gain competition between various wavelength components located at the periodic transmittance windows of the filter. As shown in Fig. 7(b), the average output power varies between 74.1 and 77.23 mW. The SNRs of >60dB indicate that the fiber laser can operate stably at different wavelengths.

Moreover, by keeping P₁ fixed and carefully adjusting the PCs in the main cavity, the state of the fiber laser can be switched from the coexistence regime to the NLP regime. As shown in Fig. 8(a), NLPs with three distinct spectral shapes are generated due to variations in the transmission curve of the NPR-based SA by tuning PCs^[37,38]. Notably, the spectrum of the blue trace exhibits the widest 20-dB bandwidth of ∼101.4nm, which corresponds to the narrowest NLP with a pedestal duration (t0) of ∼37.6ps, shown in Fig. 8(b). Meanwhile, the highest average peak power (Ppeak=Pave/frepetition ratet0) of ∼286.6W is obtained for this broadband NLP due to the nearly identical average output powers (Pave) of 74.3, 75.6, and 74.8 mW in three cases. The reason for the above phenomena is mainly due to the higher critical saturation power (CSP) of the SA obtained in this scenario. It has been demonstrated that the CSP is the key factor directly linked to the properties of NLPs, and a higher value of the CSP allows for NLPs with higher peak power and shorter pulse duration^[38]. Consequently, the corresponding spectrum significantly broadens due to the enhanced self-phase modulation effect.

When the length of PMF in the Sagnac loop filter increases from 0.2 to 2.3 m, the channel spacing Δλ of the filter decreases from 34.3 to 2.9 nm, as shown in Fig. 9. Meanwhile, the transmission spectrum exhibits a more uniform distribution accompanied by a narrower channel bandwidth in the wavelength range of 1550 to 1590 nm. The results are consistent with those in Ref. [39].

First, as shown in Fig. 10(a), switchable coexistence states with two spectral peak tuning ranges of 1560 to 1563.4 nm and 1586.5 to 1602.3 nm are obtained by carefully adjusting PCs when LPMF is 0.2 m and P₁ is 3 W. Evidently, the wavelength variation ranges observed here are relatively smaller than those in the case of LPMF=0.3m. This result can be attributed to the reduced number of comb channels in the limited gain spectral bandwidth, which imposes certain constraints on the flexible adjustment of the central wavelengths. For example, when LPMF=0.2m and LPMF=0.3m, two and three comb channels exist in the wavelength range of 1553 to 1626 nm, respectively, as shown in Fig. 9(a). Similarly, the NLPs with three different spectral curves are also generated, as shown in Fig. 10(b).

However, when LPMF reaches and exceeds 0.5 m, as shown in Fig. 10(c), the laser no longer operates in the composite mode-locked regime, but only in the broadband NLP state. The reason for the disappearance of the coexistence of NLPs and dark pulses in our laser is as follows: as LPMF increases, Δλ decreases, leading to an increased number of channels with reduced channel bandwidth within the limited gain spectral range. Since EYDF and EDF are homogeneous gain mediums^[39–41], gain competition becomes stronger with the increased number of channels. As a result, it is difficult to balance gain and loss simultaneously at multiple wavelengths, especially for synchronized pulses with different pulse operation regimes and wavelengths^[42]. On the other hand, the losses of wavelength components in each channel increase as the channel bandwidth narrows. Consequently, the intensities of lasing wavelength components decrease and fail to reach the mode-locking threshold power of the NPR-based EYDF laser. Therefore, an SA with a low saturation power and a wide operational wavelength bandwidth is required to initiate a multiwavelength mode-locked operation. For example, by introducing a semiconductor SA mirror into an NPR-based EDF laser with a 1.6-m-long PMF as a Lyot filter, multiwavelength solitons can be generated^[43].

Similarly, as losses induced by spectral filtering increase with channel number, only the wavelength components near the peak of the gain spectrum at ∼1564nm have sufficient gains to bleach the NPR-based SA. As a result, the laser can only be operated in the broadband NLP state characterized by a narrow duration and a high average peak power, as shown in Fig. 10(c). In addition, the average output power of the broadband NLP slightly decreases as LPMF increases, as shown in Fig. 10(d). The SNRs of >60dB indicate the stable operation states of broadband NLPs under different PMF lengths. Nevertheless, it should be noted that the stable NLP operation can only be maintained for ∼10min in the case of LPMF=2.3m, mainly due to the strong spectral filtering effect induced by the comb-like filter. Therefore, to obtain the coexistence of NLPs and dark pulses and expand their wavelength-tunable range, it is necessary to select an appropriate length of PMF in the Sagnac loop.

In conclusion, the coexistence of an NLP and a dark pulse with different central wavelengths was experimentally demonstrated in a net-anomalous dispersion NPR-based EYDF laser for the first time. Via external cavity filtering and polarization-resolved measurements, it has been demonstrated that the composite state is a result of the XPM between the NLP and dark pulse along two orthogonal polarization axes. Moreover, by adjusting the PC in the Sagnac filter, the output pulses exhibit two tunable central wavelengths from 1560 to 1577.8 nm and 1581.8 to 1605.4 nm, respectively. The single-wavelength NLPs with three distinct spectral shapes could also be generated by tuning PCs in the main cavity. Furthermore, the influence of PMF length on composite pulses was investigated. The coexistence states of NLPs and dark pulses were observed only when LPMF were 0.2 and 0.3 m, where the maximum wavelength-tunable range was achieved when LPMF=0.3m. With a further increase in LPMF, composite states of NLPs and dark pulses disappeared in our fiber laser.