Introduction

The mode-locked fiber laser has the advantages of compact structure, good environmental stability, high unidirectional gain, and flexible transmission, and it has shown great application potential in fiber sensing, biological imaging, fiber communication, femtosecond laser microfabrication, and other fields [1,2,3]. However, with the development of ultra-high-speed and ultra-high-capacity fiber optic communication systems, especially the technology of wavelength division multiplexing, higher requirements have been put forward for laser source. Multi-wavelength wideband tunable mode-locked fiber lasers have become a hot spot for research [4]. An interesting way to achieve the multi-wavelength wideband tunable pulse output is through passively mode-locked lasers based on optical comb filter and a broadband saturable absorber (SA). For example, in 2013, H. Ahmad et al. reported a graphene-based tunable soliton mode-locked fiber laser by Mach–Zehnder (M–Z) filter. The wavelength tunable range is 19 nm, which is from 1551 to 1570 nm [5]. Then in 2019, D. Wang et al. used a fiber Bragg grating filter as a wavelength-selective element and black phosphorus as a SA to achieve multi-wavelength switchable and tunable mode-locked operation between 1063.8 and 1064.1 nm [6]. However, in order to change the path difference of two interferometer arms, optical variable delay lines are required to combined with the standard M–Z filter, and the fiber Bragg gratings have limited bandwidth and relatively large group delay ripple [7, 8]. Fortunately, Lyot filter is a comb filter with broadband operating characteristics invented by Bernard Lyot [9]. Subsequently, it was demonstrated that Lyot filter can easily realize multi-wavelength operation with low insertion loss and large extinction ratio in fiber laser [8]. Moreover, the Lyot filter based on two-stage polarization-preserving fibers (dual-PMFs) can provide a large number of wavelength intervals by discretely changing the length of the fiber [10, 11], and its combination with a broadband SA will expand new horizons in the study of multi-wavelength tunable mode-locked fiber lasers.

In addition, in practical applications, multi-soliton state mode-locked lasers can increase the optical storage and communication capacity [12]. Complex soliton interaction dynamics and pulse evolution provide more ideas for lasers [13, 14]. In terms of the pulse action mechanism, the study of multiple solitons and soliton interactions is important for exploring the complex pulse behavior in wavelength tunable mode-locked fibers [15, 16]. Therefore, there is an urgent need to study the nature and dynamics of multiple soliton states in wavelength tunable laser systems. Fiber lasers usually operate in a multi-pulse state at high pump power because of the peak power clamping effect [17, 18]. Depending on the experimental setup, multiple pulses exhibit several different distributions in a fiber laser. For example, multiple pulses can be transmitted with the same velocity and form. And they are bounded by certain phase relations. Such multiple pulses can act as a stable whole and are called bound-state solitons [19, 20]. Meanwhile, multiple bound solitons also interact to form a whole and transmit in the optical fiber, which is called the bound state of bound solitons [21, 22]. In 2017, Li et al. observed a novel dual-wavelength soliton operation in different mode-locked states, which are a single-pulse mode-locked at 1532 nm and a bound soliton state at 1557 nm [23]. In 2019, Bowen Liu et al. formed mode-locked multi-state solitons in a dual-wavelength fiber laser using NPR-induced intracavity birefringence filtering effect [24]. In the reports of tunable mode-locked fiber lasers, complex pulse motions such as multiple soliton and soliton interactions are rarely studied.

In this paper, we report a tunable and switchable single- and dual-wavelength solitons erbium-doped hybrid mode-locked fiber laser with dual-PMFs Lyot filter. The broadband SAs are constructed by nonlinear polarization rotation (NPR) effect and WS2/MoS2 nanocomposite. The simultaneous use of two SAs in a fiber laser can reduce the saturation threshold and ensure stable pulse formation at higher power [25, 26]. The excellent performance of the dual-PMFs Lyot filter is utilized to produce a single- and dual-wavelength tunable spectral output under mode-locked operation. The single-wavelength tunable range of conventional solitons and bound-state solitons is 25.70 nm and 24.16 nm, respectively. In addition, single and bound solitons interactions in the laser are investigated, and the output of bound-state solitons and multi-bound-state solitons in the single- and dual-wavelength mode-locked state are obtained.

Sample preparation and theoretical analysis of filter

WS2/MoS2 nanocomposites were prepared by a simple liquid phase epitaxy method, which was described in the literature [27]. Firstly, 100 mg WS2 and 100 mg MoS2 powders were dispersed into 300 ml 50% IPA, respectively. And the mixed solution was sonicated by a cylindrical probe sonic tip with 80 W for 90 min. Secondly, the two solutions were centrifuged at 6000 rpm for 15 min to obtain the supernatant. Finally, in order to prepare the film of WS2/MoS2 nanocomposites, 20 ml WS2 supernatant and 20 ml MoS2 supernatant were vacuum filtrated with 0.22 μm microfiltration membrane, and then dried for 36 h in the electric vacuum drying oven. A Raman spectrometer with laser excitation wavelength of 532 nm was used to characterize the nanocomposites. The Raman spectra of the WS2/MoS2 nanocomposites (red line) and WS2 (black line) are shown in Fig. 1a. The Raman spectrum of WS2/MoS2 nanocomposites consists of the WS2-E12g peak at 354.83 cm−1, the MoS2-E12g peak at 382.74 cm−1, the MoS2-A1g peak at 410.57 cm−1, and the WS2-A1g peak at 419.83 cm−1. As compared to the pure WS2 nanosheets, the WS2-A1g peak of the nanocomposites shows a 1.62 cm−1 blue-shift from 421.45 to 419.83 cm−1, which comes from the interlayer interaction in heterostructures [28]. The results verify that WS2/MoS2 nanocomposites have been successfully prepared. Charge redistribution after WS2/MoS2 heterojunction formation can effectively accelerate the charge transfer at the heterojunction interface [28]. Therefore, WS2/MoS2 nanocomposites have great potential for application as an excellent SA material.

Fig. 1
figure 1

a Raman spectra of pure WS2 nanosheets (black line) and WS2/MoS2 nanocomposites (red line); b nonlinear transmission curve of WS2/MoS2-SA; c theoretical fitting of double-PMFs Lyot filter

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WS2/MoS2-SA is formed by attaching the nanocomposites on PDMS substrate to tapered fibers. The saturation absorption properties of WS2/MoS2-SA were studied by using a homemade laser source (1560 nm, 18.66 MHz, 500 fs). We fitted the saturation absorption data of WS2/MoS2-SA by the formula

$$ {\text{T}}\left( I \right) = 1 - \Delta T \times {\text{exp}}\left( { - {\text{I}}/I_{{\text{s}}} } \right) - T_{{{\text{ns}}}} $$
(1)

where \(\Delta {\text{T}}\) is the modulation depth, \({\text{I}}_{{\text{s}}}\) is the saturation intensity, and \({\text{T}}_{{{\text{ns}}}}\) is the unsaturated loss. As shown in Fig. 1b, the modulation depth of the WS2/MoS2-SA is 5.9%, the unsaturated loss is 10.04%, and the saturation intensity is 12.08 MW/cm2.

Here, we theoretically analyze the transmission characteristics of the dual-PMFs Lyot filter which will be used in our laser cavity to achieve single-/dual-wavelength tuning and switching. In this filter, the polarization beam is provided by a PD-ISO, which also acts as a polarizer, and the two paragraphs 14-cm-long PMFs will introduce a nonlinear birefringent phase shift. The single-mode fiber between the dual-PMFs is squeezed by a polarization controller (PC), which changes the refractive index of the contact area of the single-mode fiber and indirectly forms the birefringence effect. Therefore, the total phase shift of the filter transmission coefficient changes in the experiment, so as to realize the tuning of the laser output beam. According to the structure of dual-PMFs Lyot filter, the transmission matrix can be expressed by Jones matrix [11]:

$$ \begin{aligned} \left[ {E_{{{\text{out}}}} } \right] = & \left( {\begin{array}{*{20}c} 1 & 0 \\ 0 & 0 \\ \end{array} } \right) \times \left( {\begin{array}{*{20}c} {\cos \left( {\theta_{1} } \right)} & {\sin \left( {\theta_{1} } \right)} \\ { - \sin \left( {\theta_{1} } \right)} & {\cos \left( {\theta_{1} } \right)} \\ \end{array} } \right) \times \left( {\begin{array}{*{20}c} {e^{ - i\Delta \varphi } } & 0 \\ 0 & {e^{i\Delta \varphi } } \\ \end{array} } \right) \\ \; & \times \left( {\begin{array}{*{20}c} {\cos \left( {\theta_{2} } \right)} & {\sin \left( {\theta_{2} } \right)} \\ { - \sin (\theta_{2} )} & {\cos \left( {\theta_{2} } \right)} \\ \end{array} } \right) \times \left( {\begin{array}{*{20}c} {e^{ - i\Delta \varphi } } & 0 \\ 0 & {e^{i\Delta \varphi } } \\ \end{array} } \right) \times { }\left( {\begin{array}{*{20}c} 1 \\ 1 \\ \end{array} } \right){ }{\text{.}} \\ \end{aligned} $$
(2)
$$ \Delta \varphi = 2\pi L_{{{\text{PM}}}} \Delta n/\lambda $$
(3)

Among them, \(\left[ {E_{{{\text{in}}}} } \right] = \left( {\begin{array}{*{20}c} 1 \\ 1 \\ \end{array} } \right)\) represents the transmission matrix of incident light, \(\left[ {P_{1} } \right] = \left( {\begin{array}{*{20}c} {\cos \left( {\theta_{1} } \right)} & {\sin \left( {\theta_{1} } \right)} \\ { - \sin \left( {\theta_{1} } \right)} & {\cos \left( {\theta_{1} } \right)} \\ \end{array} } \right)\) and \(\left[ {P_{2} } \right] = \left( {\begin{array}{*{20}c} {\cos \left( {\theta_{2} } \right)} & {\sin \left( {\theta_{2} } \right)} \\ { - \sin \left( {\theta_{2} } \right)} & {\cos \left( {\theta_{2} } \right)} \\ \end{array} } \right)\) are the transmission matrix of PC1 and PC2, respectively, and \(\left[ J \right] = \left( {\begin{array}{*{20}c} {e^{ - i\Delta \varphi } } & 0 \\ 0 & {e^{i\Delta \varphi } } \\ \end{array} } \right)\) is the transmission matrix of polarization maintaining fiber. To simplify the analysis, a polarizer is set along the fast axis \(\left[ M \right] = \left( {\begin{array}{*{20}c} 1 & 0 \\ 0 & 0 \\ \end{array} } \right)\) [29]. \(\Delta \varphi\) is the phase difference caused by PMF In formula (3), \(\Delta n\) is the birefringence of PMF, which represents the refractivity difference between the fast axis and the slow axis of PMF. According to Eq. (2), the transmittance function is

$$ T = {\raise0.7ex\hbox{$1$} \!\mathord{\left/ {\vphantom {1 2}}\right.\kern-0pt} \!\lower0.7ex\hbox{$2$}}\left( {\cos^{2} \left[ {\Delta \varphi } \right] + \cos \left[ {2\theta_{2} } \right]\left( { - \sin^{2} \left[ {\Delta \varphi } \right] + \sin \left[ {2\theta_{1} } \right]} \right) + \cos \left[ {\Delta \varphi \left] {\cos } \right[2\theta_{1} \left] {\sin } \right[2\theta_{2} } \right]} \right) $$
(4)

In the experiment, and \(L_{{{\text{PM}}}}\) are fixed. \(\theta\) can be adjusted by changing the PC, in which case we take the example of \(\theta_{1} = 45^\circ\) and \(\theta_{2} = 45^\circ\)[30]. According to the output transmittance period, the phase delay should be

$$ \pi \Delta n/\lambda = 2m\pi /L_{PM} $$
(5)

where m = 0, 1, 2, 3. Thus, the free spectral range (FSR) of the Lyot filter is given by the following equation [28]

$$ FSR \cong \lambda^{2} /\Delta nL_{{{\text{PM}}}} $$
(6)

When the PC deflection angle is \(\pi /4\), the numerically simulate transmission spectral characteristic is 25 nm, which proves the excellent performance of the filter, as shown in Fig. 1c. When the polarization angle is kept constant, the stress birefringence changes slightly. The simulation result shows that this method is feasible and the position of the transmission peak can be adjusted by a small change in the total birefringence of the cavity. Therefore, a tunable output of wavelength is theoretically feasible.

In addition, by increasing the pump power and adjusting the polarization controller, it can be used to balance the two important gain peaks in the EDF gain spectrum under the influence of intensity and wavelength dependent loss mechanism [8]. Therefore, using this filtering effect, it is theoretically possible to achieve dual-wavelength or even multi-wavelength mode-locking operation.

Experimental setup

The schematic diagram of our mode-locked EDF laser cavity experimental setup is shown in Fig. 2. In the cavity, a 0.5 m Er-doped fiber (EDF, LIEKKI Er110-4/125) was used as the gain medium. The other fibers in the cavity were two PMFs with a length of 14 cm (Nufern PM1550-XP) and single-mode fibers with a total length of 10.45 m. A 980 nm laser diode (LD) was transmitted to the EDF by the 980/1550 nm wavelength division multiplexer (WDM). A polarization-dependent isolator (PD-ISO) was used to ensure the monodirectional propagation of the laser pulses in the cavity and act as a polarizer. The polarization state of the fiber was changed by adjusting the deflection angle of the polarization controller (PC). 10% of the ports in the 10/90 optical coupler (OC) provided laser output. The generation of pulse signals was observed by an ultrafast photodetector (Thorlabs Det08CFC), which was connected to an oscilloscope (Agilent Technology, DSO9104A). Finally, pulse spectrum was measured by spectrum analyzer (OSA Yokogawa AQ6370C), radio frequency (RF) signal was measured by radio frequency spectrum analyzer (N9000A, Keysight), and pulse width was measured by autocorrelator (APE PulseCheck-50), respectively.

Fig. 2
figure 2

Configuration of the mode-locked EDF laser. LD, laser diode; WDM, wavelength division multiplexer; OC, optical coupler; PC, polarization controller; SA, WS2/MoS2 nanocomposites; PD-ISO, polarization-dependent isolator

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Results and discussion

Single-wavelength mode-locked output

In the experiment, stable single-wavelength soliton mode-locked pulse can be easily obtained when the pump power is increased to 120 mW. As shown in Fig. 3, we measured the pulse characteristics at 140 mW pump power. As can be seen from Fig. 3a, the central wavelength of the spectrum is 1554.83 nm with 6.8 nm full width half maximum (FWHM) bandwidth. In addition, Fig. 3b plots the width of the mode-locking pulse and the results of fitting the autocorrelation trajectory using the Sech2 function. The accurate pulse width is 385 fs. Figure 3c shows that the pulse interval of the recorded mode-locked pulse is 53.69 ns, which is consistent with the result calculated by the length of total cavity. And its corresponding time-bandwidth product is 0.324, indicating that the mode-locked optical pulse generates a slight chirp. According to Fig. 3d, its basic repetition frequency is 18.62 MHz and its signal-to-noise ratio (SNR) is 69.2 dB (4.3 kHz resolution bandwidth). The 1500 MHz span radio frequency spectrum shows that the fiber laser works well in the continuous mode-locked state [see inset of Fig. 3d].

Fig. 3
figure 3

Traditional soliton output. a Optical spectrum; b autocorrelation trace; c oscilloscope trace; d radio frequency spectrum with a 1500 MHz span range

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Moreover, the soliton mode-locked pulses can be switched into bound-state solitons by PCs optimization when the pump power reaches 140 mW. This is due to the tendency of fiber lasers to operate in multiple soliton states, where multiple pulses can interact to form a bound-state pulse. As shown in Fig. 4, we measured the pulse characteristics at 160 mW pump power. In Fig. 4a, the modulation period for the output spectrum is 4.60 nm, which is characteristic of a typical bound-state soliton. As shown in Fig. 4b, we obtained the bound-state pulse with a soliton pulse interval of 1.77 ps and a soliton pulse width of 409 fs. We calculate by formula (7):

$$ \Delta \nu = c\Delta \lambda /\lambda^{2 } $$
(7)
Fig. 4
figure 4

Bound states of soliton output. a Optical spectrum of bound soliton; b autocorrelation trace of bound soliton; c optical spectrum of bound states of two bound solitons; d autocorrelation trace of bound states of two bound solitons

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(Δν = 563 GHz) where the  = 1565.2 nm. The spectral modulation period is opposite to the pulse interval \(\Delta \nu = 1/\tau\) (\(\Delta \nu\) = 564 GHz) [31]. It is proved that the calculated results of bound-state soliton separation agree well with the experimental results. Due to the direct interaction between multiple bound solitons, they closely combine to form bound states with discrete and fixed separated bound solitons [23, 32]. Similarly, by adjusting the angle of PC2 at the pump power of 160 mW, the spectra with dual-modulation periods of 2.64 nm and 0.38 nm are obtained, as shown in Fig. 4c. Through autocorrelation measurement, we observed that the pulse intervals of the three pulse envelopes are approximately equal. The experimental results are shown in Fig. 4d. Their soliton pulse intervals are 3.24 ps and 3.30 ps, respectively, and the interval between the two pulse envelopes is 21.44 ps, forming a new bound-state pulse output. This shows that the bound states of two bound solitons obtained in our experiment are relatively stable, which also demonstrates that these discrete bound states with fixed soliton separation propagate as a whole in the fiber.

In addition, when the mode-locked fiber laser works stably in the single-wavelength mode-locked state, the tuned output of the spectrum is obtained by adjusting the PCs to change the birefringence. We collected spectral data at the pump power of 260 mW. As shown in Fig. 5a, the central wavelength of the single-soliton spectrum is adjustable from 1543.32 to 1569.02 nm, with an adjustable range of 25.70 nm. In addition, since the amplitude of the peak spectral transmission varies with the PC state, which leads to variations in the pulse output intensity when tuned to different wavelengths. The 3-dB bandwidth of the spectrum and the pulse width vary slightly with the change of the central wavelength of the spectrum. As seen in Fig. 5b, our laser always operates in the femtosecond order. This demonstrates the excellent output characteristics of our laser and shows that the dual-PMFs Lyot filters have a good tuning range. To our knowledge, there are few reports on the tuning of bound-state spectra. When the bound solitons operate stably in the mode-locked fiber laser, the tuning of the 1546.19–1570.35 nm bound-state spectrum can be achieved by adjusting the PC, as shown in Fig. 5c. This is the result of a combination of strong interactions between solitons and the wide tuning range of the filter.

Fig. 5
figure 5

Spectral tuning. a Evolution of single-soliton spectrum during tuning; b bandwidth (Δλ) and pulse duration (τ); c evolution of bound-state soliton spectra during tuning

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Dual-wavelength mode-locked output

Then, we can achieve an asynchronous dual-wavelength output by adjusting the PC in the dual-PMFs Lyot filter to balance the two gain peaks of the EDF fiber. The threshold of the dual-wavelength mode-locked fiber laser is 140 mW. As shown in Fig. 6a, the central wavelengths of the two spectra are 1547.70 nm and 1566.92 nm, and the corresponding 3-dB bandwidths are 4.90 nm and 4.46 nm, respectively. In Fig. 6b and a stable pulse sequence in the asynchronous dual-wavelength mode-locked state can be observed. Due to the different group velocity dispersion, the pulses of the two wavelengths are in different positions in the time domain, so that two different pulse sequences are displayed in the oscilloscope. The pulse interval between the two pulses is 53.70 ns, which corresponds to the result calculated by the cavity length. As seen in Fig. 6a and b, the spectrum at 1547.70 nm has higher pulse energy and higher output intensity. Therefore, the basic repetition frequency corresponding to this wavelength of 1547.70 nm is 18.62469 MHz, and the basic repetition frequency corresponding to another wavelength of 1566.92 nm is 18.62380 MHz (47 Hz resolution bandwidth), as shown in Fig. 6c. There are beat frequencies on the left and right sides, indicating that the spectral line has high coherence two combs [33]. As shown in Fig. 6d, the pulses measured with the autocorrelator are fitted by the Sech2 function, exhibiting a pulse width of 518 fs.

Fig. 6
figure 6

Traditional soliton output. a Optical spectrum; b oscilloscope trace; c radio frequency spectrum; d autocorrelation trace

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In the dual-wavelength mode-locked state, there are still strong interactions between solitons. The dual-wavelength output spectral can be switched to different soliton mode-locked states by adjusting PC2. This new experimental phenomenon is shown in Fig. 7. Figure 7 a and b depicts the coexistence of single solitons and bound-state solitons in the same laser at the pump power of 140 mW. Figure 7a shows the single-soliton spectrum with 1541.48 nm central wavelength and the bound-state solitons spectrum with 1560.94 nm central wavelength. The corresponding 3-dB bandwidth and modulation period of the two spectra are 2.31 nm and 4.12 nm, respectively. Obviously, the mode-locked states of the two wavelengths are different in the dual-wavelength laser. Soliton pulse interval of 1.96 ps and pulse width of 608 fs can be obtained, as shown in Fig. 7b. In “Single-wavelength mode-locked output” section, we have obtained the bound states of two bound solitons with discrete and fixed separations in the single-wavelength mode-locked state. Then, we explored the bound state of the multi-bound solitons in the dual-wavelength mode-locked state. Figures 7c and d depicts the autocorrelation results in the dual-wavelength mode-locked state at 260 mW pump power. In Fig. 7c, the large pulse envelope and the two small pulse envelopes have almost the same soliton pulse interval. The soliton pulse intervals of the two pulse envelopes are 2.30 ps and 2.40 ps, respectively, and the distance between them is 24.48 ps, which is the bound state of the bound soliton formed by the interaction of two bound solitons. While keeping dual-wavelength mode-locked, we observed the bound states of three bound solitons. As shown in Fig.  7d, their soliton pulse intervals are 1.82 ps and 1.85 ps, respectively, and the distance between the two envelopes is 32.41 ps. Due to the limited scanning range of the autocorrelator, only a portion of the states in the entire autocorrelation trajectory can be recorded. With two different pulses in the time domain, one of the pulses generates multiple soliton states due to the peak power clamping effect [ 16 ], and these soliton states interact with each other to form a bound state of bound soliton. This shows that the bound states of multiple bound solitons remain in the dual-wavelength mode-locked state and do not interact with the other central wavelength pulse.

Fig. 7
figure 7

Bound states of soliton output. a Optical spectrum of bound soliton; b autocorrelation trace of bound soliton; c autocorrelation trace of bound states of two pulse bound solitons; d autocorrelation trace of bound states of three pulse bound solitons

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The excellent performance of dual-PMFs Lyot filter provides the possibility for the tunable output of dual-wavelength soliton mode-locking. The laser operated stably in a single-soliton dual-wavelength mode-locked state, and we measured the data by varying the angle of the PCs at a pump power of 260 mW. The tuning range of the left spectrum is 1541.30–1551.30 nm, and the tuning range of the right spectrum is1562.04–1568.3 nm, as shown in Fig. 8a. Surprisingly, wavelength tuning can also be achieved when the fiber laser is in different mode-locked states. As far as we know, this never been reported in the previous literatures. As shown in Fig. 8b, the overall shift of the optical spectrum in the dual-wavelength mode-locked state is to the right at the pump power of 260 mW. The optical spectral tuning range is from 1561.53 to 1566.28 nm for a bound soliton with a central wavelength, and from 1541.4 to 1547.32 nm for a single soliton with another central wavelength. This again proves the excellent functionality of the dual-PMFs Lyot filter.

Fig. 8
figure 8

Spectral tuning. a Evolution of single-soliton spectrum during tuning; b evolution of bound-state soliton spectra during tuning

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Finally, in order to verify the excellent characteristics of the dual-PMFs Lyot filter, we removed the dual-PMFs in the fiber laser and found that there is no dual-wavelength spectrum and tunable spectrum output. This also shows that the dual-PMFs Lyot plays a crucial role in the dual-wavelength generation and wavelength tunability in the laser cavity.

Conclusion

In summary, we report on a single- and dual-wavelength tunable and inter-soliton switchable hybrid mode-locked fiber laser which is based on WS2/MoS2 nanocomposites and NPR effect. Wavelength tuning is performed in the laser by using a dual-PMFs Lyot filter. For the single wavelength, the central wavelength of single solitons and bound-state solitons are tuned in the range of 25.70 nm and 24.16 nm, respectively. Meanwhile, in the same laser cavity, the dual-wavelength output is achieved by adjusting PC. Moreover, the wavelength tunability and pulse motion between solitons of the dual-wavelength mode-locked fiber laser are reported. This work provides ideas and insights for the study of multi-wavelength tunable technology and soliton pulses in different mode-locked states.