1. Introduction

Ultrafast fiber lasers that produce pico- to femto-second pulses are very interesting for numerous applications, ranging from basic scientific research to telecommunication, medical treatment, and nonlinear microscopy [1–3]. Currently, the most commonly used ultrafast lasers utilize a well-established Q-switched or mode-locked technique, in which a nonlinear optical device, called saturable absorber (SA), can transform the continuous wave into ultrashort pulse [4–7]. Key requirements for such SAs are broadband absorption, fast recovery time, low saturation intensity, controllable modulation depth, and easy integration into optical system [8–11].

Two-dimensional (2D) nanomaterials have been intensified as SAs for ultrashort pulse generation [12–14]. The family of 2D materials includes graphene, topological insulators (TIs), and transition metal dichalcogenides (TMDs) [15–20]. Among these materials, graphene is the most attractive used as SAs. Zhang et al. have firstly opened the study of atomic layer graphene as a SA to achieve mode locking [21]. Popa et al. have reported the generation of 174 fs-short pulse in a graphene mode-locked fiber laser [22]. Later, TIs have emerged as SAs, leading to 128 fs ultrashort pulse generation at 1.5 μm by management intracavity dispersion [23]. Recently, soliton mode locking has been achieved in anomalous dispersion regime utilizing TMDs based SAs [24]. 1.6 ps soliton pulse at 1.5 μm has been observed using the ReS₂ nanosheets in an erbium-doped fiber (EDF) laser [25].

Black phosphorus (BP), a novel 2D material consisting of phosphorene monolayers, has recently been rediscovered for potential applications in optoelectronics [26–28]. Similar to graphene, BP is layered material in which the layers are stacked together with van der Waals forces [29,30]. Contrary to other 2D materials, the most important feature of BP is layer-dependent direct band gap (~0.3 to ~2.0 eV), corresponding to the wavelength range from ~4.1 to ~0.6 μm [31]. This is particularly interesting for photonics, as it can offer a broadly scalable bandgap with number of layers, and thus can fill up the gap between the zero bandgap graphene and the large bandgap TMDs [28,32]. Up till now, the saturable absorption property of BP has been revealed by Lu et al [33]. By using BP-based SA, Chen et al. have achieved the first laser that is Q-switched and mode-locked at 1.5 μm [34]. Wang et al. have obtained the pulses as short as 272 fs with a BP-mode-locked fiber laser [27]. Sotor et al. have verified the possibility of ~739 fs pulse generation centered at 1910 nm based on BP-SA [35]. Currently, most of results have demonstrated that the saturable absorption of BP is polarization-sensitive [28]. Polarization-dependent absorption may introduce a polarization selection effect to the laser cavity and prevent the formation of vector solitons [36]. However, Song et al. have demonstrated that BP fabricated by liquid phase exfoliation method exhibits polarization-independent saturable absorption property, and indicates its application in vector solitons generation [36]. Thus far, no dual-wavelength vector solitons have been observed based on BP-SA.

In this paper, we report the dual-wavelength vector solitons generation mode-locked with BP-based SA. Few-layered BP is fabricated by liquid exfoliation method from the bulk material. We have demonstrated that the saturable absorption of BP is polarization-independent. The laser is capable of generating dual-wavelength polarization-locked vector solitons centered at ~1533 and ~1558 nm with bandwidths of ~3.7 and ~6.9 nm simultaneously.

2. Experimental setup

The liquid exfoliation is a simple and effective method to prepare 2D nanomaterials from layered bulk crystals to few-layer structures. In our experiment, BP nanosheets are prepared through liquid exfoliation method by using N-methypyrrolidone as dispersed liquid. We can use N-methypyrrolidone to avoid the reaction of BP with water or oxygen to decrease the oxidation. BP film is fabricated through encapsulating the BP nanosheets into the polyvinyl alcohol solution and evaporating them on a heater. Figure 1(a) is the linear absorption spectrum of BP film, which is measured by an ultraviolet spectrophotometer. The transmission wavelength ranges from the visible to near-infrared band. Figure 1(b) is the nonlinear transmission of BP film. The modulation depth of BP is ~0.35%. By optimizing the centrifugation rate and increasing the concentration of BP in polymer, we believe that the properties of BP can be further improved. The experimental setup of fiber laser is depicted in Fig. 1(c). Mode locking can be achieved by BP-based SA, which is deposited on the surface of a fiber connector. A 3.2-m EDF is utilized as the gain, which is pumped by a laser diode (LD) of wavelength 980 nm through a wavelength division multiplexer (WDM). The polarization controller (PC) is utilized to adjust the intracavity polarization. The polarization-insensitive isolator (PI-ISO) is used to ensure unidirectional propagation. The laser emission is via a fiber optical coupler (OC) with an output ratio of 10%. The total length and net cavity dispersion are ~9.8 m and ~-0.07 ps² respectively, indicating of conventional solitons generation. We can utilize a polarization beam splitter (PBS) combined with an external cavity PC to separate two orthogonal polarization components of the solitons [37]. The performance of the fiber laser is measured by an optical spectrum analyzer, a commercial autocorrelator, an oscilloscope and a radio-frequency (RF) analyzer with help of a high-speed photodetector.

 

Fig. 1 (a) Linear absorption spectrum of BP film. (b) Nonlinear transmission of BP film. (c) Experimental setup of fiber laser.

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3. Experimental results

Self-starting mode locking is observed when the pump power reaches the threshold and PC is appropriately adjusted. Once the pump power is increased to 70 mW, dual-wavelength mode-locking operation centered at ~1533 nm and ~1558 nm can be obtained, as shown in Fig. 2. Figure 2(a) presents a typical dual-wavelength laser spectrum, exhibiting almost the same peak intensity. The 3-dB spectral bandwidths are ~3.7 and ~6.9 nm, respectively. Spectrum displays soliton sidebands, showing the formation of conventional solitons [19]. Figure 2(b) presents that the repetition rates of dual-wavelength mode locking are ~20.821490 and ~20.822133 MHz, corresponding to the longer- and shorter-wavelength bands. However, in contrast to one repetition rate of single-wavelength mode-locked state, there are two independent repetition rates of dual-wavelength mode locking on the RF spectrum. The separation between the humps is ~643 Hz and keeps constant. The relationship between the RF difference Δf and central wavelength separation Δλ is theoretically analyzed as: $\Delta f=c^{\text{2}}D\Delta \lambda \text{/}{n}^{\text{2}}L$, where L, D, n, and c, are the fiber length, dispersion parameter, refractive index of fiber, and speed of light, respectively. Here, Δλ = 25 nm, L = 9.8 m, D_{SMF + EDF} = 6 ps/(nm.km), n = 1.46, and c = 3 × 10⁸ m/s. Based on the aforementioned parameters, Δf is calculated as 646 Hz, which is in agreement with the experimental observations. The signal-to-noise ratios of dual-wavelength mode locking operation are >60 dB, indicating good mode-locking stability. It is note that once self-started, the dual-wavelength mode locking can operate stable for several hours. The spectral intensity fluctuation and wavelength drift of the dual-wavelength mode-locking state are less than 0.1 dB and 0.05 nm, respectively. In addition, an inherent characteristic of the proposed SA is the high optical damage threshold. The mode locking operation worked from the self-started threshold to the maximum available pump power of 700 mW.

 

Fig. 2 (a) Optical spectra, (b) RF spectrum, (c) and (d) Polarization-resolved oscilloscope traces of dual-wavelength conventional solitons. Insert of Fig. 2(a): zoom in of spectral sidebands at ~1548 nm. Inserts of Fig. 2(c) and 2(d): zoom in of pulse trains. The red and blue curves are horizontal and vertical components, respectively.

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To verify vector property of the dual-wavelength conventional solitons, a PBS combined with an external cavity PC is spliced to output port of the laser. The polarization feature of dual-wavelength solitons is clearly presented in Figs. 2(c) and 2(d). After passing through the PBS, two orthogonally polarized components always have identical group velocity and pulse intensity without any modulation on the oscilloscope traces, indicating that the polarization of both components is fixed along the cavity. In addition, the zoom-in pulse trains of both components are shown in insets of Figs. 2(c) and 2(d). Obviously, there are two solitons in the cavity, and each soliton has the same pulse intensity but different group velocity. The two spectra components shown in Fig. 2(a) exhibit the same central wavelength and peak intensity, but clearly different sidebands distribution. Note that apart from the Kelly sidebands, which are similar in both components, the new type of spectral peak-dip sidebands is formed on the spectra. The position of extra spectral sidebands varies with the intensity of linear birefringence, and while on the horizontal axis has a spectral peak, then on the vertical axis has a spectral dip, indicating coherence energy exchange between the two components of dual-wavelength polarization-locked vector solitons [38–40]. To our knowledge, this is the first experimental observation of achieving dual-wavelength polarization-locked vector solitons based on few-layered BP-SA.

By carefully decreasing the pump power and adjusting the PC state, dual-wavelength mode locking can be transformed into single-wavelength mode locking, as shown in Fig. 3. Figure 3(a) presents a single-wavelength laser spectrum centered at ~1558 nm with ~7.1 nm 3-dB bandwidth. The orthogonal polarization components of the soliton spectra still contain Kelly sidebands and extra peak-dip sidebands. Based on the measured autocorrelation trace shown in Fig. 3(b), the soliton pulse duration is ~700 fs if a sech² shape is assumed. The time bandwidth product is ~0.6, which is larger than the transform limit value of 0.32. Therefore, the conventional soliton is slightly chirped. Figure 3(c) presents the RF spectrum on a span of 100 Hz with a resolution of 1 Hz. The fundamental repetition rate is ~20.821490 MHz, corresponding to the equally spaced pulse interval of ~48 ns, as shown in insets of Fig. 3(c). The pulse trains are stable without any signs of multiple-pulse formation. No RF spectrum modulation is observed over a wide span of 1 GHz, as shown in Fig. 3(d), indicating no Q-switching instabilities. The average output power and pulse energy of the single pulse are ~1.5 mW and ~0.07 nJ, respectively.

 

Fig. 3 (a) Optical spectra, (b) Autocorrelation traces, (c) RF spectrum with a span of 100 Hz, and (d) Wideband RF spectrum up to 1 GHz of single-wavelength conventional soliton. The insets of Fig. 3(c) are oscilloscope traces of two components.

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4. Summary

In this paper, we have experimentally reported a BP-mode-locked dual-wavelength vector soliton fiber laser for the first time to our knowledge. The SA is fabricated based on liquid exfoliation method by incorporating BP nanosheets with polyvinyl alcohol. The laser is capable of generating dual-wavelength polarization-locked vector solitons centered at ~1533 and ~1558 nm with the bandwidths of ~3.7 and ~6.9 nm simultaneously. In addition, the stable single-wavelength vector soliton centered at ~1558 nm with ~7.1 nm bandwidth and ~700 fs duration is also observed. The results indicate that, after the characteristics of graphene, BP is another polarization-independent 2D material for ultrafast vector soliton generation.