1. Introduction

In virtue of their distinct and easily controllable physical properties, two-dimensional (2D) materials have been enormously investigated, providing a well-controlled platform for various applications, such as spintronics, chemical and biological sensors, solar cells, energy field [1] and distinctive optoelectronic devices [2, 3]. In compare with traditional materials, 2D materials have some highlighted advantages. Firstly, atomic-scale thickness of 2D nanomaterials can greatly reduce the insertion loss of optoelectronic devices [4]. Secondly, electrons are ultimately limited in atomical layers, making the electronic properties sensitively depending on the structural details (such as doping, defect, thickness) [4, 5]. One can easily, conveniently and effectively controls the optoelectronic properties of 2D materials, precisely matching with specified optoelectronic devices. Thirdly, 2D materials can be simply stacked on top of each other with different types of 2D atomic crystals in order to form multilayer heterostructures, enabling the fabrication of novel optoelectronic devices with desired properties [6].

Currently, optoelectronic researches on 2D nanomaterials are mostly concentrated on graphene [7], and transition metal dichalcogenides (TMDCs) [8] such as MoS₂, WSe₂, VS₂. Despite that graphene has very wideband absorption, it also shows some limitations for optoelectronic applications arising from its zero-bandgap feature and relatively weak light absorption coefficient, which can be remedied by TMDCs. However, most TMDCs have relatively large bandgap near or in the visible region [9, 10], which limits their performances for optoelectronic applications in infrared wavelength range. Then, the researches develop another 2D material: few-layer topological insulator (TI) and have demonstrated effective optoelectronic devices in infrared wavelength [11, 12]. For its gapless surface state and insulating bulk state with limited indirect bandgap (0.3 ev) [13], TI just fill the vacancy between graphene and TMDCs. But their indirect bandgap and the intrinsic of consisting of two different elements also limit their optoelectronic applications and increase the material complexity and difficulty of preparations.

Stimulated by specific application requirements, there are strong motivations to seek for more appropriate 2D materials that could fit for certain optoelectronic devices. Recently, another material black phosphorus (BP) consisting of only one element has been fabricated to micrometer-sized successfully [14], and join the family of 2D nanomaterials [15]. As one of the three different forms of phosphorus, BP, a conceptually new type of two-dimensional (2D) material, has stimulated strong research interest due to its unique puckered honeycomb layered structure and thickness dependent direct bandgap from 0.3 to 2.0 eV ((corresponding to the wavelength range from ~4 to ~0.6 μm)) [16, 17]. In the meanwhile, BP has ultra-high electronic mobility (1000 cm²V⁻¹s⁻¹) [14], anisotropic structure among 2D nanomaterials [18]. All of these make BPs become quite suitable as building blocks for some electronic devices [14, 19, 20]. The desirable moderate direct bandgap that can fill the gap between graphene and TMDCs renders BP as an ideal optical material for infrared optoelectronic application. However, its optical properties and the corresponding optoelectronic devices had been rarely investigated.

Herein, we reported on the optical applications of multi-layer BPs, fabricated through liquid phase separation method, for ultrafast photonics. In order to boost the optical damage threshold of multi-layer BPs as well as increase the light-matter interaction strength, fiber tapered multi-layer BPs device had been fabricated by using evanescent field optical deposition method. By placing the BP based device inside a highly compact short all-anomalous dispersion all-fiber ring cavity as saturable absorber (SA), 280 fs transmission limited pulse had been directly generated out of the laser cavity. As far as we know, such narrow pulse duration may be probably the shortest pulse obtained in a SA-based all-anomalous dispersion Er-doped all-fiber cavity. By controlling the intra-cavity birefringence, the central wavelength of the soliton pulse can be largely tuned from 1549 nm to 1575 nm. Further increasing the pump power and adjusting polarization controllers, other operation states (bound soliton and noise-like soliton state) had also been experimentally verified. Our findings clearly evidence the potential of BP for ultra-short pulse generation as an effective optoelectronic material.

2. Experiment setup

The used BP nano-platelets dispersed in isopropyl alcohol (IPA) were elaborated detailly in [21] with average thickness of 15~20 nm (about ten odd layers). Then, through evanescent field based optical deposition method as used in [22] (the same tapered fiber, 40 mW, 3.5 min), the BP-SA device was successfully prepared. Through balanced synchronous twin-detector measurement method [22], we have characterized the saturable absorption property of the fabricated BP SA with modulation depth 10.1% and saturation intensity of 9.27 MW/cm², The total insertion loss of the BP-SA device is about 1.2 dB measured by a 1569 nm CW source.

To obtain ultra-short pulse, a highly compact all-fiber laser cavity with a length of 3.42 m was employed as shown in Fig. 1. A piece of 0.85 m erbium-doped fiber (EDF, LIEKKI Erbium 80-8/125) with group velocity dispersion (GVD) of −20 ps²/km was used as laser gain fiber, the rest fiber of the cavity was pigtail of devices, including 0.4 m HI 1060 fiber (−7ps²/km) and totally 2.17 m standard single mode fiber (SMF-28) (−23 ps²/km). All fibers used worked at anomalous dispersion regime. In order to sufficiently shorten the cavity length, an optical integrated component was incorporated as a substitute for wavelength-division multiplexer (WDM), 10% output coupler (OC), and polarization-insensitive isolator (PI-ISO). The laser was pumped by a 975 nm laser diode (LD). The polarization state of circulating light as well as the intra-cavity birefringence was finely adjusted by a standard polarization controller (PC). The tapered fiber covered by BP was incorporated into the cavity as SA. The output pulse state was represented by an optical spectrum analyzer (Ando AQ-6317B), a real time oscilloscope with bandwidth of 4 GHz (Agilent Technol., DSO9404A), a radio frequency (RF) spectrum analyzer (Agilent N9322C), and a second harmonic generation auto-correlator (FR-103MN).

 

Fig. 1 Experimental setup of BP-SA based fiber laser.

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3. Results and discussions

3.1 280 fs soliton pulse with tunable central wavelength

The stable mode-locking state occurred at a pump power of 95 mW. The typical single soliton state of our fiber laser was shown in Fig. 2, all measured at pump power of 105 mW. Figure 2(a) shows the measured spectrum with central wavelength of 1569.24 nm. It has a 3 dB bandwidth of 9.35 nm. In the insert, clearly Kelly spectral sidebands can be obviously seen, which certifies its soliton operation at the anomalous dispersion regime. Figure 2(b) is measured pulse autocorrelation trace and corresponding fitting curve (sech² function), from which, the pulse duration is as short as 280 fs. Therefore, the time-bandwidth-product (TBP) is calculated to be 0.32, which suggests that these outputs are transformation limited pulses. Corresponding to the other type SA based Er-doped all-anomalous dispersion all-fiber laser (SESAM, 500 fs [23]; CNT, 314 fs [24]; Graphene, 590 fs [25]; TI 385 fs [26]; MoS₂, 637 fs [27]), it is the the shortest transmission limited pulse. The output single pulse train was shown in Fig. 2(c) with nearly identical intensity distribution. Long range of pulse stability can be further confirmed by the insert of Fig. 2(c) (output pulse train in a larger scale). It has a pulse interval of 16.53 ns, which is agreed with the cavity fundamental frequency of 60.5 MHz, verifying its single pulse state. It can be further affirmed by the RF spectrum shown in Fig. 2(d) measured with a resolution bandwidth (RBW) of 10 Hz. The first RF peak is located at 60.5 MHz without any extra spectral components. In addition, the the signal to noise ratio (SNR) is high to 68 dB, which further confirms the high stability of our fiber laser. For comparison, we show the measured RF spectrum of continuous wave (CW) in the insert. Apart from fundamental frequency, it has a lot of other random frequency components.

 

Fig. 2 Single soliton state at pump power of 105 mW: (a) Optical spectrum; (b) autocorrelation trace and Sech² fitting; (c) Output pulse train; (d) RF spectrum.

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Using the auto recording function of optical spectrum analyzer, we had also examined the long-term stability of the fiber laser as shown in Fig. 3. It had been adjusted into the auto record spectrum profile every 3-hour. After 24 hours, the spectrum profiles were kept nearly unchanged, showing fine long-term stability.

 

Fig. 3 Long-term pulse stability: optical spectra measured at a 3-hour interval over 24 hours.

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Due to the existence of the intra-cavity artificial birefringence filtering effects (because of the over-bending of the optical fibers in the PCs), the soliton central wavelength could be largely tuned. As shown in Fig. 4, just by adjusting PCs, the central wavelength of the soliton emitting can be continuously tuned from 1549 nm to 1575 nm. Noting that during tuning process, the lowest order of sidebands can be changed from 1522 nm to 1606.5 nm, which nearly approaches to the edge of the gain bandwidth. We can therefore conclude that the tunable range is not limited by the operation wavelength of the BP-SA but the gain bandwidth of the gain fiber. Given that BPs show broadband saturable absorption response [22], operation bandwidth limitation from BP-SAs can be mitigated. By using other gain medium with wider gain bandwidth, we therefore anticipated that wider tuning range can be realized.

 

Fig. 4 Evolution of optical spectra during tuning process.

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3.2 Femtosecond Bound soliton operations

In all-anomalous dispersion regime, the natural balance between the optical dispersion and the nonlinearity can result in the formation of optical soliton. However, once the intra-cavity pulse energy exceeds a threshold value, the excessive nonlinearity can lead to the pulse breakup effect, which further limit the pulse energy and introduce the appearance of additional soliton pulse [28]. In the current fiber laser cavity, once the pump power was increased higher than 110 mW, pulse breakup effect can occur because of the excessive accumulated nonlinearity. With a pump power over 202 mW, three different bound soliton states could be observed through carefully adjusting the intra-cavity PCs.

Figure 5(a) shows the typical spectrum of two bound soliton state with obvious and well-distributed strong modulation on the spectral profile. The modulation period is about 2.7 nm, corresponding to a pulse-to-pulse separation of 3.05 ps according to Fourier transformation, which had been further evidenced by the corresponding intensity autocorrelation trace as shown in Fig. 5(b). It has a typical autocorrelation profile of bound solitons with one main peak accompanied by two additional peaks. As can be seen, the peak separation is exactly 3.05 ps, which matched with the spectral modulation period. The two additional peaks have nearly half intensity of the main peak, indicating that the two pulses in bound have the same intensity. Then, under the same pump power, by slightly adjusting PCs, the modulation depth on the spectrum could gradually become weaker as Fig. 5(c) showing. Correspondingly, the intensity difference of peaks in autocorrelation trace became larger as Fig. 5(d) showing. Therefore, these two pulses in bound have different intensity. It can be concluded that the spectral modulation depth can result in peak intensity difference of pulses in bound state [29]. Of course, in our experiment, the pulse-to-pulse separation between bound soliton could be tuned as well through further adjusting PCs. With the increase of the pulse separation, the modulation period on the spectrum became smaller. In addition, we even obtained triple bound soliton state through increasing pump power and carefully adjusting PCs, shown in Figs. 5(e) and 5(f). From which, the five peaks possesses equal interval of 5.35 ps and nearly the same intensity ratio in autocorrelation trace. These mean that these three pulses in bound have the same interval from each other and almost the same intensity [29]. As it should be, when we changed the orientation of the PCs slightly, the peak separations and intensity differences of three solitons in autocorrelation trace could be tuned. The triple bound pulses could have different interval or intensity.

 

Fig. 5 Three different bound soliton states: (a), (c) Spectra of two bound pulses; (b), (d)auto-correlator trace of two bound solitons; (e), (f) Spectrum and auto-correlator trace of three bound solitons respectively.

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3.3 Noise-like operation state

As further increasing pump power, regular mulita-soliton pulses started to collapse and finally formed a new soliton with randomly amplitude and width. With that, the whole process repeated. Then, the fast relaxation time of BP introduced a strong interaction among these newly formed pulses so that these pulses were tightly bunched together with tiny pulse separation. Thus, by further increasing the pump power up to 380 mW, another type of soliton state, called noise-like, was obtained, as shown in Fig. 6. Figure 6(a) presents its optical spectrum with a 3 dB bandwidth of 18 nm. It exhibits the typical spectrum characteristic of noise-like soliton (smooth without Kelly sideband). The noise-like soliton state can be further verified by the auto-correlation trace measured with max scanning range of 50 ps, shown in Fig. 6(b). It has a narrow pulse riding on a broad pedestal, indicating that they are random noise-like pulses inside the mode-locked pulse profile.

 

Fig. 6 Output spectrum (a) and corresponding AC trace (b) of the noise-like soliton emitted from our fiber laser.

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4. Discussions

The generation of soliton in all-anomalous dispersion fiber laser depends on the balance between intra-cavity optical fiber dispersion and nonlinear optical effects. However, there is a constant nonlinear phase delay ($\pi /4$accumulating over propagation distance$Z_0$, $Z_0\approx {\tau }^2/2{\beta }_2$ is the soliton period, where$\tau$is pulse width and${\beta }_2$is GVD) that cannot be balanced by nonlinearity [30]. In a ring all-anomalous dispersion cavity, the obtainable shortest pulse that can steadily maintain need to fulfill $L<2Z_0$(L is the cavity length) [30]. For a 1 ps pulse,$Z_0=22.7$m, assuming a typical GVD = −22 fs²/mm for silica at 1550 nm, L<45.4 m [31]. In order to obtain the emission of 280 fs pulses, the cavity length should be shorter than 3.56 m. The cavity length in this work is about 3.42 m, which exactly satisfy this requirement. It is therefore concluded that short cavity may favor for the ultra-short pulse generation.

5. Conclusions

We have fabricated a new type of BP-based saturable absorber by incorporating mulit-layer BPs, which had been prepared through liquid phase exfoliation, with tapered fiber by using evanescent field optical deposition. After incorporating the fiber tapered BP-SA into an all-anomalous dispersion fiber laser, ultra-short pulse with record pulse duration down to 280 fs had been directly obtained out of the fiber laser cavity. Thanks to the controllable intra-cavity birefringent filtering effect, the central wavelength of mode-locking operation can be continuously tuned from 1549 nm to 1575 nm. Similar as other saturable absorbers, different soliton operation states (bound soliton states and noise-like soliton) had also been observed in the same laser cavity, which suggests that BP-SA can indeed operate as an effective saturable absorber for unreveiling soliton dynamics. Our experimental results exhibit that BP could be an ultra-fast 2D optoelectronic material in applications of IR or mid-IR devices.