1. Introduction

Optical vortex beams have been an active area of research for their unique properties such as doughnut spatial profiles and orbital angular momentum (OAM) [1,2]. Due to these characteristics, vortex beams are associated with many applications such as optical tweezers [3], super-resolution microscopes [4], quantum information processing [5], free-space communication systems [6], etc. In particular, high intense optical vortex pulses can open up various fields including high quality material processing [7], controllable specificity of chiral matter [8], nonlinear frequency conversion [9], and high-field laser physics [10]. Since the first demonstration of the direct emission of pulsed optical vortex with tunable orbital angular momentum from solid-state cavity in 2012 [11], the directly generated pulsed vortex laser has attracted increasing interests due to its characteristics like robust structure, low cost, and high power laser operation. However, direct vortex generation always has the question as to the purity of helicity and the maintenance of OAM. Owning to the degeneracy of LG modes with opposite handedness, the generated doughnut-shaped output often tends to be an incoherent superposition of opposite-handed modes, meaning the average OAM close to be zero and sacrificing some application potentials [12]. Therefore, stable and pure optical vortex sources are highly desirable in practice. Most recently, methods to distinguish the degenerated LG modes based on introducing different losses to them have been researched, for example, inserting nanoscale thickness wires or a tilted uncoated YAG plate [13,14]. But being two separate optical elements, both the helicity controller and Q-switch added to resonator will unavoidably introduce large insertion loss and result in structural complexity. As a new and interesting two-dimensional (2D) material, black phosphorus has been lately rediscovered as an irreplaceable broadband saturable absorber (SA), especially for the infrared part of the spectrum comparing with other 2D layer materials, due to its unique electronic and optical properties [15–17]. Thus, a function-integrated optical element for generation of well-defined vortex pulses was expected to be fabricated by transferring this material to helicity controller.

In this letter, we exploited a home-made black phosphorus plate (BPP) to simultaneously realize the Q-switched modulation and helicity control for vortex laser at ~1.6 µm in a compact cavity configuration, and finally pulsed optical vortex with controllable topological charge of l = + 1, −1, + 2, −2 were produced. To our best knowledge, this is the first time to verify the efficient modulation for different order transverse modes by black phosphorus material. Moreover, the home-made BPP provides a new way to enable the realization of well-determined pulsed vortex in a very simple resonator.

2. Experimental results and discussion

The ultrathin black phosphorus nanosheets were prepared by liquid exfoliation of the bulk sample [18]. In detail, black phosphorous ground powders of ≈0.2 mg through grinding the bulk BP (Smart Elements, purity 99.998%) using a mortar was immersed in 15 mL of dimethylformamide (DMF). The mixture solution was then sonicated in ice water for 8 hours. The temperature of the bath was maintained below 30 °C throughout using a water cooling coil. Afterward, the solution was centrifuged for 30 min in 2000 rpm and the top 50% of the solution was collected and filtered using a Sigma-Aldrich vacuum filtration assembly on a polytetrafluoroethylene (PTFE) membrane filter of 0.1 µm pore size under argon protection. The filtered film was then thoroughly washed 3 times by isopropyl alcohol (IPA) to remove the solvent residue. Thereafter, the stacked flakes were dispersed in IPA liquid, as shown in Fig. 1(a), and was drop cast on one side of a 0.3 mm-thick polished glass plate using a pipette and dried in the clean room at room temperature for 24 hours. To confirm that the BP nano-platelets had been successfully transferred on the glass plate, we performed a morphology analysis with an atomic force microscopy (AFM). Figures 1(b) and 1(c) give the AFM image and the typical height profiles of BP nano-platelets implying that the average thickness of the phosphorene sheets should be about 4 nm. Given that the thickness of 0.6 nm for single layer BP, the as-prepared phosphorene sheets are ~7 layers thick, which means that the band gap of our BP sheets is about 0.71 eV and suitable for being used as an optoelectronic device working at a wavelength shorter than 1.75 µm [16,19]. The transmission of fabricated BPP was measured to be 94% at 1645 nm by a spectrophotometer.

 

Fig. 1 (a) BP liquid sample prepared in the laboratory; (b) AFM image and (c) typical height profiles of the phosphorene sheets.

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To investigate the BPP’s ability of vortex modulation in bulk lasers, we chose 1.0 at. %-doped Er:YAG transparent ceramic with dimension of 2mm*3mm*14.5mm and highly reflective coating at pump wavelength region as gain medium. A fiber-coupled CW diode laser at 1532 nm (fiber core diameter of 200 µm and numerical aperture of 0.1) was employed as pumping source. By a specially fabricated mirror and an optics coupling system, as discussed in our previous work [20], an annular pump beam was focused into the Er:YAG, which was wrapped with indium foil and placed in a Cu holder of 17 °C, cooled by water. A 3-cm straight plane-concave cavity we constructed was composed of a plane input mirror with high transmission (HT) at 1532 nm and high reflectivity (HR) at 1645 nm, as well as a 10% transmissive output coupler (OC) for 1645 nm with a radius of curvature of 200 mm, as shown in Fig. 2(a), to satisfy the best mode-matching conditions between annular pump beam and LG₀₁ mode. The BPP was placed into the cavity close to OC. The right image in Fig. 2(a) is the intensity distribution of output beam captured by a mid-infrared camera (Xenics-1.7).

 

Fig. 2 (a) Schematic of experimental setup used to excite the pulsed vortex laser and the intensity profile of the output; (b) Output polarization state at absorbed pump power of ~7.5 W; (c)The produced interference patterns with different tilt angles of BPP.

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Firstly, we measured the polarization states of laser with a Glan-Taylor prism and found that the output beam was nearly linear-polarized with a long-axis-to-short-axis intensity ratio of 20:1, as illustrated by Fig. 2(b). This lasing behavior might be attributed to thermal birefringence inside the gain medium [21]. Thereafter, the spiral-propagation symmetry and degeneracy of LG_{0, + 1} and LG_0,-1 modes were expected to be broken through introducing different Fresnel reflection losses by the uncoated polished side of BPP based on their discriminating Poynting vectors [14]. Using a home-made Mach-Zehnder interferometer, the interference patterns were recorded. Through optimizing the position and fine-tuning the angle of the BPP, the interference fringes could be stable at one handedness when the BPP was tilted to 4° (or −3.5°), while this helicity selection mechanism was invalid and the inference fringes turned disordered structure when tilted angle was close to 0° (as shown in Fig. 2(c)). For further confirmation of the output mode, we measured the beam-quality factor (M²) of the output beam, and the value of 2.1 is coincident well with the theoretical value, i.e. 2, of LG₀₁ mode. Although in this work the mode purity was not quantitatively characterized as in [22,23], the M² parameter and clear helix fringes could sufficiently demonstrate the output was stable and well-determined LG_0,-1 or LG_{0, + 1} mode [24]. Thus we are able to confirm the BPP can efficiently function as a helicity controller in this vortex laser.

Then we investigated the laser performance under Q-switched operation regime. The output laser oscillating near the threshold was observed to run in disordered self-pulses with pulse jitter as described in [25]. When the absorbed pump power was increased to 6.99 W, stable vortex pulses fixed in LG_0,-1 (or LG_{0, + 1}) mode were obtained. Their average output powers and the corresponding pulse energies versus the absorbed pump power are given in Fig. 3. Under 7.62 W absorbed pump power, the maximum average output power of the stable Q-switched LG_0,-1 laser with left-handedness was 86 mW corresponding to a pulse energy of 2.15 μJ, and maximum 87 mW average power of pulsed LG_{0, + 1} laser with right-handedness was obtained with 2.4 μJ pulse energy. The relatively low laser efficiencies were attributed to the insertion loss introduced by the tilted BPP in pursuit for the purity of transverse mode. As we continued to increase the pump power, the passive Q-switched pulses started to become unstable, which could be understood mainly being caused by the over-saturation of BP absorber [26]. Figure 4 respectively shows the two modes’ dependences of the pulse durations and repetition rates on the absorbed pump power. Upon increasing the incident pumped power, the pulse width became narrower and the repetition frequency became higher in both left- and right-handed beams. When fixed at left-handedness, the generated Q-switched pulses had the highest repetition rate of 40 kHz and the shortest pulse width of 2.3 μs. With the helicity being fixed at right-handedness, the highest pulse repetition rate was 36.3 kHz and the shortest pulse width was 2.55 μs. Their typical oscilloscope pulse trains at the maximum average output power are respectively displayed in Fig. 5. The inset are the temporal shapes of the corresponding narrowest single pulses.

 

Fig. 3 Average output power and pulse energy versus the absorbed pump power.

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Fig. 4 Pulse repetition rate and pulse width versus the absorbed pump power.

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Fig. 5 BP-Q-switched pulse trains of vortex laser with opposite handedness, and the corresponding typical single pulses under 7.62W absorbed pump power.

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Such function-integrated BPP was also applied to achieve high-order well-determined LG modes pulses in our experiment. We adopted an OC mirror with 100 mm radius of curvature and adjusted the length of resonator to appropriately reduce the lasing modes’ sizes, making LG₀₂ the best one to match with pump beam. The tilted angles for selecting the helicity of LG₀₂ modes, i.e. 3.6° and 3.3°, were found a little smaller than LG₀₁ modes, which might due to the smaller overlap areas of LG₀₂ modes than LG₀₁ modes with the same annular pump [27]. Thus a little difference between Fresnel losses for the two opposite-handed LG₀₂ modes could induce larger difference between their oscillation thresholds [28]. When the average output power was ~77 mW, well-distinguished LG_{0, + 2} and LG_0,-2 mode pulses with respectively the shortest pulse width of 3.2 µs and 2.9 µs were successfully obtained in this work, which also verified the homogeneity and validity of the home-made BPP. Figure 6 gives their corresponding interference fringes, and the helicity could be switched from each other by adjusting the plate’s tilt angle. Higher order LG pulses are also expected to be generated in this route and they have promising applications in future optical communication, quantum entanglement manipulation, etc.

 

Fig. 6 Interference patterns of (a) LG_{0, + 2} mode and (b) LG_0,-2 mode.

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3. Conclusions

In summary, we realized the generation of 1645 nm vortex pulses with well-defined helicity from a compact Er:YAG ceramic laser. A ring-shaped pump beam was used to selectively excite LG₀₁ mode with annular intensity profile. Both the robust helicity control and Q-switched modulation for vortex laser were based on an intracavity BPP fabricated by liquid deposition method. Consequently, LG_0,-1 mode pulses with maximum pulse energy of 2.15 μJ and LG_{0, + 1} mode pulses with maximum 2.4 μJ pulse energy were obtained individually, as well as pulsed LG_{0, ± 2} laser beams. Our experimental results sufficiently validated the efficient pulse modulation for different order transverse modes by black phosphorus material for the first time, as far as we know. Such method is also expected to be applicable for generation of higher-order LG mode pulses with well-determined handedness.