A vortex beam is a classic type of spatially structured light beam that shows a spiral wavefront with a centrally located phase singularity and carries an orbital angular momentum (OAM) of $lh$ ($l$ is the topological charge; $h$ is the reduced Planck constant) per photon [1–4]. The current research of the vortex beam mainly addresses vortex generation [5–7], OAM manipulation [4,8], and special optical vortex [9,10]. Owing to these distinctive properties, vortex beams attracted much attention in optical communication [11,12] and optical tweezers [13] as soon as being discovered. In order to serve various demands of applications, spatial and temporal modulation such as the spatiotemporal coherence control of a vortex beam is creating extensive concern. Previous studies have shown that spatial coherence modulation makes vortices perform unique optical effects, which are different from those of conventional completely coherent vortices and extend a new branch called the “partially coherent vortex beam” [14,15]. Conspicuous behavior of a partially coherent vortex beam is that intensity distribution would be transformed from a hollow profile into a solid core along with degeneration of spatial coherence [10]. This effect can achieve Gaussian, flat, or hollow profiles of beam intensity easily via spatial coherence modulation, which allows a vortex beam to demonstrate great performance in particle trapping [16]. Moreover, the degree of spatial coherence of a partially coherent vortex beam is confirmed to be capable of self-reconstruction, further extending its applications in information transmission and recovery [10]. Practical applications such as free space optical communication may be challenged by atmospheric turbulence-like scintillation of light intensity, where a partially coherent vortex beam behaves better in decreasing scintillation than a partially coherent beam [17].

Up to now, most of the reported vortex fiber lasers have employed a defined cavity structure [18–20]. As we know, the demonstration of a cavity-structured fiber laser with stable temporal characteristics is, however, not trivial for the influence of a common self-pulsing factor [21–23]. Further, modulation of an obtained vortex fiber laser is difficult. Hence, a temporal stable laser source is crucial for the spatiotemporal modulation of a vortex fiber laser [24–27].

At this point, a temporally stable random fiber laser (RFL) could be a remarkable option for light sources to generate a vortex beam. As a new type of laser regime, an RFL employs Rayleigh scattering (RS) to provide randomly distributed feedback and stimulated Raman scattering (SRS) to realize power amplification [28,29]. Different from the rare-earth-doped fiber lasers, whose emission windows are located at several discrete wavebands, an RFL enabled by Raman gain in the passive fiber has become a ready-made and well-suited platform to obtain a wavelength-tunable output. Besides, low coherence of an RFL leads to weak speckle effect in imaging, which can generate vortex beams with more homogeneous intensity distribution and may be of great help for optical tweezers. The simple structure of an RFL also attracts great attention for its potential to realize cost-effective practical applications. Due to these unique properties, RFLs have been widely used in optical communication [30,31], remote sensing [32], frequency conversion [33], and ultrafast lasing [34]. Since the first demonstration of an RFL, many efforts on power scaling [35–38], polarization [39,40], and spectral manipulation [41,42] have been made. As a significant manifestation, temporal property of an RFL has also been of great interest. Previously studies have demonstrated experimentally that, an RFL, especially if pumped by an amplified spontaneous emission (ASE) source [23], demonstrates ideal temporal stability with suppressed amplitude fluctuation, which allows an RFL to exhibit superior quality in various applications, such as midinfrared laser [43] and pulsing operation [44,45]. It is promising that the demonstration of a vortex RFL could incubate novel practical applications and further offer a platform for investigation of the vortex beam’s temporal modulation and an RFL’s optical field control.

In this paper, a vortex RFL with a controllable OAM mode has been proposed and experimentally realized for the first time to the best of our knowledge. Distinct spiral phase behaviors derived from an annular vortex beam with a dark hollow can be distinguished, and the topological charge of the vortex beam can range from $-50\mathrm{t}\mathrm{o}50$ with nearly watt-level output power. Verification and wavefront analysis have been accomplished via a triangular toroidal interference setup; fractional phases are also performed, indicating that the generated vortex RFL can provide a potential source for many applications, such as imaging, sensing, and communication.

Figure 1(b) illustrates the interferometer with a triangular toroidal structure, formed by a beam splitter (BS), a reflector with the reflectivity $>99.9\%$ at 1000–1400 nm, and the SLM. In the transmissive path, the function of SLM is to manipulate the vortex RFL, while it is also utilized as a reflective mirror in the reflective path. After reconvergence inside the BS, the interference light is reflected, and real-time interferograms are captured by a CCD camera after being focused via a convex lens. By loading different holograms onto the SLM, the desired laser modes can be gathered.

To verify the spiral phase of generated vortex RFL, an interferometer is constructed. A matter to be aware of is that the coherence property of RFL has not been investigated systematically thus far, while it is a common view for researchers that the spatiotemporal coherence of a random laser is lower than that of a conventional laser, which enables an RFL to demonstrate better performance in many applications such as speckle-free imaging [46,47]. In this work, the temporal coherence plays a dominant role, as a passive fiber only supports two propagation modes in the wavelength range around 1090 nm, which is unsatisfied for the spatial coherence to be regarded. Besides, the real-time output spectra of an RFL are obtained in Ref. [48], and the average total spectrum can be seen as an intensity envelope with a wide bandwidth, which determines the temporal coherent length (about a few millimeters in this work). Therefore, it is difficult to employ the common parallelogram path, namely, the Mach–Zehnder (M–Z) interferometer, in regulating the optical path difference (OPD), where the incident beam is separated into two completely independent beams, and the interference performances are affected largely by the temporal coherence feature of the RFL. To address this challenge, we utilize a triangular loop [see Fig. 1(b)]. Two beams pass through three sides of the same triangle in the loop, consequently ensuring that OPD is strictly zero and even further simplifying the setup. The interference fringes of vortex RFL with $l$ from 1 to 5 acquired by the CCD camera are shown in Fig. 3(c). It can be distinguished that the generated interference fringes vanish at the center of each interferogram, where a phase singularity exists, and form a fork pattern located in the center. Further, the number of the disappeared fringes is the same as in the topological charge $l$. At this point, the validity and the spiral phase of vortex RFL generated above are confirmed.

In fact, apart from the SLM, there are many other devices that can achieve vortex conversion, such as the spiral phase plate (SPP) and the mode-selective coupler (MSC). The SPP is widely applied in the generation of a vortex beam [49–53] with the advantages of convenient operation and high-power affordability. The MSC allows an all-fiber structure of the vortex beam generation [54–57] by virtue of operation stability, low intermode crosstalk, and rapid response rate. However, these two modulators are confined to single-functionality, which means that, for one wavelength, vortex beams can be generated only with a single topological charge, making it difficult to reach large topological charges. In this work, generation and verification of the vortex RFL are in demand for the extensible control of the topological charge and real-time monitoring of vortex beam. From our perspective, the SLM, which can realize dynamically controllable vortex beams with flexible operation, high control precision, and high resolution, is a preferable option among various modulators of vortex conversion.

In summary, a vortex RFL with controllable OAM mode is successfully developed and experimentally realized. The topological charge of the vortex beam can range from $-50\mathrm{t}\mathrm{o}50$ with nearly watt-level output power, and the spiral wavefront distribution is verified by implementing a triangular toroidal interferometer for a generated random laser with special coherence property. The intensity distributions of vortex spots are extremely rounded and homogeneous, which reveal central dark hollows; further, helical wavefront behaviors can be distinguished as unambiguous fork shapes. Fractional vortex RFLs are also analyzed, indicating that the generated vortex RFL follows the same physical laws as common vortices. This work may not only offer a new approach to temporal modulation of vortex beams and optical field control of an RFL but also provide an alternative laser source for vortex beams to expand their application in imaging, sensing, and communication.

Acknowledgment. We are grateful to T. Hou for his important help with this work.