In the context of multifunctional operation and diversified application requirements, how to expand the controllable degrees of freedom of vortex beams has become an urgent scientific problem to be solved. Compared to traditional vortex beams with one phase singularity, multi-singularity vortex beams generated by vortex coherent superposition can achieve precise control on phase singularities, significantly enriching the control methods of phases in structured light fields. Light sources are crucial for the application of structured beams. Compared to highly coherent structured beams, partially coherent structured beams are proven to have the ability of anti-turbulence scintillation and speckle suppression, which demonstrate significant advantages in atmospheric transmission and imaging. As a common partially coherent fiber laser, random fiber lasers (RFLs) which employ Rayleigh scattering in passive fibers to provide random distributed feedback are widely adopted as illumination sources for structured light fields. Currently, various typical structured beams such as LP₁₁ mode, vortex beam, and cylindrical vector beam have been generated and controlled based on RFLs. However, there are no reports on RFL-based multi-singularity vortex beams. The combination of the partial coherence of RFLs and singularity control of structured beams can expand the multidimensional manipulation of structured light fields, and the application scope in many fields such as optical tweezers, free-space communication, and speckle correlation imaging. Here, multi-singularity vortex beams generated by an RFL are firstly proposed and demonstrated. The RFL with a central wavelength of 1081.3 nm is constructed and employed as the illumination. By coherent superposition between Laguerre-Gaussian (LG) beams with different topological charges, multi-singularity vortex beams with controllable singularity numbers are achieved.

Coherent superposition of two zero-order LG beams is simulated and analyzed. The distribution of superimposed light field is given by Eq. (4), and intensity and phase distributions of superposition states with different topological charges are obtained. The RFL is experimentally built with a backward-pumped half-opened cavity, as shown in Fig. 5(a). The pump light is provided by a 1030 nm ytterbium-doped fiber oscillator, and the output end is connected with a cladding power stripper (CPS) to filter out the cladding light. A circulator (Cir) is mounted after the CPS to protect the pump source from backward light. Subsequently, by employing a 1030 nm/1080 nm wavelength division multiplexer (WDM), the 1030 nm pump light is injected into a 5 km single-mode fiber (SMF) with a core/cladding diameter of 8 μm/125 μm. The generated 1081.3 nm signal light is reflected by a highly reflective fiber Bragg grating (HR FBG, the center wavelength of 1081.3 nm and reflective bandwidth of 0.07 nm), and then it is emitted via the WDM. The laser gain of the RFL is provided by stimulated Raman scattering in the SMF, and the feedback is offered by both random distributed scattering in the SMF and point feedback of the HR FBG. By utilizing the RFL as the illumination, a spatially optical path is constructed to generate a multi-singularity structured light field [Fig. 5(b)]. The Gaussian beam from the RFL is firstly collimated and expanded, and then transmitted into horizontally polarized beam with high polarization degree and adjustable intensity by two polarization beam splitters (PBS1, PBS2) and a half wave plate (HWP). After a 50∶50 non-polarization beam splitter (BS), the horizontally polarized beam is divided into a transmitted beam and a reflected beam, which are incident at different positions of the spatial light modulator (SLM) after being reflected. By loading different phase maps on the SLM, two vortex beams with different topological charges can be obtained. Meanwhile, interference is conducted on the two vortex beams by the BS to form a vortex superposition state with multiple singularities. The intensity of the superimposed beam is focused via a lens and collected by a CCD camera.

The superimposed intensity distributions of zero-order LG beams with different topological charges perform petal patterns, and the number of petals is l1-l2. Meanwhile, the phase distributions of the superimposed beams vary according to different topological charges. The phase distributions obtained by superimposing two zero-order LG beams with equal absolute value and opposite signs of topological charges are shown in Fig. 1, with no spiral phase wavefront. Superposition states generated by zero-order LG beams with unequal absolute values of topological charges are described in Figs. 2, 3, and 4, and have the characteristic of spiral phase wavefront with newborn phase singularities due to phase coupling. The newborn singularity number is l1-l2, and the total singularity number is l1-l2+1. The topological charge of the central singularity corresponds to the topological charge of the LG beam with a smaller diameter. The absolute values of topological charges of the newborn singularities are 1, which are uniformly distributed around the central singularity.

The output characteristics of the RFL are demonstrated in Fig. 6. The central wavelength of the random laser is located at 1081.3 nm with a generation threshold of 2.36 W and a maximum power of 2.26 W, corresponding to a slope efficiency of 58.91%. Further power enhancement is limited by the stimulated Raman scattering effect. The 3 dB bandwidth of the RFL gradually widens with the increasing pump power, reaching a maximum of 0.23 nm. The vortex superposition states using the RFL as the illumination are plotted in Figs. 7 and 8. The experimental beam spots are consistent with the simulation results. By changing the topological charge of the LG beam, the singularity number of the generated multi-singularity vortex beam can be flexibly switched.

Partially coherent multi-singularity vortex beams generated by an RFL are firstly proposed and demonstrated. The superposition state of two zero-order LG beams is simulated. The results indicate that vortex superposition states with equally absolute values and opposite signs of topological charges show no spiral phase distribution, while the states with unequal absolute values of topological charges generate new phase singularities due to phase coupling between the two LG beams. Additionally, a random distributed feedback fiber laser with a central wavelength of 1081.3 nm is constructed, with a maximum output power of 2.26 W. By employing the RFL as the illumination, a spatially triangular interference path is built to achieve coherent superposition of vortex beams. Multi-singularity vortex beams with various intensity distributions are generated, and newborn singularities are uniformly distributed around the central singularity. The total singularity number is l1-l2+1, which can be flexibly tuned by adjusting the topological charges of the two LG beams. This work may expand the application scope of RFLs, and provide light sources for many fields such as particle trapping, vortex optical multiplexing communication, and imaging.