As an indispensable complement to an integer vortex beam, the fractional vortex beam has unique physical properties such as radially notched intensity distribution, complex phase structure consisting of alternating charge vortex chains, and more sophisticated orbital angular momentum modulation dimension. In recent years, we have noticed that the fractional vortex beam was widely used for complex micro‐particle manipulation in optical tweezers, improving communication capacity, controllable edge enhancement of image and quantum entanglement. Moreover, this has stimulated extensive research interest, including the deep digging of the phenomenon and physics based on different advanced beam sources and has led to a new research boom in micro/nano‐optical devices. Here, we review the recent advances leading to theoretical models, propagation, generation, measurement, and applications of fractional vortex beams and consider the possible directions and challenges in the future.

In an optical vortex (OV) field, the orbital angular momentum (OAM) distribution strongly depends on the intensity, which results in difficulty in OAM independent modulation. To overcome this limitation, we propose a grafted optical vortex (GOV) via spiral phase reconstruction of two or more OVs with different topological charges (TCs). To remain the annular shape of the GOV's intensity, the Dirac δ-function is employed to restrict the energy in a ring. Theoretical analysis and manipulation experiments of polystyrene microspheres show that the magnitude and direction of the GOV's local OAM are controllable by modulating the grafted TCs while the intensity remains constant. The results of this work provide an ingenious method to control the local tangential force on the light ring, which will promote potential applications in optical trapping and rotating micro-particles.

For optical tweezers, a tiny focal spot of the trapping beam is necessary for providing sufficient intensity-gradient force. This condition results in a limited small trapping range to guarantee stable trapping of the particle. Exploiting structured light, i.e., an optical vortex beam, the trapping range can be enlarged by adjusting its doughnut ring diameter. However, the trapped particle scarcely remains static due to the optical spanner action of the orbital angular momentum of the vortex beam. To enlarge the trapping range and simultaneously ensure stable trapping, we propose a beam, referred to as a mirror-symmetric optical vortex beam (MOV). Essentially, MOV is constructed by using two opposite optical spanners and a pair of static optical tweezers. The optical spanners attract the particle to the site of the static optical tweezers, which realizes long-range optical trapping. Through detailed force-field analysis, it is found that MOV could perform these setting functions. In experiments, yeast cells are manipulated in a long range of ∼25 μm, which is 3 times longer than that of the Gaussian beam. Further, the trapping range is easily adjusted by changing a parameter as desired. This technique provides versatile optical tweezers, which will facilitate potential applications for particle manipulation.

Twist phase is a nontrivial second‐order phase that only exists in a partially coherent beam. Such twist phase endows the partially coherent beam with orbital angular momentum (OAM) and has unique applications such as in super‐resolution imaging. However, the manipulation and the detection of the twist phase are still far from easy tasks in experiment. In this work, we present a flexible approach to generate a famous class of twisted Gaussian Schell‐model (TGSM) beam with controllable twist phase by the superposition of the complex field realizations using a single phase‐only spatial light modulator. The precise control of the amplitude and phase of the field realizations allows one to manipulate the strength of the twist phase easily. In addition, we show that the twist factor, a key factor that determines the strength of twist phase and the amount of OAM, can be measured by extracting the real part of the complex degree of coherence of the TGSM beam. The experiment is carried out with the help of the generalized Hanbury Brown and Twiss experiment as the generated TGSM beam obeys Gaussian statistics. The flexible control and detection of the twist phase are expected to find applications in coherence and OAM‐based ghost imaging.

In this study, an anomalous ring-connected optical vortex array (ARC-OVA) via the superposition of two grafted optical vortices (GOVs) with different topological charges (TCs) has been proposed. Compared with conventional OVAs, the signs and distribution of the OVs can be individually modulated, while the number of OVs remains unchanged. In particular, the positive and negative OVs simultaneously appear in the same intensity ring. Additionally, the size of the dark core occupied by the OV can be modulated, and the specific dark core is shared by a pair of plus–minus OVs. This work deepens our knowledge about connected OVAs and facilitates new potential applications, especially in particle manipulation and optical measurement.

Traditional fractional vortex beams are well-known “jump” beams: that is, their net topological charge jumps by unity as the effective topological charge of the source passes a half-integer value. Here, we propose an anomalous multi-ramp fractional vortex (AMRFV) beam. Unlike the traditional fractional vortex beams, an AMRFV beam can be designed to have arbitrary jumps in topological charge at any critical threshold of the source charge. We walk through some examples of AMRFV beams using simulations and present a clear interpretation of the multi-jump characteristic based on the evolution of phase singularities.