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.

Acquiring topological charge in real-time for vortex beams encounters numerous challenges due to the turbulent atmosphere and coherence degradation. We propose an experimental scheme employing the strong detail extraction capability of deep neural networks to recognize the topological charge of partially coherent vortex beams propagating through the turbulent atmosphere and encountering unknown obstacles. Notably, coherence modulation has demonstrated advantages in deep neural network-based recognition. By comparing with high-coherence vortex beams, the deep neural network accurately recognizes topological charges for low-coherence vortex beams using only half of the available dataset. Furthermore, when the turbulent atmosphere and obstacles were considered, the accuracy of low-coherence vortex beams surpassed that of high-coherence vortex beams with equal amounts of training data. Additionally, the encrypted optical communication using partially coherent vortex beams was demonstrated. The coherence parameter significantly enhanced the channel capacity. This study holds potential for applications in free-space optical communication.

For a partially coherent Bessel–Gaussian (PCBG) vortex beam, information regarding the topological charge (TC) is hidden in the phase of the cross-spectral density (CSD) function. We theoretically and experimentally confirmed that during free-space propagation, the number of coherence singularities is equal to the magnitude of the TC. In contrast to the Laguerre–Gaussian vortex beam, this quantitative relationship only holds for the case with an off-axis reference point for the PCBG vortex beam. The phase winding direction is determined by the sign of the TC. We developed a scheme for CSD phase measurement of PCBG vortex beams and verified the aforementioned quantitative relationship at different propagation distances and coherence widths. The findings of this study may be useful for optical communications.

A partially coherent beam under the combined action of a Hermite-Gaussian correlated function and vortex phase, named the HGCSMLG_0l beam has been explored both theoretically and experimentally. The statistical properties, such as the intensity and distribution of the degree of coherence (DOC) on propagation are analyzed in detail, based on the deduced equations. We find that the intensity is determined dominantly by the non-conventional correlated function when the coherence length is comparatively small and by vortex phase when the coherence length is large. The modulus of the DOC is not vulnerable to coherence width, rather, it is affected by both non-conventional correlated function and vortex phase. Our results are verified well by the experiment results.

Measuring the complete complex correlation matrix of a partially coherent vector beam is extremely important for transmission calculation, encryption, and decryption for free-space optical communication and optical imaging. Based on self-referencing holography, we introduce a simple and efficient setup to measure the complex-valued cross spectral density matrix of a partially coherent vector beam, without any priori assumptions or approximations of the source. To verify the feasibility of our method, 2 $\times$ 2 complex-valued cross spectral density components in the matrix function of particularly correlated radially polarized partially coherence beam have been measured. The experimental measurements are in good agreement with the theoretical model.