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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.

Zero-order and higher-order Bessel beams are well-known nondiffracting beams. Namely, they propagate with invariant profile (intensity) and carry a fixed orbital angular momentum. Here, we propose and experimentally study an anomalous Bessel vortex beam. Unlike the traditional Bessel beams, the anomalous Bessel vortex beam carries decreasing orbital angular momentum along the propagation axis in free space. In other words, the local topological charge is inversely proportional to the propagation distance. Both the intensity and phase patterns of the generated beams are measured experimentally, and the experimental results agree well with the simulations. We demonstrate an easy way to modulate the beam’s topological charge to be an arbitrary value, both integer and fractional, within a continuous range. The simplicity of this geometry encourages its applications in optical trapping and quantum information, and the like.

The deformation, flicker, and drift of a light field owing to complex media such as a turbulent atmosphere have limited its practical applications. Thus, research on invariants in randomly fluctuated light fields has garnered considerable attention in recent years. Coherence is a statistical property of light, while its full and quantitative characterization is challenging. Herein, we successfully realize the orthogonal modal decomposition of partially coherent beams and introduce the application of coherence entropy as a global coherence characteristic of such randomly fluctuated light fields. It is demonstrated that coherence entropy remains consistent during propagation in a unitary system by unraveling complex channels. As representative examples, we study the robustness of coherence entropy for partially coherent beams as they propagate through deformed optical systems and turbulent media. Coherence entropy is anticipated to serve as a key metric for evaluating the propagation of partially coherent beams in complex channels. This study paves the way for a broader application scope of a customized low-coherence light field through nonideal optical systems and complex media. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

The analytical nonparaxial propagation formula of an anomalous hollow beam (AHB) with orbital angular momentum (OAM) in free space is derived based on the generalized Raleigh–Sommerfeld diffraction integral. The nonparaxial properties of AHB with OAM such as intensity, phase and OAM density distributions are studied in detail, using the pertinent nonparaxial propagation formula. The comparison between the paraxial and nonparaxial results is also carried out. The results show that the nonparaxial properties of an AHB with OAM are determined by the initial beam parameters, such as beam waist size and topological charge and propagation distance. [ABSTRACT FROM AUTHOR]