Quantum mechanics

Topological quantum number

Coherence (philosophical gambling strategy)

Gravitational singularity

Optical vortex

Coherence theory

Vortex

Singularity

Computer science

Thermodynamics

Physics

Database

Mathematics

Optics

Superconductivity

Condensed matter physics

Geometry

Measure (data warehouse)

Combinatorics

Topology (electrical circuits)

Coherence length

Dislocation

Science China Physics Mechanics and Astronomy

It has been over 30 years since the concept of optical vortices was first proposed by Coullet et al. in 1989, and the field of structured beams has grown extremely. In the last two decades, partially coherent vortex beams (PCVBs) have received increasing interest in the fields of optical manipulation, optical communication, optical imaging, etc., and great progress has been made in the area of the coherence singularities, generation methods, topological charge measurements, and promising applications of PCVBs. In this review, we firstly outline the basic concepts of PCVBs. We explicate the relationship between the coherence vortices and optical vortices, and the evolution behavior of optical vortices to coherence vortices is summarized in detail. We discuss a special form of coherence singularity, ring dislocation, mathematically and physically. The ring dislocation in the correlation functions under low coherence is dependent on the mode indices, which provide a feasible approach to measure mode indices of PCVBs. Subsequently, we summarize the various methods for measuring the topological charge of PCVBs, highlight the measurement method based on the cross-correlation function, and a physical explanation on the relation between ring dislocation and topological charge is given. After that, we review the recent advances on experimental generation of several kinds of PCVBs. Lastly, we give an overview on the potential applications of PCVBs.

Partially coherent vortex beams: Fundamentals and applications