Coherence engineering of partially coherent vortex fields: theory, metrology, and applications

Partially coherent vortex fields combine optical singularities with controllable statistical correlations, forming an important research platform at the intersection of singular optics, statistical optics, and structured-light science. Since the publication of the 2019 review on vortex beams with low spatial coherence, the field has witnessed substantial advances. In particular, coherence has evolved from a statistical parameter that modifies vortex beams into a designable degree of freedom for engineering structured optical fields through tailored correlation functions. By manipulating second-order correlation structures, coherence engineering enables the generation of multidimensional optical states, the control of propagation dynamics, and the realization of functionalities beyond conventional field engineering approaches. This review summarizes major developments since 2019, highlighting progress in source engineering, coherence-controlled propagation physics, intelligent metrology, and emerging applications. Particular attention is given to correlation-engineered fields, robustness and angular-momentum transport in complex environments, machine-learning-assisted characterization, and applications in optical manipulation, communications, information security, imaging, and sensing. We further discuss emerging directions including multidimensional coherence engineering, coherence topology, spatiotemporal structured light, and intelligent photonics. These developments suggest that the field is undergoing a transition from field engineering toward correlation engineering, in which tailored correlation structures are becoming fundamental resources for controlling optical fields, information, and topology.