Research progress on manipulating spatial coherence structure of beam and its

Optical coherence is a fundamental characteristic of light that plays a significant role in un-derstanding interference, propagation, light-matter interaction, and other fundamental aspects of classical and quantum wave fields. The study of optical coherence has led to a wide range of applications, including optical coherence tomography, ghost imaging, and free-space optical communications. In recent years, the complex spatial structure of optical coherence embedded in partially coherent light beams has garnered increasing attention due to the novel physical effects it induces, such as self-shaping, self-focusing, and self-splitting of beams in free space. Partially coherent light beams with non-classical spatial coherence structures have found use in many innovative applications, including overcoming the classical Rayleigh diffraction limit in optical imaging, reducing the side effects of atmospheric turbulence in free-space optical communications, coherence-based optical encryption, and robust optical signal transmission. In this article, we present a systematic review of the manipulation and measurement of the spatial coherence structure of optical beams, their propagation and light-matter interaction, as well as the applications of partially coherent light beams with structured optical coherence. We begin with the representation of the cross-spectral density function for a partially coherent light beam using Gori's nonnegative definite condition and Wolf's coherent-mode decomposition theory. We then discuss in detail two different strategies for experimentally manipulating the spatial coherence structure, one based on the generalized van Cittert-Zernike theorem and the other on the coherent-mode decomposition theory. Next, we provide an overview of recent progress in measuring the complex spatial coherence structure of partially coherent light beams using methods based on self-referencing holography, generalized Hanbury Brown and Twiss experiment, and incoherent modal decomposition. We study the novel physical properties of partially coherent light beams with non-conventional spatial coherence structures during their propagation in free space and through a highly focused system, as well as their interaction with atmospheric turbulence. We also discuss the effect of structured optical coherence in reducing the negative effects of atmospheric turbulence. Finally, we present the applications of spatial coherence structure engineering in optical imaging, optical encryption, robust information transmission through complex media, particle trapping, refractive index measurement, beam shaping, and ultrahigh precision angular velocity measurement. Optical coherence structure not only provides a new degree of freedom for light manipulation but also offers an effective tool for novel light applications.