Partially coherent beams with nonconventional correlation functions have displayed many extraordinary properties, such as self-focusing and self-splitting, which are totally different from those of partially coherent beams with conventional Gaussian correlated Schell-model functions and are useful in many applications, such as optical trapping, free-space optical communications, and material thermal processing. In this paper, we present a review of recent developments on generation and propagation of partially coherent beams with nonconventional correlation functions.

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.

Analytical formulas are derived for the propagation of a partially coherent twisted anisotropic Gaussian Schell-model (TAGSM) beam in a turbulent atmosphere. Propagation properties of a TAGSM beam in a turbulent atmosphere are investigated in detail. It is found that a TAGSM beam will become a circular beam in a turbulent atmosphere, and low coherence and larger twist have an effect of anticircularization of the beam spot. The beam spot spreads more rapidly for lower coherence, larger twist, or stronger turbulence.

Partially coherent beam is preferred in many applications, such as free-space optical communications, remote sensing, active laser radar systems, etc., due to its resistance to the deleterious effects of atmospheric turbulence. In this paper, after presenting a historical overview on propagation of optical beams in turbulent atmosphere, we describe the basic theory for treating the propagation of optical beams in turbulent atmosphere and we mainly introduce recent theoretical and experimental developments on propagation of partially coherent beam in turbulent atmosphere. Recent progress on the interaction of a partially coherent beam with a semirough target in turbulent atmosphere and the corresponding inverse problem are also reviewed.

We introduce one kind of partially coherent beam with a nonconventional correlation function named the Hermite-Gaussian correlated Schell-model (HGCSM) beam. It is found that a HGCSM beam exhibits self-splitting properties on propagation in free space, i.e., the initial single beam spot evolves into two or four beam spots in the far field depending on the initial beam orders, which are closely related to the beam width and coherence widths of the HGCSM beam, and a focused HGCSM beam exhibits splitting and combining properties near the focal plane. Furthermore, we report experimental generation of a HGCSM beam and demonstrate splitting and combining properties of a focused HGCSM beam in experiment. The phenomenon of correlation-induced self-splitting will be useful for attacking multiple targets, trapping multiple particles, and guiding atoms.

Information encryption with optical technologies has become increasingly important due to remarkable multidimensional capabilities of light fields. However, the optical encryption protocols proposed to date have been primarily based on the first-order field characteristics, which are strongly affected by interference effects and make the systems become quite unstable during light–matter interaction. Here, we introduce an alternative optical encryption protocol whereby the information is encoded into the second-order spatial coherence distribution of a structured random light beam via a generalized van Cittert–Zernike theorem. We show that the proposed approach has two key advantages over its conventional counterparts. First, the complexity of measuring the spatial coherence distribution of light enhances the encryption protocol security. Second, the relative insensitivity of the second-order statistical characteristics of light to environmental noise makes the protocol robust against the environmental fluctuations, e.g, the atmospheric turbulence. We carry out experiments to demonstrate the feasibility of the coherence-based encryption method with the aid of a fractional Fourier transform. Our results open up a promising avenue for further research into optical encryption in complex environments.