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.

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.

We introduce a general optical system for synthesis of partially coherent vector beams with a variety of correlation functions. In particular we employ it for generation of the family of beams, termed the specially correlated radially polarized (SCRP) beams and examine their free-space propagation both theoretically and experimentally. Our results clearly show that a SCRP beam exhibits unique features on propagation in comparison with those of beams with conventional correlation functions. The technique for modulation of the correlation functions and, hence, the coherence state of a SCRP beam in the source plane leads to efficient control of its intensity distribution and its degree of polarization on propagation, which is of importance in particle trapping and material thermal processing applications.

Laguerre-Gaussian correlated Schell-model (LGCSM) vortex beam is introduced as an extension of LGCSM beam which was proposed [Opt. Lett. 38, 91 (2013) Opt. Lett. 38, 1814 (2013)] just recently. Explicit formula for a LGCSM vortex beam propagating through a stigmatic ABCD optical system is derived, and the propagation properties of such beam in free space and the focusing properties of such beam are studied numerically. Furthermore, we carry out experimental generation of a LGCSM vortex beam, and studied its focusing properties. It is found that the propagation and focusing properties of a LGCSM vortex beam are different from that of a LGCSM beam, and we can shape the beam profile of a LGCSM vortex at the focal plane (or in the far field) by varying its initial spatial coherence. Our experimental results are consistent with the theoretical predictions, and our results will be useful for particle trapping.