The distribution of degree of coherence of a partially coherent vortex beam reveals rich information about the vortex phase, and it is known that one can determine the topological charge (or orbital angular moment) of a partially coherent vortex beam from its degree of coherence distribution in the focal plane (or in the far field). In this letter, we demonstrate both numerically and experimentally that the degree of coherence distribution of a partially coherent vortex beam that is blocked by an opaque obstacle can self-reconstruct in the focal plane. Thus, one still can determine the topological charge of an obstructed partially coherent vortex beam from its degree of coherence distribution in the focal plane. Our results can find application in information transmission and recovery.

Determination of the topological charge (TC) of a vortex beam is of significant importance in various applications such as high-capacity optical communications and micromanipulations. Though many kinds of methods, until now, have been proposed to measure the TC, most of them will fail if the measured vortex beam is partially blocked by an opaque obstacle. In this Letter, we have introduced an efficient method to determine the TC of an incomplete vortex beam (partially blocked by an obstacle) using its reconstructed phase distribution under propagation. The numerical and experimental results showed that the sign and magnitude of the TC can be simultaneously determined by counting the number of phase singularities and the directions of the phase variations around the singularities occurring in the reconstructed phase pattern, respectively. Our method works even when half of the vortex beam is blocked.

Ghost imaging with partially coherent light through two kinds of atmospheric turbulences: monostatic turbulence and bistatic turbulence, is studied, both theoretically and experimentally. Based on the optical coherence theory and the extended Huygens–Fresnel integral, the analytical imaging formulae in two kinds of turbulence have been derived with the help of a tensor method. The visibility and quality of the ghost image in two different atmospheric turbulences are discussed in detail. Our results reveal that in bistatic turbulence, the visibility and quality of the image decrease with the increase of the turbulence strength, while in monostatic turbulence, the image quality remains invariant when turbulence strength changes in a certain range, only the visibility decreases with the increase of the strength of turbulence. Furthermore, we carry out experimental demonstration of lensless ghost imaging through monostatic and bistatic turbulences in the laboratory, respectively. The experiment results agree well with the theoretical predictions. Our results solve the controversy about the influence of atmospheric turbulence on ghost imaging.

Having shown early promise, free-space optical (FSO) communications face formidable challenges in the age of information explosion. The ever-growing demand for greater channel communication capacity is one of the challenges. The inter-channel crosstalk, which severely degrades the quality of transmitted information, creates another roadblock in the way of efficient implementation of FSO communication systems. Here, we advance theoretically and realize experimentally a potentially high-capacity FSO protocol that enables high-fidelity transfer of an image or set of images through a complex environment. In our protocol, we complement random light structuring at the transmitter with a deep learning image classification platform at the receiver. Multiplexing unique, independent, mutually orthogonal degrees of freedom available to structured random light can potentially significantly boost the channel communication capacity of our protocol without introducing any deleterious crosstalk. Specifically, we show how one can multiplex the degrees of freedom associated with the source coherence radius and a spatial position of a beamlet within an array of structured random beams to greatly enhance the capacity of our communication link. The superb resilience of structured random light to environmental noise, as well as extreme efficiency of deep learning networks at classifying images, guarantees high-fidelity image transfer within the framework of our protocol.

The analytical expression of the cross-spectral density function of a twisted anisotropic Gaussian Schell-model (TAGSM) beam transmitting in turbulent ocean is derived by applying a tensor method. The statistical properties, including spectral density, the strength of twist and beam width of the propagating beam are studied carefully through numerical examples. It is demonstrated that the turbulence of ocean has no effect on the rotation direction of the beam spot during propagation. However, the beam shape will degrade into a Gaussian profile under the action of oceanic turbulence with sufficiently long propagation distance, and a beam with a larger initial twist factor is more resistant to turbulence-induced degeneration. As oceanic turbulence becomes stronger, the beam spot spreads more quickly while the twist factor drops more rapidly upon propagation. The physical mechanisms of these phenomena are addressed in detail. The obtained results will be helpful in optical communication systems underwater.

A partially coherent beam under the combined action of a Hermite-Gaussian correlated function and vortex phase, named the HGCSMLG_0l beam has been explored both theoretically and experimentally. The statistical properties, such as the intensity and distribution of the degree of coherence (DOC) on propagation are analyzed in detail, based on the deduced equations. We find that the intensity is determined dominantly by the non-conventional correlated function when the coherence length is comparatively small and by vortex phase when the coherence length is large. The modulus of the DOC is not vulnerable to coherence width, rather, it is affected by both non-conventional correlated function and vortex phase. Our results are verified well by the experiment results.