The propagation of vortex beams through weak-to-strong atmospheric turbulence is simulated and analyzed. It is demonstrated that the topological charge of such a beam is a robust quantity that could be used as an information carrier in optical communications. The advantages and limitations of such an approach are discussed.

Partially coherent beams hold much promise in free-space optical communications for their resistance to the deleterious effects of atmospheric turbulence. We describe the basic theoretical and computational tools used to investigate these effects, and review the research to date.

We demonstrate how the unusual mathematics of transfinite numbers, in particular, a nearly perfect realization of Hilbert’s famous hotel paradox, manifests in the propagation of light through fractional vortex plates. It is shown how a fractional vortex plate can be used, in principle, to create any number of “open rooms,” i.e., topological charges, simultaneously. Fractional vortex plates are therefore demonstrated to create a singularity of topological charge, in which the vortex state is completely undefined and in fact arbitrary. These results hint that transfinite mathematics is much more common and important to optical systems than previously imagined.

We undertake a computational and experimental study of an advanced class of structured beams, partially coherent radially polarized vortex (PCRPV) beams, on propagation through atmospheric turbulence. A computational propagation model is established to simulate this class of beams, and it is used to calculate the average intensity and on-axis scintillation index of PCRPV beams. On comparison with other classes of structured beams, such as partially coherent vortex beams and partially coherent radially polarized beams, it is found that the PCRPV beams, which structure phase, coherence and polarization simultaneously, show marked improvements in atmospheric propagation. The simulation results agree reasonably well with the experimental results. These beams will be useful in free-space optical communications and remote sensing.

Close to the ground, it is generally known that atmospheric turbulence exhibits strong anisotropy, which affects the performance of applications such as free-space optical (FSO) communication. In this paper, we establish a theoretical model for calculating the spiral spectrum, also called the orbital angular momentum (OAM) spectrum, of a Laguerre-Gaussian (LG) beam after propagation through anisotropic turbulence along a horizontal link. This model isolates the effects of anisotropy from other parameters of the turbulence. On the basis of this model, the effects of the anisotropy on the probability density of the OAM spectrum and its corresponding modal crosstalk are studied through numerical examples. Our simulation results show that the width of the OAM spectrum will increase or slightly decrease depending on the specific nature of the anisotropy. In addition, it is demonstrated that the inner scale is more likely to cause modal crosstalk than the outer scale. Some strategies to reduce modal crosstalk in anisotropic turbulence are also discussed. Our results may be useful in OAM-based FSO communication at ground level.

It is now well‐appreciated that a bandlimited wave can possess oscillations much more rapidly than those predicted by the bandlimit itself, in a phenomenon known as superoscillation. Such superoscillations are required to be of dramatically smaller amplitude than the signal they are embedded in, and this has initially led researchers to consider them of limited use in applications. However, this view has changed in recent years and superoscillations have been employed in a number of systems to beat the limits of conventional diffraction theory. In this review, we discuss the current state of research on superoscillations in terms of superresolved imaging and subwavelength focusing, including the use of special non‐diffracting and Airy beams to carry transverse superoscillating patterns. In addition, we discuss recent analogous works on using superoscillations to break the temporal resolution limit, and also consider the recently introduced inverse of superoscillations, known as suboscillations.