Deterministic vortices evolving from partially coherent fields

In recent years, research on optical wavefield singularities has led to various applications such as micromanipulation, optical trapping, imaging, and free-space optical communications. A common singularity is the optical vortex, characterized by a line of zero intensity and a helical phase structure. Another important area of optics is optical coherence theory, with applications like intensity interferometry, ghost imaging, and optical coherence tomography. Partially coherent beams are known for their resistance to atmospheric turbulence, which is useful for improving free-space optical communications. This raises the question of whether combining optical vortices and partial coherence yields benefits, though it has been believed there is a conflict between the two. A vortex represents a deterministic phase structure in a spatially coherent field, while a partially coherent field has nondeterministic phases. Vortices can appear in two-point coherence functions (coherence vortices), but field vortices associated with zero intensity are typically absent in partially coherent fields.

It was recently found that a class of partially coherent beams, known as Rankine vortex beams, can evolve into a deterministic vortex in the far zone due to their relationship with Gaussian Schell-model vortex (GSMV) beams. However, for applications like optical manipulation and free-space optical communications, a partially coherent beam that can produce a deterministic vortex at any propagation distance is more desirable. In this paper, we demonstrate that such beams, which we call deterministic vortex beams (DVBs), can be designed using fractional Fourier transforms (FracFTs) to manifest a deterministic vortex at any range and degree of spatial coherence. 

In conclusion, we show that it is possible to create partially coherent beams with deterministic vortices at any desired propagation distance. Though this study focused on a vortex beam of order 1, higher-order vortices can be generated by modifying the order of the GSMV beam at the source. Our findings may have applications in free-space optical communication and further illuminate the relationship between coherence and singular optics.