self-focusing circular coherent vortex beams*

Studies on partial coherence have shown how structuring the statistical properties of light can change its behavior in radical ways. Circular coherence sources, which are perfectly coherent along any ring that is concentric to the beam center, have the potential to preserve the spiral phase structures of optical vortices on propagation, especially under turbulence conditions. 

In this study, we create circular coherent vortex beams by imposing circular coherence on Laguerre-Gaussian (LG) beams, which carry optical vortices. The second-order coherence properties, such as cross-spectral density (CSD), spectral density, degree of coherence, and coherence singularities (correlation vortices and ring dislocations) are investigated at the source plane and in free-space propagation up to 3km. To view the beam profiles with coherence singularities, we project the four-variable CSDs into a two-variable space by fixing one of the two observing points.

At the source plane, both amplitude and phase distributions of circular coherent vortex beams for different azimuthal orders show coherence singularities. The propagation of CSDs follow the Huygens' principle, showing its behavior at 1 km, 2 km, and 3 km, respectively. It is shown that CSDs shift toward the origin near 1 km; this is a manifestation of the self-focusing effect of the beams. When the distance is larger than 1 km, CSDs start spreading as the free-space diffraction becomes dominant. The amplitude and phase of the beams on propagation illustrate that both the zero amplitude and spiral phase structure maintain on the beam axis, a property that makes them good candidates for applications such as free-space optical communication. We also compare the propagation profile of a coherent beam (focused by a lens) and that of a circular coherent beam with the same component coherent beam. The intensity distribution of the circular coherent beam appears smoother in the focal area. Additionally, a wider range of spatial frequency might be conveyed by the circular coherent beam, which leads to another potential application for lensless imaging.