Spatial correlation properties of twisted partially coherent light focused by diffractive axicons

Abstract

We investigate the spatial coherence properties of a twisted, partially coherent field in the focal region of diffractive axicons. We demonstrate that the focused field is a combination of an infinite number of weighted, mutually uncorrelated, helical components, whose weights depend on both the coherence width and the twist strength, and the total helicity of the field inverts its handedness depending on the twist handedness and vanishes at the nontwist limit. Depending on the variances of whichever the effective coherence width, the twist strength, the twist handedness of the illumination, or the shape of the axicon phase function, substantive changes will intervene on the distribution of the spatial coherence degree of the focused field. In particular, the twist strength of the illumination influences both the phase and amplitude of the spatial degree of coherence, while the twist handedness just inverts its phase. In addition, the spectral degree of coherence of the focused field possesses phase singularities, and their locations and shapes are affected by the coherence and twist properties of the illumination and the shape of the axicon phase function.