Synthesis of partially coherent Bessel-mode vortex-beams with radial coherence

Abstract

Partially coherent Bessel-mode vortex-beams with radial coherence are introduced. The generated beams are fully coherent at pair of points along the same radial coordinate. The field is completely incoherent for pairs of points belonging to different angular positions. By using the coherent-mode structure of propagation invariant fields, the analytical expression of the propagated cross-spectral density, representing fields with radial coherence, is derived. It is shown that beams of this type can be generated in a Fourier transforming optical system. An important feature of the synthesized beams is their ability of being invariant under propagation. The behaviour of the degree of coherence is analysed in terms of the eigenvalues of the modal structure. A numerical ensemble of realizations, at both planes of the considered system, was generated. From this ensemble, the spectral intensity of the proposed beams was obtained. The numerical results show a well-defined principal thin ring of maximum intensity followed by secondary concentric rings, in complete agreement with theoretical predictions. We believe that presented scheme can trigger new research routes in the synthesis of fields with structured coherence.