Effect of primary illumination apodization on generating the Bessel mode vortex beams

We investigate the effect of primary illumination properties on partially coherent Bessel mode vortex beams. Based on the coherent mode representation, we show that a wide class of such vortices can be obtained by applying well-known apodization functions to the primary illumination. In particular, we find that the combined effect of apodization windows with high topological charges induces transitions of high intensity gradient from the vortex core to the outer vortex rim. The specific choice of apodization filters leads to a change on the spatial degree of coherence as a function of the topological charge. This suggests a synthesis procedure to generate partially coherent vortex beams where the intensity gradient can be shaped by changing the degree of coherence and the topological charge.