Partially coherent bessel vortex superposition with linear charge increase and aligned maxima

In this paper the generation of a partially coherent optical vortex composed by the incoherent superposition of $N$ coaxial Bessel vortex beams with linearly increasing topological charges and aligned intensity maxima is proposed. To generate this beam concentric ring slits with increasing topological charges and random phase shifts are optically Fourier transformed. The radii of the ring slits are chosen in such a way that maxima of their corresponding Bessel functions are coincident. It is demonstrated that the resulting beam radius is independent of the topological charges involved in the superposition and the beam is propagation invariant. The Bessel vortex addition is experimentally generated by means of a phase only liquid crystal spatial light modulator LC-SLM.