Formation of optical vortices using coherent laser beam arrays
  We present a novel proposal to generate an optical vortex beam by using the coherent-superposition of multi-beams in a radial symmetrical configuration. In terms of the generalized Huygens-Fresnel diffraction integral, we have derived the general propagation expression for the coherent radial laser arrays. Based on the derived formulae, we have analyzed the effects of the beamlet number, the separation distance of the beamlets and the topological charge on the intensity and phase distributions of the resulted beams. Our simulation results show that optical vortices could be efficiently formed and generated due to the interference and superposition effect of all the beamlets, during the propagation process of the coherent radial laser arrays with the initial well-organized phase distributions through the free space. In the focusing system, the resulted beam near the focusing plane has the strong rotation effect with the phase helicity. 
Li-Gang Wang, Li-Qin Wang, and Shi-Yao Zhu