A comparison of far-field properties of radial noncanonical vortex airy beam arrays and radial noncanonical vortex Gaussian beam arrays

Based on the vector angular spectrum representation and stationary phase method, the analytical far-field vectorial expressions of radial noncanonical vortex Airy beam arrays (NVAiBAs) and radial noncanonical vortex Gaussian beam arrays (NVGBAs) are derived, and used to investigate their far-field vectorial properties, e.g. center optical vortices and energy fluxes of these corresponding beams, where the effect of noncanonical strength, topological charge, initial phase index and the number of beamlet on far-field vectorial properties of these corresponding beams is emphasized, respectively. The results show that the topological charge of center optical vortices in the far field is equal to initial phase index for the case of the radial NVAiBAs, whereas for radial NVGBAs the topological charge not only lies on initial phase index, but also is closely related to the odevity and sign of optical vortices embedded in beamlet, where mathematical analysis is made to explain the topological charge of center optical vortices, and the limitation of the number of beamlet to the topological charge of center optical vortices is also discussed. In addition, energy fluxes of radial NVAiBAs and NVGBAs exhibit different space orientations by controlling noncancial strength and present larger dark zones by increasing topological charge of beamlet, respectively. Finally, the relationship between the center optical vortices and energy fluxes of radial NVAiBAs and NVGBAs in even or odd N beamlets is also revealed, respectively.