Propagation of anomalous vortex beams beyond the paraxial approximation

The propagation properties of an anomalous vortex beam(AVB) beyond the paraxial approximation are studied. Based on the vectorial Rayleigh-Sommerfeld formulas, the electric field of the AVB beyond the paraxial approximation are derived analytically. Simulations are performed to investigate the intensity distribution characteristics and the far-field behaviours of the non-paraxial AVB. The influences of the topological charge, the beam order, and the natural expansion parameter f on the propagation of the non-paraxial AVB are also explored in detail. The results show that the natural expansion parameter f plays an important role in determining whether an AVB can evolve into an elegant Laguerre-Gaussian beam in the far field. There is a critical value of the natural expansion parameter f, and the AVB can become the elegant Laguerre-Gaussian beam in the far field only when the natural expansion parameter f is less than this critical value. Furthermore, the critical value increases with smaller topological charge or larger beam order. These results provide guidelines for generation of elegant Laguerre-Gaussian beams, which has potential application in optical vortex communication systems.