The defocused helical structure of two superposed vortex beams

Vortex beams have drawn much attention for their distinct properties. When vortex beams propagate along optical axis, they exhibit complicated physical phenomena. Under tight focusing condition, we investigate the defocusing behavior of two superposed vortex beams with opposite but arbitrary topological charge. The results reveal that the intensity distribution of the focus will be petal-shaped if the two topological charges have opposite sign, where the number of intensity lobes in the focal plane is |m - n + 2|. Meanwhile, we find that the focusing intensity of topological charge m = -n would not appear the helical structure when a defocusing occurs. Otherwise, the defocusing would result in the helical structure of intensity when m ≠ -n, and the rotation of helical structure depends on the sign of m + n. Of which clockwise rotation of defocus intensity is related to the negative m + n, and anti-clockwise direction corresponds to the positive m + n. Furthermore, the helical degree of the helical intensity also depends on the magnitude of m + n. The interesting results obtained in this paper will lead to further advances in the field of optical vortices.