Probing topological charge of discrete vortices

Discrete vortex, formed by a one-dimensional (1D) ring array of lasers, contains high output power as compared to a conventional continuous vortex, therefore, has attracted considerable interest due to widespread applications in various fields. We present a method for probing the magnitude and sign of the topological charge (TC) of an unknown discrete vortex, by analyzing the interference pattern of a 1D ring array of lasers. The interference pattern of an unknown discrete vortex with TC$\neq 0$ is averaged with the interference pattern of TC= 0, which gives rise to a variation in the fringe visibility as a function of laser number (j) in a 1D ring array. The number of dips observed in the fringe visibility curve is found to be proportional to the magnitude of TC of a discrete vortex. The sign of TC is determined by averaging the interference patterns of unknown discrete vortex (TC$\neq 0$) with known TC= +1. The number of dips in the fringe visibility curve decreases by one for a positive TC, and increases by one for a negative TC. Further, we have verified our method against the phase disorder, and it is found that the phase disorder does not influence an accurate determination of TC of a discrete vortex. The working principle as well as numerical and experimental results are presented for the discrete vortices with TC from small to large values. An excellent agreement between the experimental results and numerical simulations is found. Our method can be useful in the applications of discrete vortices.