Probing Topological Charge of Discrete Vortices

Abstract

ABSTRACT A discrete vortex, formed by a one-dimensional (1D) ring array of lasers, has high output power as compared with a conventional continuous vortex, and 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 (l) 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 𝑙≠0 is averaged with the interference pattern corresponding to 𝑙=0, which gives rise to a variation in the fringe visibility as a function of the 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 the topological charge of a discrete vortex. After determination of the magnitude, the sign of 𝑙≠0 is determined by averaging its interference pattern with the interference pattern corresponding to 𝑙=1. The number of dips in the fringe-visibility curve decreases by 1 for positive l values and increases by 1 for negative l values. Further, we verify our method against the phase disorder, and it is found that the phase disorder does not influence accurate determination of the topological charge of a discrete vortex. The working principle as well as numerical and experimental results are presented for discrete vortices with topological charges from small to large values. Excellent agreement between the experimental results and the numerical simulations is found. Our method can be useful in applications of discrete vortices especially where conventional continuous vortices have power limitations.