Investigation of the total topological charge of the superposition of parallel identical Laguerre– Gaussian beams with a single ring

In this research, a superposition identical parallel Laguerre–Gaussian beams with sole rings is investigated. We numerically and theoretically demonstrated that the total topological charge of the superposition is equal to the topological charge of each constituent element in the far field and in the origin plane if the weight factors of the superposition are real. It was prooved that if there is the phase delay between the beams than the total topological charge of the superposition is altered.