Topological charge of a superposition of identical parallel single-ringed Laguerre-Gaussian beams

We study a superposition of several identical parallel single-ringed Laguerre-Gaussian beams. Both for the initial plane and for the far field, we show analytically and confirm numerically that if the weighting coefficients of the superposition are real-valued (i.e. all the beams have the same phase, but may have different amplitudes), the net topological charge of the superposition is equal to the topological charge of each constituent beam. It is also shown that a phase delay between the beams allows changing the net topological charge of the superposition. By measuring the net topological charge it is possible to analyze the received optical signal in a data transmission system that utilizes vortex beams, combining spatial multiplexing and orbital angular momentum multiplexing.