Common topological charge of several similar off-axis vortex light beams of arbitrary rotationally symmetric shape

We investigate the topological charge of superposition of parallel identical vortex beams of arbitrary shape – either Laguerre-Gaussian beams or Bessel-Gaussian beams or some other vortex beams with a rotationally symmetric intensity distribution. It is known that if all beams in the superposition are in-phase then the topological charge of the whole superposition is equal to the topological charge of each constituent beam, n. We show that if the beams are arranged on a circle with their phases linearly increasing on this circle, so that the phase difference between the neighboring beams equals 2πp/N, where N is the number of beams and р is integer, then the superposition has the topological charge n+p.