Common Topological Charge of a Superposition of Several Identical Off-Axis Vortex Beams with an Arbitrary Circularly Symmetric Transverse Shape

We investigate the common topological charge of a superposition of parallel identical vortex beams with an arbitrary transverse shape, either Laguerre–Gaussian beams or Bessel–Gaussian beams or some other vortex beams with rotationally symmetric intensity distribution. It is known that if all the beams in the superposition have the same phase then the common topological charge of the whole superposition equals the topological charge of each constituent beam n. We show that if the beams are located on a circle and their phases increase linearly along this circle so that the phase delay between the neighbor beams on the circle is 2πp/N with N being the number of beams and p being an integer number, then the common topological charge of the superposition is equal to n + p.