Abstract
The spectra of optical vortices and orbital angular momentum of combined singular beams were investigated in the form of a superposition of Laguerre - Gauss or Bessel – Gauss modes with “resonant” amplitudes depending on a real parameter. If this parameter is an integer, then the orbital angular momentum of the singular beam is equal to this number. If the real parameter is fractional, then the orbital angular momentum can be either significantly greater or much less than the integer closest to the parameter value. For a non-integer value of the beam parameter, a large number of superposition beams with integer topological charges contribute to its amplitude. For an integer beam parameter, only one mode with a topological charge equal to the value of the beam parameter contributes to the amplitude.
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