Avalanche instability of the orbital angular momentum higher order optical vortices

Theoretical and experimental studies of spectra of optical vortices and orbital angular momentum (OAM) carried by combined singular beams are presented. The combined beams are composed of superposition of Laguerre-Gauss or Bessel-Gauss modes with "resonant" amplitudes depending on a real parameter. If the parameter is an integer, then the OAM of the singular beam is equal to this number. If the real parameter is fractional, then the OAM can be either substantially larger or much smaller than the integer closest to the parameter value. For a non-integer value of the beam parameter, a large number of beams from superposition with integer topological charges contribute to its amplitude. For an integer beam parameter, the contribution to the amplitude is made by only one mode with a topological charge equal to the value of the beam parameter. In the experiment, singular beams with fractional OAMs were shaped using a binary amplitude diffraction grating consistent with the phase function of the singular beam. The measured correlation degree between the initial beam and the beam reconstructed from the vortex spectrum was no less than 90%.