Main description:

Discusses the topological charge of an optical vortex is equal to the number of screw dislocations or the number of phase singularities in the beam cross-section
Presents a single approach based on the M. Berry formula
Describes the topological competition between different optical vortices in a superposition
Demonstrates the stability of the topological charge to random phase distortions and insensitivity to amplitude distortions
Contains many numerical examples, which clearly show how the phase of optical vortices changes during propagation in free space and the topological charge is preserved

Contents:

1. Topological charge of superposition of vortices. Conservation of topological charge. 2. Evolution of an optical vortex with an initial fractional topological charge. 3. Topological charge superposition of only two Laguerre-Gaussian or Bessel-Gaussian beams with different parameters. 4. Optical vortex beams with an infinite topological charge. 5. Transformation of an edge dislocation of a wavefront into an optical vortex. 6. Fourier-invariant and structurally stable optical vortex beams. 7. Topological charge of polarization singularities. 8. Conclusion.