Generation of optical phase singularities by computer-generated holograms

Laser beams that contain phase singularities can be generated with computer-generated holograms, which in the simplest case have the form of spiral Fresnel zone plates. There has recently been considerable interest in op-tical fields that exhibit phase singularities, which manifest themselves as isolated dark spots in the modal patterns of certain lasers. Each dark spot has a topological charge that represents the number of 2vr accumulated when the phase gradient is inte-grated around it. The wave fronts near a singular-ity have a helical structure, while the field at the singularity must be zero because of the ambiguous phase; hence the dark spot. It has been shown theoretically how, under the influence of nonlinear interactions, frequency-degenerate transverse modes can lock together with