Dark and superdark theorems with applications to helical beams (beams with a topological charge) which are not vortex beams.

Relying on the time averaged Poynting vector expressed in terms of beam shape coefficients, dark and superdark theorems are discussed generalizing a previously published dark theorem. The superdark theorem allows one to characterize helical beams (that is to say beams possessing a topological charge) in terms of beam shape coefficients, and to demonstrate that beams with a topological charge equal to ± 2 are not necessarily vortex beams, although it is erroneously traditional to state that helical beams are all vortex beams. • Dark and superdark theorems are established in terms of beam shape coefficients of GLMT. • They allow one to decide on the properties of light intensities (null or not) on the axis of a beam. • And then to decide whether a beam with topological charge is a vortex beam or not. • We may then exhibit examples of beams with topological charges which are not vortex beams. [ABSTRACT FROM AUTHOR]