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 are not necessarily vortex beams, although it is erroneously traditional to state that helical beams are all vortex beams.

中文翻译：

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暗和超暗定理及其在非涡旋光束的螺旋光束（具有拓扑电荷的光束）上的应用

依靠以光束形状系数表示的时间平均坡印廷矢量，讨论了暗定理和超暗定理，概括了先前发表的暗定理。超暗定理允许人们根据光束形状系数来表征螺旋光束（即具有拓扑电荷的光束），并证明拓扑电荷等于 的光束不一定是涡旋光束，尽管它是错误的传统说明螺旋光束都是涡旋光束。