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A light beam with phase singularity (PS) characterized with azimuthallysymmetric angular positions (APs) can be constructed by the rotationallysymmetric superposition of n (n is N) fractional vortex light beams withidentical charges. The profile of this light beam deforms after propagationowing to its orbital angular momentum (OAM) noneigenvalue, and the deformationdegree can be evaluated by the degree of phase dislocation associated with thePS. The expectation value of the mean deviation of its OAM from itscharacteristic charge value and the variation of the degree of phasedislocation obey a proportional relation. This light beam offers a quantifiableexample of a complementarity relation between the observers of optical OAM andAP, which are the OAM noneigenvalue and intensity AP variation, respectively.

Quantifiable example of complementarity relation between optical orbital angular momentum and angular position