Centrifugal transformation of the transverse structure of freely propagating paraxial light beams

Superpositions of coaxial Laguerre-Gaussian modes with common waists and the same Gaussian envelopes are known to form beams whose transverse structures experience the self-similar transformation during free beam propagation: the beam shape remains the same except for the divergence and rotation around the propagation axis. We show that under certain conditions this transformation can be represented as if every point of the beam cross section performs a centrifugal straight-line fly off.