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Turbulence effects on fluctuations of the aperture-averaged orbital angular momentum.

A complete asymptotic theory for the aperture-averaged orbital angular momentum (OAM) variance is developed for both weak and strong fluctuation conditions, based on the asymptotic expansions of the Feynman path-integral solution for the fourth-order coherence function of a spherical wave propagating through a random inhomogeneous medium. We show that the OAM fluctuation averaging is very different for circular-symmetric and non-circular-symmetric apertures. Aperture averaging of the OAM fluctuations does not obey the standard "square root" law, and the weak/strong fluctuation conditions for the aperture-averaged OAM are not defined solely by the values of the scintillation index of the incident wave.