Fluctuations of the aperture-averaged orbital angular momentum after propagation through turbulence

Abstract: In the paper [1] it was shown that for paraxial propagation of scalar waves, the transverse linear momentum and orbital angular momentum (OAM) are related to the wave coherence function. Although both of these quantities are conserved during free-space propagation, they fluctuate for beam propagation in a random inhomogeneous medium. We hereby present an extension of this theory to the case of OAM fluctuations of a spherical wave intercepted by a finite aperture. A complete asymptotic theory for the aperture-averaged 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"square root" law, and that the weak/strong fluctuation conditions for the aperture-averaged OAM are not defined by the values of the scintillation index of the incident wave.