  We have experimentally quantified the temporal structural diversity from the
coordinate fluctuations of a laser beam propagating through isotropic optical
turbulence. The main focus here is on the characterization of the long-range
correlations in the wandering of a thin Gaussian laser beam over a screen after
propagating through a turbulent medium. To fulfill this goal, a
laboratory-controlled experiment was conducted in which coordinate fluctuations
of the laser beam were recorded at a sufficiently high sampling rate for a wide
range of turbulent conditions. Horizontal and vertical displacements of the
laser beam centroid were subsequently analyzed by implementing the symbolic
technique based on ordinal patterns to estimate the well-known permutation
entropy. We show that the permutation entropy estimations at multiple time
scales evidence an interplay between different dynamical behaviors. More
specifically, a crossover between two different scaling regimes is observed. We
confirm a transition from an integrated stochastic process contaminated with
electronic noise to a fractional Brownian motion with a Hurst exponent H = 5/6
as the sampling time increases. Besides, we are able to quantify, from the
estimated entropy, the amount of electronic noise as a function of the
turbulence strength. We have also demonstrated that these experimental
observations are in very good agreement with numerical simulations of noisy
fractional Brownian motions with a well-defined crossover between two different
scaling regimes.
