# Multiscale permutation entropy analysis of laser beam wandering in isotropic turbulence

## TL;DR

This study uses multiscale permutation entropy to analyze laser beam wandering caused by isotropic turbulence, revealing long-range correlations, a transition between stochastic behaviors, and quantifying electronic noise effects.

## Contribution

It introduces a multiscale permutation entropy approach to characterize the complex dynamics of laser beam wandering in turbulence, including noise quantification and regime transitions.

## Key findings

- Identified a crossover between stochastic regimes in beam wandering
- Quantified electronic noise as a function of turbulence strength
- Confirmed experimental results with numerical simulations of fractional Brownian motion

## Abstract

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.