Turbulence Induced Photon Statistics with Classical Beam propagation in Free Space Optical Communications

TL;DR

The paper tackles turbulence-induced degradation in free-space optical communications by developing a theory of collective dipole synchronization in dielectric media and validating it with phase-space quantum tomography. It combines a nonlinear coupled-oscillator model (including dipole–dipole coupling, gradient forces, and inertial effects) with a nonlinear phase-retrieval solver (P3-type TIE), Wigner tomography, and photon-number statistics to quantify suppression of turbulence. Experimental data from a programmable turbulence emulator (PRPP) and PMMA rods show a systematic reduction in photon-number variance: the Fano factor moves from super-Poissonian under raw turbulence toward near-Poissonian (and even slightly sub-Poissonian) statistics as the propagation length in PMMA increases, with information-theoretic and geometric divergences (KL, JS, Bhattacharyya, Fisher–Rao) uniformly supporting stronger compensation for two rods than one. The work introduces a passive, physics-based mechanism for turbulence mitigation in free-space optics and provides a rigorous diagnostic framework linking classical phase distortions to quantum-statistical behavior, with potential impact on robust, low-cost optical links.

Abstract

This study examines the influence of optical turbulence on field statistics using a nonlinear reconstruction and quantum phase-space formalism. Turbulence-distorted intensity sequences were processed through a nonlinear P3-type partial differential equation to retrieve the embedded phase, thereby reconstructing the complete complex optical field. The recovered fields were subsequently projected onto a Gaussian local oscillator to generate quadrature ensembles, enabling Wigner function tomography via Radon inversion. Photon-number distributions were obtained from the overlap of the reconstructed Wigner functions with Fock-state kernels, allowing direct evaluation of statistical moments and the Fano factor. Comparative analysis across four experimental configurations, Set 1: uncorrected turbulence, Set 2: turbulence with a single PMMA slab, Set 3: turbulence with dual PMMA slabs, and Set 4: free-space reference revealed the modification of phase noise and photon statistics due to partial compensation. Notably, the evolution of the Fano factor traced the transition among Poissonian, super-Poissonian, and near-sub-Poissonian regimes, quantitatively capturing the degree of turbulence mitigation achieved by the PMMA elements. This framework establishes a quantitative link between turbulence-induced phase distortions and quantum statistical behavior of reconstructed optical fields.

Figures (21)

• Figure 1: Schematic representation of the experimental optical configuration. A continuous-wave laser beam passes through a spatial filter assembly (SFA), is redirected by mirrors M1 and M2, traverses a programmable rotating phase plate (PRPP) for turbulence introduction, propagates through one or two PMMA rods for compensation, and is finally recorded by a CCD camera. This setup enables systematic investigation of turbulence effects and mitigation through dielectric media.
• Figure 2: Data analysis workflow (Scheme I). Each of the four experimental sets (Set 1: free-space baseline; Set 2: raw turbulence; Set 3: single PMMA rod; Set 4: double PMMA rods) comprises 200 recorded intensity frames. For each set, a reference frame (typically the temporal mean or median) is established, and pairwise scintillation indices are computed to quantify intensity fluctuation statistics across the ensemble.
• Figure 3: Data analysis workflow (Scheme II). The acquired image sets undergo statistical processing including power fluctuation analysis, kernel density estimation, and computation of distributional distance metrics. Reference frames are extracted from each set, enabling quantitative comparison of turbulence-induced statistical deviations and compensation efficacy through divergence measures and information-geometric distances.
• Figure 4: Original Image and Corresponding KDE Fitted Image for Turbulence-free Beam for Set 4
• Figure 5: Original Image and Corresponding KDE Fitted Image for Set 1: Raw Turbulence