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

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.