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

TL;DR

This paper investigates how optical turbulence affects photon statistics in free-space optical communications by reconstructing the quantum state of light and analyzing the impact of turbulence mitigation techniques.

Contribution

It introduces a nonlinear reconstruction method combined with quantum phase-space formalism to analyze turbulence effects on photon statistics in free-space optics.

Findings

Turbulence modifies phase noise and photon statistics.

PMMA slabs partially mitigate turbulence effects.

Fano factor evolution indicates transition between statistical regimes.

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.