Conventional Scintillation Statistics with Turbulence Impacted Coupled Dipole Oscillation

TL;DR

This work addresses turbulence-induced scintillation in free-space optical propagation by developing a generalized Lorentz oscillator model that includes second- and third-order nonlinear restoring forces ($\beta_i|\mathbf{r}_i|\mathbf{r}_i$, $\alpha_i|\mathbf{r}_i|^2\mathbf{r}_i$) and dipole-dipole coupling through dyadic Green's functions, augmented with gradient-force corrections and d'Alembert-based inertial analysis. Through modal diagonalization, the authors show that synchronized dipole oscillations form collective modes that oppose rapid field redistribution caused by turbulence; a perturbation force $\delta \mathbf{F}_{\text{Pert}}(t)=\mathbf{F}'_{\text{Inertia}}-\mathbf{F}_{\text{Inertia}}$ governs compensation efficacy. Experimental verification uses PMMA rods placed in a turbulence environment generated by a pseudo-random phase plate with Kolmogorov spectrum, recording 200 frames per configuration (baseline, turbulence-only, and turbulence with one or two rods). The results demonstrate substantial reductions in the scintillation index, from $\sigma_I^2$ of about 0.63 under turbulence to as low as 0.28 with dual rods, and a concomitant decrease in temporal variance and higher-order statistics, indicating restored beam stability through passive dipole-mediated synchronization. Overall, the study provides a passive, physics-based mechanism for turbulence mitigation that can enhance free-space optical communication and remote sensing in moderate turbulence, with practical considerations regarding insertion losses and regime-dependent effectiveness.

Abstract

We investigate the propagation of optical fields through polymethyl methacrylate (PMMA) rods under atmospheric turbulence conditions, employing a generalized Lorentz dipole oscillator model with nonlinear restoring forces and dipole-dipole coupling. The theoretical framework incorporates second- and third-order anharmonic terms ($β_i|r_i|r_i$ and $α_i|r_i|^2r_i$) alongside dyadic Green's function-mediated coupling between localized dipoles. Gradient forces arising from spatially non-uniform field distributions and Lorentz force perturbations are incorporated through d'Alembert's principle, revealing an effective inertia mechanism that opposes rapid field redistribution. Modal diagonalization demonstrates that synchronized dipole oscillations can compensate turbulence-induced wavefront distortions, with the perturbation force $δF_{\text{Pert}}(t) = F'_{\text{Inertia}} - F_{\text{Inertia}}$ governing the compensation efficacy. Experimental verification employs a pseudo-random phase plate (PRPP) generating Kolmogorov-spectrum turbulence, with 200 frames recorded across four configurations: baseline, turbulence-only, and turbulence with one or two PMMA rods. Statistical analysis quantifies scintillation index variations. Results indicate that dipole-dipole coupling energy transitions enable partial turbulence compensation when stronger suppression observed for longer propagation paths through increased synchronization.

Figures (8)

• Figure 1: Schematic representation of the experimental configuration employing two PMMA rods
• Figure 2: Schematic flowchart illustrating the data acquisition and analysis methodology
• Figure 3: Spatial intensity distributions across all experimental configurations. The panels display representative beam profiles at the detector plane for: (a) Set 1 - turbulence-only propagation showing significant wavefront distortion and speckle formation; (b) Set 2 - single PMMA rod configuration demonstrating partial intensity stabilization; (c) Set 3 - dual PMMA rod configuration exhibiting enhanced beam profile regularization; (d) Set 4 - baseline reference without turbulence showing ideal Gaussian distribution. Color maps represent normalized intensity values with warmer colors indicating higher intensity regions.
• Figure 4: Temporal intensity fluctuation traces for selected detector pixels across all experimental configurations. Each panel displays intensity time series I(t) normalized to the mean intensity $\langle I \rangle$ for 200 consecutive frames. (Top to Bottom) Set 1 (turbulence-only) exhibits large-amplitude stochastic fluctuations with deep fading events characteristic of strong scintillation; Set 2 (single PMMA rod) shows reduced fluctuation amplitude and suppressed extreme intensity excursions; Set 3 (dual PMMA rods) demonstrates further stabilization with minimal intensity variance; Set 4 (no turbulence) displays stable intensity baseline with only instrumental noise contributions. Multiple traces per configuration represent different spatial locations across the beam profile, revealing spatial heterogeneity in turbulence compensation effects.
• Figure 5: Temporal evolution of scintillation index across 200-frame sequences for all experimental configurations. The scintillation index $\sigma_I^2(t)$ is computed using a sliding window of 10 consecutive frames to quantify local temporal variations in turbulence strength. Set 1 (red curve) shows elevated scintillation index values in the range 0.5-0.8, indicating moderate-to-strong turbulence regime. Set 2 (blue curve) demonstrates systematic reduction to the 0.3-0.5 range through single PMMA rod compensation. Set 3 (green curve) achieves further suppression to 0.2-0.4, approaching weak turbulence regime characteristics. Set 4 (black curve) establishes baseline with $\sigma_I^2 < 0.1$, limited primarily by instrumental noise contributions. Temporal variations reflect the stochastic nature of turbulence dynamics introduced by PRPP rotation.