Spatio-Temporal Scintillation Mitigation via Polarizations Coupled Higher-Order Correlation

Abstract

We present a unified theoretical framework linking second and fourth order statistical correlations of stochastic electromagnetic beams to the scintillation index observed after propagation through Kolmogorov atmospheric turbulence. We derive the beam coherence polarization matrix and its propagation law in a random medium. An algebraic connection is established between the second order polarization matrix J, its fourth order Gram counterpart obtained from the square of J, the classical degree of polarization P, the fourth order degree of polarization, and the scintillation index of the beam intensity. A key result is a closed form purity relation connecting the trace of the squared polarization matrix to the square of its trace, which shows that unpolarized natural beams exhibit a large scintillation index. The analysis demonstrates that scintillation can be reduced by polarizing the beam using suitable polarizer sets. This reduction occurs independently of the atmospheric turbulence strength parameter. Experimental results further show that simultaneous control of coherence and polarization, achievable using a pseudo random phase plate, provides a practical approach for minimizing scintillation in free space optical communication links.

Figures (12)

• Figure 1: Schematic of the experimental optical setup. A He-Ne laser beam is spatially filtered and collimated (SFA), passed through the rotating PRPP to introduce Kolmogorov turbulence, transmitted through 0–5 thin-film polarizers, and recorded on a CCD camera. The PRPP rotor provides temporal variation of the turbulence realizations across the 200 frames captured per experimental set.
• Figure 2: Representative raw CCD intensity frames at frames 0, 50, 100, 150, and 199 for Sets 1–7. Set 1 (raw turbulence, no polarizer) exhibits highly distorted, randomly varying beam patterns. Sets 2–6 show progressively less distortion as more polarizers are added. Set 7 is the turbulence-free reference.
• Figure 3: Selected-pixel (peak intensity for 0th frame) tracking across 200 frames for Sets 1–7. The red dot in each panel marks the frame-wise pixel position that presented maximum intensity on 0th frame for each set. Erratic migration of the peak pixel in Set 1 reflects strong turbulence-induced beam wander. The migration is progressively suppressed with an increasing number of polarizers (Sets 2–6), and is minimal in the reference Set 7.
• Figure 4: Two-dimensional elliptical Gaussian fits to the CCD intensity frames for each experimental set at representative frame indices. The Gaussian fitting decouples genuine beam-shape evolution from detector noise and provides consistent beam-parameter time series for scintillation analysis.
• Figure 5: Frame-by-frame time series of the Gaussian-fitted beam parameters for Sets 1–6: centroid positions $\mu_x$ and $\mu_y$ (top row), beam widths $\sigma_x$ and $\sigma_y$ (middle row), cross-correlation $\sigma_{xy}$ and integrated beam volume (bottom row). Set colours follow the same convention as Figures \ref{['fig:raw']}–\ref{['fig:pointed']}.