Spatiotemporal Stabilization of Turbulence-Distorted Gaussian Beams via Waveguide Spatial Filtering

Abstract

Optical beams propagating through atmospheric turbulence undergo spatiotemporal intensity fluctuations that deviate significantly from an ideal Gaussian profile. In this work, we present a unified theoretical and experimental framework for quantifying and mitigating these turbulence-induced distortions by coupling a higher-order statistical characterization technique with optical waveguide spatial filtering. The statistical characterization employs a Cholesky-whitened Gram--Charlier expansion that decomposes the two-dimensional beam intensity distribution into a Gaussian core augmented by third- and fourth-order cumulant corrections, thereby isolating skewness and excess kurtosis as quantitative non-Gaussianity indicators. Concurrently, the propagation of the distorted beam through a dielectric waveguide is analyzed to demonstrate that higher-order spatial modes, which carry the dominant share of turbulence-induced structural distortions, encounter a cutoff condition governed by the normalized frequency parameter and subsequently undergo exponential attenuation along the propagation direction. The waveguide thus acts as a passive spatial mode filter that selectively transmits the fundamental guided mode while suppressing radiative higher-order modes. The fitted beam volume, derived from the Gram--Charlier intensity model, serves as a unified scalar diagnostic that tracks the frame-by-frame evolution of turbulence-induced structural changes. Experimental measurements validate the theoretical predictions, demonstrating a substantial reduction in intensity fluctuations and a recovery of Gaussian beam statistics after waveguide propagation.

Figures (11)

• Figure 1: Schematic of the experimental optical setup. A He-Ne laser beam is spatially filtered and collimated (SFA), redirected by mirror M1, passed through the rotating PRPP to introduce Kolmogorov turbulence, redirected by mirror M2, and coupled into an optical fibre waveguide before detection on a CCD camera. The PRPP rotor provides temporal variation of the turbulence realizations across the 200 frames captured per experimental set.
• Figure 2: Selected raw beam intensity frames at five temporal indices (0, 50, 100, 150, 199) for all four experimental datasets. Red star markers indicate the pixel location selected for single-pixel scintillation analysis. The raw turbulence frames (Set 1) exhibit severe spatial fragmentation, while the fibre-filtered sets (Sets 2 and 3) display smooth, near-Gaussian intensity profiles comparable to the undistorted reference (Set 4).
• Figure 3: Gram--Charlier fitted beam intensity frames at five temporal indices for all four experimental datasets. The fitted profiles for raw turbulence (Set 1) are compact and asymmetric, while those for Sets 2--4 are broad and approximately circularly symmetric, confirming spatial mode recovery by the waveguide.
• Figure 4: Frame-by-frame shape metrics for Sets 1--3 derived from the Gram--Charlier analysis. From top-left to bottom-right: beam widths $\sigma_x$ and $\sigma_y$, off-diagonal covariance $\sigma_{xy}$, centroid coordinates $\mu_x$ and $\mu_y$, fitted power volume $V_{\mathrm{frame}}$, skewness norm $|\mathrm{skew}|_3$, kurtosis norm $|\mathrm{kurt}|_4$, and volume-based scintillation index. Waveguide propagation substantially reduces the amplitude and variance of all non-Gaussianity metrics relative to the raw turbulence baseline.
• Figure 5: Normalized pixel intensity as a function of frame index for representative pixels in each dataset. The dashed red line indicates the dataset-specific background reference level $I_b$. Set 1 (top) exhibits highly intermittent, sparsely populated intensity, while Set 4 (bottom) shows near-constant intensity across all 200 frames. Sets 2 and 3 demonstrate intermediate behaviour consistent with partial scintillation mitigation.