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

TL;DR

This paper introduces a combined theoretical and experimental approach to quantify and reduce turbulence-induced distortions in Gaussian beams using statistical characterization and waveguide filtering, improving beam stability.

Contribution

It develops a unified framework employing Gram--Charlier expansion and waveguide filtering to mitigate atmospheric turbulence effects on optical beams.

Findings

Waveguide filtering effectively suppresses higher-order modes.

Significant reduction in intensity fluctuations observed.

Beam statistics are restored to Gaussian after 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.