Global coherence of Laguerre–Gaussian beams propagating through atmospheric turbulence: a dominant-scale approximation approach

Atmospheric turbulence imposes severe limitations on free-space optical (FSO) communication systems by inducing phase distortions that degrade the beam’s spatial coherence. Despite this, the propagation characterization of structured light fields, particularly Laguerre–Gaussian (LG) beams carrying orbital angular momentum (OAM), is considered to be important for next-generation FSO systems utilizing mode-division multiplexing (MDM). In this work, we present a closed-form analytical derivation for the ensemble-averaged global coherence function (GCF) of LG beams in the weak turbulence regime. The GCF reveals an optimal beam width for a given propagation distance. By employing a dominant-scale approximation, effectively relating the turbulence coherence scale to the effective beam width, we derive a compact design metric that explicitly captures the scaling laws with respect to the radial mode index ( p ), azimuthal topological charge ( ℓ ), and turbulence strength ( C n 2 ). Our analytical results also show that higher-order LG modes experience accelerated coherence degradation compared to fundamental Gaussian beams, primarily due to their expanded effective cross-sectional area sampling larger volumes of the turbulent medium. The analytical predictions are independently verified with Monte Carlo simulations. These results establish a rigorous yet tractable framework for quantifying modal decoherence in structured-light propagation through turbulent media.