[2605.30304] Analytical mannequin for structured gentle propagation by way of a turbulent ambiance

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Summary:We develop an easy analytical framework for the propagation of spatial gentle modes by way of a turbulent ambiance. Constructed upon the split-step strategy with the mode-based optical discipline illustration, it instantly assesses how turbulence-induced part fluctuations deplete the optical energy within the authentic mode and re-distribute it into neighboring spatial modes. Importantly, this energy switch scales linearly with the propagation distance in a uniform channel, yielding a easy resolution for arbitrary distances within the type of a matrix exponential. The switch price is set by the spatial spectral overlap between the turbulence spectrum and the acceptance spectrum for a pair of interacting spatial modes. The mannequin predicts the typical energy in every spatial mode and is actual when a single mode strongly dominates all others. Our predictions present fairly good settlement with simulations as much as medium-to-strong turbulence ranges. The mannequin additionally confirms the scalings with mode order beforehand often known as empirical observations.