How does turbulence scramble laser beams carrying orbital information?

Turbulent air scrambles structured laser beams — a headache for quantum communications and remote sensing. This framework reduces the messy physics to a matrix exponential: power leaking from one spatial mode into others grows linearly with distance, with rates set by how much the turbulence spectrum overlaps with each pair of modes. The model matches simulations through medium-to-strong turbulence and analytically confirms scaling rules that were previously only observed empirically.