Robust structured light in atmospheric turbulence

Structured light is routinely used in free-space optical communication channels, both classical and quantum, where information encoded the spatial structure of mode for increased bandwidth. Both real-world experimentally simulated turbulence conditions have revealed that structured modes are perturbed some manner by turbulence, resulting amplitude phase distortions, consequently, much attention has focused on whether one type more robust than another, but with seemingly inconclusive contradictory results. We present complex forms invariant under propagation through atmosphere: true eigenmodes atmospheric turbulence. provide a theoretical procedure obtaining these confirm their invariance numerically experimentally. Although we demonstrated approach its generality allows it to be extended other channels too, such as aberrated paths, underwater, fiber.