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