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. 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, and consequently, much attention has focused on whether one mode type is more robust than another, but with seemingly inconclusive and contradictory results. We present complex forms of structured light that 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 aberrated paths, underwater, and in optical fiber.

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.

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Vectorial structured light, where the polarization is inhomogeneously distributed in space, has found a myriad of applications in both 2D and 3D optical fields. Here, we present an experimental study of the invariance and distortion of vectorial light through a real-world medium of atmospheric turbulence. We show that the amplitude and polarization structure are both severely distorted by the turbulent medium, yet the non-separability of these two degrees of freedom remains invariant. We monitor this invariance under a range of beam types and atmospheric conditions, over extended time periods, revealing the unitary nature of atmospheric turbulence in our experiment. Our results provide conclusive evidence that invariance and distortion are not mutually exclusive and that the degree of classical entanglement remains unaltered through such channels, and will be of interest to the large community interested in classical and quantum communication in free space.

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