When structured light is propagated through the atmosphere, turbulence results in modal scattering and distortions. An extensively studied example is that of light carrying orbital angular momentum (OAM), where the atmosphere is treated as a phase distortion and numerical tools extract the resulting modal cross-talk. This approach focuses on the light itself, perturbed by the atmosphere, yet does not easily lend itself to physical insights, and fails to ask a pertinent question: where did the OAM that the beam gained or lost come from? Here, we address this by forgoing the beam and instead calculating the OAM of the atmosphere itself. With this intuitive model we are able to draw general conclusions on the impact of atmospheric turbulence on OAM beams, which we confirm experimentally. Our work alters the perspective on this problem, opening new insights into the physics of OAM in turbulence, and is easily extended to other structured light fields through arbitrary aberrations.

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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.

Spatial filtering is a commonly deployed technique to improve the quality of laser beams by optically filtering the noise. In the “textbook” example, the noise is usually assumed to be high frequency and the laser beam, Gaussian. In this case, the filtering is achieved by a simple pinhole placed at the common focal plane of two lenses. Here, we explain how to generalize the concept of spatial filtering to arbitrary beam profiles: spatial filtering of structured light. We show how to construct the spatial filters using a range of structured light examples and highlight under what conditions spatial filtering works. In the process, we address some misconceptions in the community as to how and when spatial filters can be applied, extend the concept of spatial filtering to arbitrary beam types, and provide a theoretical and experimental framework for further study at both the undergraduate and graduate level.

In the version of this article initially published, there was an error in the expression directly following equation ( 3) where the text now reading "where |v 1 〉=T B |u 1 〉 and |v 2 〉= T B |u 2 〉" appeared initially as "where |v 1 〉 =T B + t 12 |u 2 〉 and |v 2 〉 = T B . " The error has been corrected in the HTML and PDF versions of the article.