Free-space optical communication through the atmosphere is limited by turbulence — the wavefront arriving at the receiver is distorted, and the signal must be separated from the noise. The standard approach is mode-selective: choose a particular basis of spatial modes (Hermite-Gaussian, Laguerre-Gaussian, orbital angular momentum) and design a demultiplexer to sort the incoming light into those modes.
This paper finds that which modal basis you choose matters far less than how much spatial area (footprint) your basis covers. A compact two-plane refractive system, optimized via stochastic gradient descent over an ensemble of turbulence realizations, approaches the performance of ideal modal projection — and it does so regardless of the specific mode set. The footprint is the dominant variable; the basis is a detail.
The optimization target matters: designing for a single turbulence realization produces brittle systems that fail on the next one. Designing over the full turbulence ensemble produces robust demultiplexers that handle whatever the atmosphere throws at them. The constraint of optimizing against uncertainty — averaging over what you can't predict — enables generalization rather than limiting performance.
The field spent decades arguing about which modal basis is best. The answer is that the argument was about the wrong variable.