Deep diffractive optical neural networks for detecting skyrmionic topologies of light and their live training

Optical skyrmions are topological forms of structured light offering an unbounded encoding alphabet robust to perturbations. However, their practical use is limited by the absence of a topological detector, since states distinguished by their topological invariant, N, are not necessarily orthogonal. Here, we demonstrate the first deterministic detector for optical skyrmions using a deep diffractive neural network trained in real time, with the number of training parameters reduced by a factor of 1000. The network comprises two independent processing channels, each containing five diffractive layers, that map input topologies onto spatially separated output channels, enabling identification of N. We demonstrate the detector using 81 topologies constructed from vectorial Laguerre-Gaussian modes, achieving high accuracy even at noise levels that preclude conventional Stokes polarimetry. Finally, we transmit and recover an image encoded using a 15-level topological alphabet with negligible crosstalk, demonstrating a practical route towards topology-enabled optical communication.