How to Build the "Optical Inverse" of a Multimode Fibre

When light propagates through multimode optical fibres (MMFs), the spatial information it carries is scrambled. Wavefront shaping reverses this scrambling, typically one spatial mode at a time-enabling deployment of MMFs as ultrathin microendoscopes. Here, we go beyond sequential wavefront shaping by showing how to simultaneously unscramble all spatial modes emerging from an MMF in parallel. We introduce a passive multiple-scattering element-crafted through the process of inverse design-that is complementary to an MMF and undoes its optical effects. This "optical inverter" makes possible single-shot widefield imaging and super-resolution imaging through MMFs. Our design consists of a cascade of diffractive elements, and can be understood from the perspective of both multi-plane light conversion, and as a physically inspired diffractive neural network. This physical architecture outperforms state-of-the-art electronic neural networks tasked with unscrambling light, as it preserves the phase and coherence information of optical signals flowing through it. We show, in numerical simulations, how to efficiently sort and tune the relative phase of up to similar to 400 step-index fibre modes, reforming incoherent images of scenes at arbitrary distances from the fibre facet. Our optical inverter can dynamically adapt to see through experimentally realistic flexible fibres-made possible by moulding optical memory effects into its design. The scheme is based on current fabrication technology so could be realised in the near future. Beyond imaging, these concepts open up a range of new avenues for optical multiplexing, communications, and computation in the realms of classical and quantum photonics.