Self-configuring high-speed multi-plane light conversion

Multi-plane light converters (MPLCs) - also known as diffractive neural networks - convert an orthogonal set of optical fields into any other orthogonal set via a unitary transformation. MPLC design typically involves optimising a digital model. However, inherently high levels of complexity mean that even a minor mismatch between this model and the physically realised MPLC leads to a severe reduction in performance. Here we create a self-configuring MPLC, converging in minutes while automatically absorbing unknown misalignments and aberrations into the design. To achieve this we introduce 'multi-plane wavefront shaping' - allowing multiple spatial light modes to be reshaped simultaneously. Convergence is accelerated via a high-speed MPLC platform incorporating a kHz-rate phase-only light modulator. Using this approach we demonstrate arbitrary optical transformations and universal mode sorters. Our work paves the way towards ultra-high-fidelity MPLCs with potential applications to optical communications, photonic computing and imaging.