Automatic on-chip separation of partially coherent light into its mutually incoherent components

While partial coherence often degrades interference and information transfer, its correlations can be engineered to enhance imaging and optical information processing. However, approaches based on tomography and numerical reconstruction do not physically separate unknown fields into their coherence modes—that is, their orthogonal and mutually incoherent components. Here we demonstrate the separation of partially coherent light into coherence modes. We use variational processing in layered self-configuring interferometers on a silicon photonic circuit. This process finds the eigenvectors and eigenvalues of the coherency matrix, characterizing the state while leaving it intact and separated after optimization. We show that spatially orthogonal, mutually incoherent beams can be routed to separate outputs even when their intensity profiles overlap. Our experiment separates the two strongest coherence modes from a nine-input sampling of overlapping fields from two independent lasers; operation beyond two modes is verified in a rank-3 experiment. The number of physical components scales linearly with the rank r of the coherency matrix, through r in situ gradient-based optimizations enabled by electronic drive-frequency multiplexing of the phase shifters. We benchmark performance against an on-chip mixture-based tomographic method. These results establish a scalable framework for programmable coherence analysis and control.