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Programmable on-chip synthesis and reconstruction of partially coherent two-mode optical fields

Partially coherent light is typically studied in the context of freely propagating continuous fields. Recent developments have indicated the existence of a `coherence advantage' in multimode optical communications, where partially coherent light outperforms coherent light. However, exploiting partial coherence in such applications requires manipulating multimode field coherence in programmable on-chip platforms. We present here the first example of on-chip synthesis and characterization of two-mode optical fields in an integrated on-chip hexagonal mesh of Mach-Zehnder interferometers. Starting with incoherent two-mode light, we adjust the degree of coherence on the chip with non-unitary transformations, construct $2\times2$ unitary transformations to synthesize prescribed coherence matrices, and reconstruct the coherence matrices via measurements of the spatial Stokes parameters. These results indicate the possibility of deploying programmable photonics for producing large-dimensional structured partially coherent light for applications in communications, cryptography, sensing, and spectroscopy.