Single-shot on-chip measurement of the modal Stokes parameters.

Integrated photonics has recently facilitated the manipulation of multimode partially coherent light in a compact mesh of Mach-Zehnder interferometers. A critical task in this context is on-chip reconstruction of the coherence matrix through a sequence of measurement configurations, thus giving rise to a speed bottleneck stemming from temporal delays in tuning on-chip phase shifts. Here, we demonstrate single-shot reconstruction of the coherence matrix for two-mode partially coherent light by parallelizing the on-chip measurements of the modal Stokes parameters, thereby exchanging space for time. Although a larger chip area is required, the reconstruction is limited only by detection speed, thus potentially paving the way to real-time reconstruction of coherence matrices for applications in high-speed communications, cryptography, computation, and sensing.