Photon-number-resolving segmented detectors based on single-photon avalanche-photodiodes

We investigate the feasibility and performance of photon-number-resolved photodetection employing single-photon avalanche photodiodes (SPADs) with low dark counts. While the main idea, to split n photons into m detection modes with a vanishing probability of more than one photon per mode, is not new, we investigate here a important variant of this situation where SPADs are side-coupled to the same waveguide rather than terminally coupled to a propagation tree. This prevents the nonideal SPAD quantum efficiency from contributing to photon loss. We propose a concrete SPAD segmented waveguide detector based on a vertical directional coupler design, and characterize its performance by evaluating the purities of Positive-Operator-Valued Measures (POVMs) in terms of number of SPADs, photon loss, dark counts, and electrical cross-talk.