  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 no 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 vertical
directional coupler design, and characterize its performance by evaluating the
purities of positive-operator-valued measurements (POVMs) in terms of SPAD
number $m$, photon loss, and dark counts.
