  We measure the nonlinearity of a telecom-wavelength superconducting nanowire
single-photon detector via incoherent beam combination. At typical photon count
rates and detector bias current, the observed relative deviation from a
perfectly linear response is in the order of 0.1% when the flux is doubled.
This arises from a balance between the counteracting nonlinearities of
deadtime-induced detector saturation and of multi-photon detections. The
observed behaviour is modelled empirically, which suffices for a correction of
measured data. In addition, statistical simulations, taking into account the
measured recovery of the detection efficiency, provide insight into possible
mechanisms of multi-photon detection.
