  In a recent publication we have proposed a numerical model that describes the
detection process of optical photons in superconducting nanowire single-photon
detectors (SNSPD). Here, we review this model and present a significant
improvement that allows us to calculate more accurate current distributions for
the inhomogeneous quasi-particle densities occurring after photon absorption.
With this new algorithm we explore the detector response in standard NbN SNSPD
for photons absorbed off-center and for 2-photon processes. We also discuss the
outstanding performance of SNSPD based on WSi. Our numerical results indicate a
different detection mechanism in WSi than in NbN or similar materials.
