  To analyze the switching dynamics and output performance of a superconducting
nanowire single photon detector (SNSPD), the nanowire is usually modelled as an
inductor in series with a time-varying resistor induced by absorption of a
photon. Our recent experimental results show that, due to the effect of kinetic
inductance, for a SNSPD made of a nanowire of sufficient length, its geometry
length can be comparable to or even longer than the effective wavelength of
frequencies contained in the output pulse. In other words, a superconducting
nanowire can behave as a distributed transmission line so that the readout
pulse depends on the photon detection location and the transmission line
properties of the nanowire. Here, we develop a distributed model for a
superconducting nanowire and apply it to simulate the output performance of a
long nanowire designed into a coplanar waveguide. We compare this coplanar
waveguide geometry to a conventional meander nanowire geometry. The simulation
results agree well with our experimental observations. With this distributed
model, we discussed the importance of microwave design of a nanowire and how
impedance matching can affect the output pulse shape. We also discuss how the
distributed model affects the growth and decay of the photon-triggered
resistive hotspot.
