  We demonstrate single-photon counting at 1550 nm with titanium-nitride (TiN)
microwave kinetic inductance detectors. Energy resolution of 0.4 eV and
arrival-time resolution of 1.2 microseconds are achieved. 0-, 1-, 2-photon
events are resolved and shown to follow Poisson statistics. We find that the
temperature-dependent frequency shift deviates from the Mattis-Bardeen theory,
and the dissipation response shows a shorter decay time than the frequency
response at low temperatures. We suggest that the observed anomalous
electrodynamics may be related to quasiparticle traps or subgap states in the
disordered TiN films. Finally, the electron density-of-states is derived from
the pulse response.
