  Superconductivity in disordered systems close to an incipient localization
transition has been an area of investigation for many years. It has been noted
that in such highly disordered superconductors, anomalous spectral weight
develops in their conductivity near and below the superconducting gap energy.
In this work we investigate the low frequency conductivity in disordered
superconducting NbN thin films close to the localization transition with
time-domain terahertz spectroscopy. In the normal state, strong deviations from
the Drude form due to incipient localization are found. In the superconducting
state we find substantial spectral weight at frequencies well below the
superconducting gap scale derived from tunneling. We analyze this spectral
weight in the context of a model of disorder induced broadening of the
quasiparticle density of states and effective pair-breaking. We find that
although aspects of the optical and tunneling data can be consistently modeled
in terms of this effect of mesoscopic disorder, the optical conductivity
returns to the normal state value much faster than any model predicts. This
points to the non-trivial interplay of superconductivity and disorder close to
localization.
