  Recently a generic model has been proposed for the single-particle properties
of gapless superconductors with simultaneously present pair-conserving and
pair-breaking impurity scattering (the so-called Dynes superconductors). Here
we calculate the optical conductivity of the Dynes superconductors. Our
approach is applicable for all disorder strengths from the clean up to the
dirty limit and for all relative ratios of the two types of scattering,
nevertheless the complexity of our description is equivalent to that of the
widely used Mattis-Bardeen theory. We identify two optical fingerprints of the
Dynes superconductors: (i) the presence of two absorption edges and (ii) a
finite absorption at vanishing frequencies even at the lowest temperatures. We
demonstrate that the recent anomalous optical data on thin MoN films can be
reasonably fitted by our theory.
