  Amorphous mixed titania-tantala coatings are key components of Bragg
reflectors in the gravitational wave detectors (GWDs). Attaining the lowest
possible values of optical absorption and mechanical losses in the coatings is
of paramount importance for GWDs, and this requires a complex optimization of
the coating deposition and post-deposition annealing. We present here a
systematic investigation of the optical properties and internal friction of
amorphous mixed titania-tantala coatings grown by ion beam sputtering. We
consider coatings with six different cation mixing ratios and we study them
both in the as-deposited and annealed state. By exploiting spectroscopic
ellipsometry data and modelling, along with ancillary techniques, we retrieved
the dielectric function of the coatings in a wide spectral range. When varying
the mixing ratio and performing the annealing we find monotonic trends for most
of the aforementioned properties. Remakably, the post-annealing Urbach energy
displays a definite minimum for a mixing ratio around 20%, very close to the
composition of the coatings showing the lowest optical absorption for GWDs
applications. We suggest that the observed minimum in the Urbach energy depends
not only on the mixing ratio, but also on the annealing parameters. On the
other hand, the minimum coating loss angle was found to be weakly dependent on
the considered measurement frequency and to lie within a rather broad range of
Ti content, suggesting that the search for an absolute minimum following
post-deposition annealing should be rather sought in the study of the best
annealing parameters for each specific cation ratio considered. This work
constitutes a reference for the optical properties of the amorphous mixed
titania-tantala coatings, and highlights the relevance of the Urbach energy in
the optimization process of materials for high-performing Bragg reflectors.
