Far-infrared transmittance and reflectance studies of oriented ${\mathrm{YBa}}_2$${\mathrm{Cu}}_3$${\mathrm{O}}_{7\mathrm{-}\mathrm{\delta }}$ thin films

We have measured both the transmittance (scrT) and reflectance (scrR) for several ${\mathrm{YBa}}_2$ ${\mathrm{Cu}}_3$ ${\mathrm{O}}_{7\mathrm{-}\mathrm{\delta }}$ thin films over the frequency range from 20 to 360 ${\mathrm{cm}}^{\mathrm{-}1}$ at temperatures between 20 and 300 K. The films, grown on MgO substrates by pulsed laser ablation, are highly a-b-plane oriented. We use scrT and scrR to extract the optical conductivity, and find good agreement with results from Kramers-Kronig analysis of reflectance measurements alone. The transmittance is consistent with a two-component dielectric function consisting of Drude (free-carrier) and midinfrared (bound-carrier) absorption. The Drude relaxation rate varies linearly with temperature, and compares well with values obtained from the measured dc resistivity. We use a two-fluid model for the superconducting state and obtain a BCS-like temperature dependence for the superfluid density. A superconducting gap is not observed in our spectra.