Far-infrared transmission studies of a c-axis-oriented superconducting MgB 2 thin film

We have reported far-infrared transmission measurements on a c-axis-oriented superconducting ${\mathrm{MgB}}_{2}$ thin film in the frequency range $30--250 {\mathrm{cm}}^{\ensuremath{-}1}.$ We found that these measurements were sensitive to the scattering rate $1/\ensuremath{\tau}$ and the superconducting gap 2\ensuremath{\Delta}. By fitting the experimental transmission spectra at 40 K and below, we obtained $1/\ensuremath{\tau}$ and $2\ensuremath{\Delta}(0)$ to be $(700--1000) {\mathrm{cm}}^{\ensuremath{-}1}$ and $42 {\mathrm{cm}}^{\ensuremath{-}1},$ respectively. These two quantities suggest that the ${\mathrm{MgB}}_{2}$ film belongs to the dirty limit.