Infrared conductivity of BaFe$_2$As$_2$ superconductors: Effects of in-plane and out-of-plane doping

We measured the \emph{in-plane} optical conductivity of a nearly optimally doped ($T_{c}$ = 39.1 K) single crystal of Ba$_{0.6}$K$_{0.4}$Fe$_{2}$As$_{2}$. Upon entering the superconducting state the optical conductivity vanishes below $\sim$ 20 meV, indicating a fully gapped system. A model with two different isotropic gaps is required to describe the optical response of this material. The temperature dependence of the gaps indicate a strong interband interaction, but no impurity scattering induced pair breaking is present. This contrasts to the large residual conductivity observed in optimally doped Ba(Fe$_{1-x}$Co$_{x}$)$_{2}$As$_{2}$ and strongly supports an $s_\pm$ gap symmetry for both compounds.