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Three dimensionality of band structure and a large residual quasiparticle population in Ba$_{0.67}$K$_{0.33}$Fe$_2$As$_2$ as revealed by the c-axis polarized optical measurement

We report on a c-axis polarized optical measurement on a Ba$_{0.67}$K$_{0.33}$Fe$_2$As$_2$ single crystal. We find that the c-axis optical response is significantly different from that of high-T$_c$ cuprates. The experiments reveal an anisotropic three-dimensional optical response with the absence of the Josephson plasma edge in R($ω$) in the superconducting state. Furthermore, different from the ab-plane optical response, a large residual quasiparticle population down to $T\sim\frac{1}{5}T_c$ was observed in the c-axis polarized reflectance measurement. We elaborate that there exist nodes for the superconducting gap in regions of the 3D Fermi surface that contribute dominantly to the c-axis optical conductivity.