  The temperature dependence of the optical properties of the delafossite
PdCoO$_2$ has been measured in the a-b planes over a wide frequency range. The
optical conductivity due to the free-carrier (intraband) response falls well
below the interband transitions, allowing the plasma frequency to be determined
from the $f$-sum rule. Drude-Lorentz fits to the complex optical conductivity
yield estimates for the free-carrier plasma frequency and scattering rate. The
in-plane plasma frequency has also been calculated using density functional
theory. The experimentally-determined and calculated values for the plasma
frequencies are all in good agreement; however, at low temperature the
optically-determined scattering rate is much larger than the estimate for the
transport scattering rate, indicating a strong frequency-dependent
renormalization of the optical scattering rate. In addition to the expected
in-plane infrared-active modes, two very strong features are observed that are
attributed to the coupling of the in-plane carriers to the out-of-plane
longitudinal optic modes.
