Anisotropy of the optical conductivity of high Tc cuprates

The optical conductivity along and perpendicular to the planes is calculated assuming strong k-dependence of the scattering rate and the c-axis hopping parameter. Closed analytical expressions for the optical conductivy along these directions are obtained, and are shown to be integrable at low and high frequencies. A large and qualitatively different frequency dependence for both polarizations follows directly from the model. The expression for the in-plane conductivity has an effective scattering rate proportional to frequency, and can be easily generalized to provide a simple analytical expression, which may replace the Drude formula in the case of non-Fermi liquids.