Anisotropy of the optical conductivity of high-T-c cuprates

The optical conductivity along (σxx) and perpendicular (σzz) to the planes is calculated assuming strong k∥ dependence of the scattering rate and the c-axis hopping parameter. The closed analytical expressions for σxx(ω) and σzz(ω) 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 σxx(ω) 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.