  We report the complex dielectric function along and perpendicular to the IrO2
planes in the layered perovskite Sr2IrO4 determined by spectroscopic
ellipsometry in the spectral range from 12 meV to 6 eV. Thin high quality
single crystals were stacked to measure the c-axis optical conductivity. In the
phonon response we identified 10 infrared-active modes polarized within the
basal plane and only four modes polarized along the c-axis, in full agreement
with first-principle lattice dynamics calculations. We also observed a strong
optical anisotropy in the near-infrared spectra arising from direct transitions
between Ir 5d t2g Jeff = 1/2 and Jeff = 3/2 bands, which transition probability
is highly suppressed for light polarized along the c-axis. The spectra are
analyzed and discussed in terms of relativistic LSDA+U band structure
calculations.
