  Crystalline semiconductors may exist in different polytypic phases with
significantly different electronic and optical properties. In this paper, we
calculate the electronic structure and optical properties of diamond, Si and Ge
in the lonsdaleite (hexagonal-diamond) phase. We use an empirical
pseudopotentials method based on transferable model potentials, including
spin-orbit interactions. We obtain band structures, densities of states and
complex dielectric functions calculated in the dipole approximation for light
polarized perpendicular and parallel to the c-axis of the crystal. We find
strong polarization dependent optical anisotropy. Simple analytical expressions
are provided for the dispersion relations. We find that in the lonsdaleite
phase, diamond and Si remain indirect gap semiconductors while Ge is
transformed into a direct gap semiconductor with a significantly smaller band
gap.
