Group velocity of light in uniaxial crystals

Using the wave vector surface, we have derived the analytical expressions for the group velocities of the extraordinary light and the ordinary light traveling in an optically uniaxial crystal. Our formulas are in terms of either the wavevector direction or the ray direction, and they use only the principal refractive indices and their frequency dispersions. The algebraic equation for the group velocity surface of the crystal is also derived. While the group velocity is in the same direction as the ray velocity, numerical calculation shows that in the visible region the group velocity is slower than the ray velocity, and the difference between them becomes significant at short wavelengths.