Splitting of triply degenerate refractive indices by photonic crystals

The refractive index is inherently triply degenerate in conventional crysta ls, but this degeneracy is lifted and the refractive index is split into a phase, a group, and a "fan" index by photonic crystals. These indices are e xplained as three different sections passing through the photonic band stru cture. We observed the fan index, which describes beam divergence and is de fined by the local curvature of the equienergy section, range from near zer o to almost infinity. This paper provides a unified description of photonic and conventional crystal optics, and may enable previously inconceivable o ptical designs.