A rigorous theory is developed for light refraction by a photonic crystal
PC with arbitrary lattice-type and

surface orientation. First, the refraction of a planar wave incident upon a photonic crystal surface is analyzed.

We rigorously prove the equal partition of propagating PC modes by a surface under a general condition. The

concept of surface-orientation-dependent mode degeneracy has been proposed and its relationship to quasi-

periodic surfaces unfolded. With modes partitioned and the degeneracy properly recognized, a subset of the

solved PC modes is identifi ed to uniquely represent all PC modes that can be excited by an incident wave.