Description: A rigorous theory is developed for light refraction by a photonic crystal PC with arbitrary lattice-type andsurface 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. Theconcept 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 thesolved PC modes is identi
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