  Optical selection rules for one-dimensional graphene nanoribbons are
analytically studied and clarified based on the tight-binding model. A
theoretical explanation, through analyzing the velocity matrix elements and the
features of wavefunctions, can account for the selection rules, which depend on
the edge structure of nanoribbon, namely armchair or zigzag edges. The
selection rule of armchair nanoribbons is \Delta J=0, and the optical
transitions occur from the conduction to valence subbands of the same index.
Such a selection rule originates in the relationships between two sublattices
and between conduction and valence subbands. On the other hand, zigzag
nanoribbons exhibit the selection rule |\Delta J|=odd, which results from the
alternatively changing symmetry property as the subband index increases. An
efficiently theoretical prediction on transition energies is obtained with the
application of selection rules. Furthermore, the energies of band edge states
become experimentally attainable via optical measurements.
