Selection rules for optical transition probabilities in superlattices

Based on numerical evaluations of the transition probabilities, and using true superlattice eigenfunctions derived from the theory of finite periodic systems, new superlattice selection rules are obtained. We show that the evaluation of the large number N   of the possible recombination transitions reduces by a factor of two. We also show that taking into account these selection rules, the theoretical calculations for specific blue emitting GaN?(In_xGa_1-xN?In_yGa_1-yN)ⁿ?GaN$\text{GaN}?({\text{In}}_x{\text{Ga}}_{1-x}\text{N}?{\text{In}}_y{\text{Ga}}_{1-y}\text{N}{)}^n?\text{GaN}$ superlattices agree with those reported by Nakamura et al. [1].