Coupling reducing k-points for supercell models of defects in three-dimensional photonic crystals

The optimum choice of k-point for supercell calculations of defect states in a three-dimensional photonic crystal is investigated for the case of a supercell with a simple cubic (SC) structure. By using the k-point (1/4,1/4,1/4) it is possible to eliminate the symmetric part of the repeated-image couplings for the first three neighbour shells in the SC lattice. This result is shown to hold also for the case of non-equivalent axes (e.g. a distorted lattice, or an asymmetric defect structure). A specific example of a donor defect in a woodpile structure demonstrates that use of this k-point can lead to order-of-magnitude gains in computational efficiency.