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Robustness of one-dimensional photonic band gaps under random variations of geometrical parameters
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The supercell method is used to study the variation of the photonic bandgaps in one-dimensional photonic crystals under random perturbations to thicknesses of the layers. The results of both plane wave and analytical band structure and density of states calculations are presented along with the transmission coefficient as the level of randomness and the supercell size is increased. It is found that with the supercell size fixed at 1024 unit cells, higher bandgaps disappear first as the randomness is gradually increased. The lowest bandgap is found to persist up to a randomness level of 55%. However, as the supercell size is increased all bandgaps are observed to approach pseudogaps but with very low density of states. It is shown that harmonics of a relatively small cluster of closely spaced defects largely account for the bulk of the modes that populate the photonic bandgaps.