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In this study, two fast and accurate methods of inverse iteration with multigrid acceleration are developed to compute band structures of photonic crystals of general shape. In particular, we report two-dimensional photonic crystals of silicon air with an optimal full band gap of gap-midgap ratio Deltaomega/omega(mid)=0.2421, which is 30% larger than ever reported in the literature. The crystals consist of a hexagonal array of circular columns, each connected to its nearest neighbors by slender rectangular rods. A systematic study with respect to the geometric parameters of the photonic crystals was made possible with the present method in drawing a three-dimensional band-gap diagram with reasonable computing time.
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Chern et al. (2003) studied this question.
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