Large full band gaps for photonic crystals in two dimensions computed by an inverse method with multigrid acceleration

Abstract

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.