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Photonic band gap structures and their applications have gained a great deal of interest in recent years, with the primary focus on designing structures that have specific optical characteristics. However, little attention has been given to solving the inverse problem of determining the optimum photonic lattice given a desired output. In this paper, we address this need using optimization techniques to design two-dimensional photonic crystals to arbitrarily guide light in two dimensions. By switching the rods of this lattice on and off (rod or no rod), the optimization algorithm arrives at a solution (distribution of the rod in this lattice) that minimizes the cost function. The performance of the optimization is driven by the proper selection of both the cost function and optimization algorithm.
Mohammed et al. (Mon,) studied this question.