In this paper, dispersion relations (DRs) of photonic crystals (PhCs) are computed by multilayer perceptron (MLP) and extreme learning machine (ELM) artificial neural networks (ANNs). Bi-and tri-dimensional optimized structures presenting distinct DRs and photonic band gaps (PBGs) were selected for case studies. Optical properties of a set of PhCs with similar geometries and different dimensions were calculated by an electromagnetic solver in order to provide input data for ANN training and testing. We demonstrate that simple-and fast-training ANN models are capable of providing accurate DRs' curves in a very short time. Index Terms-Dispersion relation, extreme learning machine, multilayer perceptron, photonic crystal, photonic band gap. I. INTRODUCTION P HOTONIC crystals are optical structures composed of a periodical distribution of dielectric materials by which light propagation is affected. Such structures may be designed for defining DRs presenting frequency ranges in which light cannot propagate in certain directions: a phenomenon called photonic band gap (PBG) [1], whose characteristics enable the engineering of technologies for light control [2]. PBG-based devices design generally relies upon electromagnetic solvers based on numerical methods such as finite element method [3] and block-iterative frequency-domain methods [4], among others, and becomes time and memory consuming when dealing with structure optimization or solving inverse problems. Such iterative analyses are particularly computationally
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