Optimization of photonic crystal nanocavities based on deep learning

An approach to optimizing the Q factors of two-dimensional photonic crystal (2D-PC) nanocavities based on deep learning is hereby proposed and demonstrated. We prepare a data set consisting of 1000 nanocavities generated by randomly displacing the positions of many air holes in a base nanocavity and calculate their Q factors using a first-principles method. We train a four-layer neural network including a convolutional layer to recognize the relationship between the air holes' displacements and the Q factors using the prepared data set. After the training, the neural network is able to estimate the Q factors from the air holes' displacements with an error of 13% in standard deviation. Crucially, the trained neural network can estimate the gradient of the Q factor with respect to the air holes' displacements very quickly using back-propagation. A nanocavity structure with an extremely high Q factor of 1.58 x 10(9) was successfully obtained by optimizing the positions of 50 holes over similar to 10(6) iterations, taking advantage of the very fast evaluation of the gradient in high-dimensional parameter spaces. The obtained Q factor is more than one order of magnitude higher than that of the base cavity and more than twice that of the highest Q factors reported so far for cavities with similar modal volumes. This approach can optimize 2D-PC structures over a parameter space of a size unfeasibly large for previous optimization methods that were based solely on direct calculations. We believe that this approach is also useful for improving other optical characteristics. (C) 2018 Optical Society of America under the terms of the OSA Open Access Publishing Agreement