Abstract
Abstract Devices based on two-dimensional photonic-crystal nanocavities, which are defined by their air hole patterns, usually require a high quality (Q) factor to achieve high performance. We demonstrate that hole patterns with very high Q factors can be efficiently found by the iteration procedure consisting of machine learning of the relation between the hole pattern and the corresponding Q factor and new dataset generation based on the regression function obtained by machine learning. First, a dataset comprising randomly generated cavity structures and their first principles Q factors is prepared. Then a deep neural network is trained using the initial dataset to obtain a regression function that approximately predicts the Q factors from the structural parameters. Several candidates for higher Q factors are chosen by searching the parameter space using the regression function. After adding these new structures and their first principles Q factors to the training dataset, the above process is repeated. As an example, a standard silicon-based L3 cavity is optimized by this method. A cavity design with a high Q factor exceeding 11 million is found within 101 iteration steps and a total of 8070 cavity structures. This theoretical Q factor is more than twice the previously reported record values of the cavity designs detected by the evolutionary algorithm and the leaky mode visualization method. It is found that structures with higher Q factors can be detected within less iteration steps by exploring not only the parameter space near the present highest-Q structure but also that distant from the present dataset.
Highlights
Photonic nanocavities based on artificial defects in two-dimensional (2D) photonic-crystal (PC) slabs [1,2,3,4,5,6,7,8,9,10,11] have received significant attention as structures that enable preservation of photons for extended times in small modal volumes. 2D-PC slab cavities are usually defined by defects in the triangular air hole lattice of the PC
We propose an iterative optimization method to overcome this problem: here, the candidate structures for higher-Q factors identified by the regression function at the present iteration step are added to the training dataset for the step
This approach comprises the repetition of the following four steps: training of neural network (NN) to learn the relationship between cavity structure and the Q factor using the present dataset, generation of candidate structures using the trained NNs, calculation of their Q factors, and adding the new structures and Q factors to the dataset
Summary
Photonic nanocavities based on artificial defects in two-dimensional (2D) photonic-crystal (PC) slabs [1,2,3,4,5,6,7,8,9,10,11] have received significant attention as structures that enable preservation of photons for extended times in small modal volumes. 2D-PC slab cavities are usually defined by defects in the triangular air hole lattice of the PC. The analytic inverse problem approaches are based on approximations that relate the cavities’ structural parameters to the mode fields, and allow us to explicitly determine an optimized cavity geometry with less leaky components [13,14]. The Gaussian envelope and leaky position visualization approaches improve cavity designs based on the differences between the mode field calculated for the actual structure and the ideal mode field, which is artificially generated and has a minimum of leaky components [2,3,17] The comparison of these fields enables identification of spatial positions where leakage of photons occurs. More systematic and automated methods of exploring high-dimensional parameter spaces are required to fully utilize the potential of 2D-PC nanocavities
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