Iterative optimization of photonic crystal nanocavity designs by using deep neural networks

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.