  An approach to optimizing the Q factors of two-dimensional photonic crystal
(2D-PC) nanocavities based on deep learning is proposed and demonstrated. We
prepare a dataset consisting of 1000 nanocavities generated by randomly
displacing the positions of many air holes of a base nanocavity and their Q
factors calculated by a first-principle 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 dataset.
After the training, the neural network becomes 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 based on
back-propagation. A nanocavity structure with an extremely high Q factor of
1.58 x 10^9 is successfully obtained by optimizing the positions of 50 air
holes over ~10^6 iterations, having taken advantage of the very fast evaluation
of the gradient in high-dimensional parameter space. 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
based solely on direct calculations. We believe this approach is also useful
for improving other optical characteristics.
