  Devices based on two-dimensional photonic-crystal (2D-PC) 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 of 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.
