  Innovative machine learning techniques have facilitated the inverse design of
photonic structures for numerous practical applications. Nevertheless, within
these approaches, the quantity of data and the initial data distribution are
paramount for the discovery of highly efficient photonic devices. These devices
often require simulated data ranging from thousands to several hundred thousand
data points. This issue has consistently posed a major hurdle in machine
learning-based photonic design problems. Therefore, we propose a novel data
augmentation algorithm grounded in the adjoint method, capable of generating
more than 300 times the amount of original data while enhancing device
efficiency. The adjoint method forecasts changes in the figure of merit (FoM)
resulting from structural perturbations, requiring only two full-wave Maxwell
simulations for this prediction. By leveraging the adjoint gradient values, we
can augment and label several thousand new data points without any additional
computations. Furthermore, the augmented data generated by the proposed
algorithm displays significantly improved FoMs owing to the precise FoM change
predictions enabled by the adjoint gradients. We apply this algorithm to a
multi-layered metalens design problem and demonstrate that it consequently
exhibits a 343-fold increase in data generation efficiency. After incorporating
the proposed algorithm into a generative adversarial network (GAN), the
optimized metalens exhibits a maximum focusing efficiency of 92.93%, comparable
to the theoretical upper bound (93.80%).
