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Nanophotonic devices have enabled microscopic control of light with an unprecedented spatial resolution by employing subwavelength optical elements that can strongly interact with incident waves. However, to date, most nanophotonic devices have been designed based on fixed-shape optical elements, and a large portion of their design potential has remained unexplored. It is only recently that free-form design schemes have been spotlighted in nanophotonics, offering routes to make a break from conventional design constraints and utilize the full design potential. In this review, we systematically overview the nascent yet rapidly growing field of free-form nanophotonic device design. We attempt to define the term “free-form” in the context of photonic device design, and survey different strategies for free-form optimization of nanophotonic devices spanning from classical methods, adjoint-based methods, to contemporary machine-learning-based approaches.

Innovative machine learning techniques have facilitated the inverse design of photonic structures for numerous practical applications. Nevertheless, 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 new 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. 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, the optimized metalens exhibits a maximum focusing efficiency of 92.93%, comparable to the theoretical upper bound. • A new data augmentation approach is proposed, utilizing the adjoint method to augment photonic data. • The proposed algorithm augments given data more than 300 times and enhances device efficiency. • When integrated with GAN, the optimized multi-layer metalens attains near-optimal focusing efficiency (92.93%). • The algorithm resolves the necessity of large data sets in machine learning-based photonic design problems. [ABSTRACT FROM AUTHOR]