Deep-learning enabled photonic nanostructure discovery in arbitrarily large shape sets via linked latent space representation learning

The vast array of shapes achievable through modern nanofabrication technologies presents a challenge in selecting the most optimal design for achieving a desired optical response. While data-driven techniques, such as deep learning, hold promise for inverse design, their applicability is often limited as they typically explore only smaller subsets of the extensive range of shapes feasible with nanofabrication. Additionally, these models are often regarded as ‘black boxes,’ lacking transparency in revealing the underlying relationship between the shape and optical response. Here, we introduce a methodology tailored to address the challenges posed by large, complex, and diverse sets of nanostructures. Specifically, we demonstrate our approach in the context of periodic silicon metasurfaces operating in the visible wavelength range, considering large and diverse shape set variations. Our paired variational autoencoder method facilitates the creation of rich, continuous, and parameter-aligned latent space representations of the shape–response relationship. We showcase the practical utility of our approach in two key areas: (1) enabling multiple-solution inverse design and (2) conducting sensitivity analyses on a shape's optical response to nanofabrication-induced distortions. This methodology represents a significant advancement in data-driven design techniques, further unlocking the application potential of nanophotonics.