Rational design of arbitrary topology in three-dimensional space

Recent advances in nanotechnology have led to the emergence of metamaterials with unprecedented properties through precisely controlled topologies. To explore metamaterials with nanoscale topologies, interest in three-dimensional nanofabrication methods has grown and led to rapid production of target nanostructures over large areas. Additionally, inverse design methods have revolutionized materials science, enabling the optimization of microstructures and topologies to achieve the desired properties without extensive experimental cycles. This review highlights the recent progress in inverse design methods applied in proximity-field nanopatterning. It introduces novel approaches, such as adjoint methods and particle swarm optimization, to achieve target topologies and high-resolution nanostructures. Furthermore, machine learning algorithms for inverse design are explored, demonstrating the potential efficacy of the phase-mask design. This comprehensive review offers insights into the progress of inverse design using phase modulation to realize target topologies of nanostructures.