Comprehensive Enumeration of Three-Dimensional Photonic Crystals Enabled through Deep Learning Assisted Fourier Synthesis

Abstract: Three-dimensional (3D) photonic structures enable numerous applications through their unique ability to guide, trap, and manipulate light. Constructing new functional photonic crystals remains a significant challenge since traditional design principles based on band structure calculations require numerous time-consuming computations. Additionally, traditional design is based on enumerated structures making it difficult to find novel functional geometries. Here, we propose an ultra-fast photonic crystal performance prediction method to enable efficient structure optimization of arbitrary 3D photonic crystals even with multiple variable modulation. Our methodology combines Fourier synthesis-enabling the creation of any smooth geometry within a crystallographic space group-with deep learning, which facilitates efficient photonic characterization within the vast parameter space. Over 2 million structures can be explored within 2 hours using a mainstream desktop workstation. The ideal structures with desired band properties, such as large photonic bandgap, specific frequency ranges, etc., could be rapidly discovered. We systematically confirmed the well-documented assumption that the most significant photonic bandgaps are found in minimal surface morphologies, in which the single diamond (dia net) with Fd3m (227) symmetry reigns supreme among known photonic structures, followed by the chiral single gyroid (srs net) with I4132 (214) symmetry. Additionally, a less well-known 3D photonic crystal with lcs topology within Ia3d (230) was rediscovered to exhibit a wide complete photonic bandgap, comparable to the diamond and the gyroid net. Our method not only validates the assumed hierarchy of photonic structures but also lays the foundation for the tailored design of functional materials and offers fresh insights into the advancement of next-generation optical devices and information technology.