Data-Driven Design Rules for Three-Dimensional Photonic Crystals

Photonic crystals are crystalline systems composed of multiple materials whose patterning results in the selective reflectance of light. Historically, design principles for three-dimensional photonic crystals have remained limited to how to optimize photonics response, thereby limiting synthetic guidance in non-ideal systems. This work introduces a data-driven approach to uncover such principles; we transform a data set comprising 1,200 crystalline templates (and tens to hundreds of band structures per template) from band structures into photonic densities of states (PDOS), which serve as statistical fingerprints for property-structure analyses. We exploit hybrid supervised-unsupervised dimensionality reduction and clustering to reveal low-dimensional maps of this high-dimensional latent space that capture both structural similarity and gap size, enabling sensitivity analyses across symmetry classes and material distributions. Results show that photonic band gap (PBG) size is primarily correlated with the volume fraction and connectivity of high-dielectric media (optimal gaps occur at fractions of 0.2-0.3), while global lattice symmetry plays a secondary, less critical role. Networks with tetrahedral or gyroidal connectivity consistently support photonic band gaps even under local and global symmetry distortions. These findings broaden conventional design rules to include aspects of local topology and material complexity, providing a foundation for the future design of photonic structures.