# Data-Driven Design Rules for Three-Dimensional Photonic Crystals

## TL;DR

This paper uses data-driven methods to discover new design rules for 3D photonic crystals, focusing on material distribution and connectivity rather than just symmetry.

## Contribution

The novel contribution is a data-driven framework that identifies structural and material factors influencing photonic band gaps in non-ideal systems.

## Key findings

- Photonic band gap size is most strongly linked to the volume fraction and connectivity of high-dielectric materials.
- Tetrahedral and gyroidal structures maintain band gaps even with symmetry distortions.
- Global lattice symmetry has a secondary influence on photonic band gaps.

## Abstract

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.