Label-Efficient Generative Inverse Design and Design-Rule Discovery in Freeform Topological Photonics

Abstract

Topological photonic crystals support robust, disorder-resilient light transport protected by their band-structure topology, yet their design remains confined to a small set of symmetry-defined templates. The surrounding freeform design space, where optimal performance and new functionality may reside, is difficult to access because of its high dimensionality and costly full-wave simulation needed for evaluating each candidate. % Here we report generative inverse design of freeform valley photonic crystals. A label-free diffusion prior learns the distribution of three-fold rotationally symmetric geometries from 7,689 unlabeled designs that cost 0.15~s each to produce, while a convolutional surrogate is trained on 1,666 full-wave band-gap simulations costing 4.28~min each, exploiting a 1,700-fold cost asymmetry. Across nine target band gaps up to $225~$meV, we generate and verify by full-wave simulation 270 valley photonic crystal designs, reaching a mean absolute error of $1.4$--$6.7$~meV within the labeled range and retaining below $5.1\%$ fractional error at targets $25\%$ beyond its upper bound, while a label-conditioned diffusion model trained on the same label data performs substantially worse. Beyond inverse design, the trained model functions as an instrument for discovering structure--property relations. At a target band gap where the labeled set contains only five designs, it generates hundreds, resolving geometric trends that are statistically inaccessible in the training data and yielding interpretable rules for large-gap valley photonic crystals. Our results establish surrogate-guided diffusion as a label-efficient route to freeform topological-photonic design, and as a means of extracting design principles where physical intuition and simulation labels are both scarce.